refactor with own translation package

Makefile

@@ -0,0 +1,44 @@
+# Makefile for lualatex
+
+# Paths and filenames
+SRC_DIR  = src
+OUT_DIR  = out
+MAIN_TEX = main.tex   	# in SRC_DIR
+MAIN_PDF = main.pdf  	# in OUT_DIR
+
+# LaTeX and Biber commands
+
+LATEX = lualatex
+BIBER = biber
+
+LATEX_OPTS := -output-directory=$(OUT_DIR) -interaction=nonstopmode -shell-escape
+
+.PHONY: default release clean scripts
+
+default: english
+release: german english
+# Default target
+english: 
+	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[english]{babel}/' $(SRC_DIR)/$(MAIN_TEX)
+	-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
+	mv $(OUT_DIR)/$(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_en_Formulary.pdf
+
+german:
+	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[german]{babel}/' $(SRC_DIR)/$(MAIN_TEX)
+	-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
+	mv $(OUT_DIR)/$(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_Formelsammlung.pdf
+
+SCRIPT_DIR = scripts
+PY_SCRIPTS = $(wildcard $(SCRIPT_DIR)/*.py)
+PY_SCRIPTS_REL = $(notdir $(PY_SCRIPTS))
+scripts:
+	-#cd $(SCRIPT_DIR) && for file in $(find -type f -name '*.py'); do echo "Running $$file"; python3 "$$file"; done
+	cd $(SCRIPT_DIR) && $(foreach script,$(PY_SCRIPTS_REL),echo "Running $(script)"; python3 $(script);)
+
+# Clean auxiliary and output files
+clean:
+	rm -r $(OUT_DIR)
+
+# Phony targets
+.PHONY: all clean biber
+

readme.md

@@ -0,0 +1,113 @@
+# Formulary
+This is supposed to be a compact, searchable collection of the most important stuff I learned during my physics studides,
+because it would be a shame if I forget it all!
+
+## Building the PDF
+### Dependencies
+Any recent **TeX Live** distribution should work. You need:
+- `LuaLaTeX` compiler
+- several packages from ICAN
+- `latexmk` to build it
+
+### With GNU make
+1. In the project directory (where this `readme` is), run `make german` or `make english`.
+2. Rendered document will be `out/<date>_<formulary>.pdf`
+
+### With Latexmk
+1. Choose the language: In `main.tex`, set the language in `\usepackage[english]{babel}` to either `english` or `german`
+2. In the `src` directory, run `latexmk -lualatex main.tex`
+3. Rendered document will be `out/main.pdf`
+
+### With LuaLatex
+1. Choose the language: In `main.tex`, set the language in `\usepackage[english]{babel}` to either `english` or `german`
+2. Create the `.aux` directory
+3. In the `src` directory, run
+    - `lualatex  -output-directory="../.aux"  --interaction=nonstopmode --shell-escape "main.tex"` **3 times**
+4. Rendered document will be `.aux/main.pdf`
+
+# LaTeX Guideline
+Here is some info to help myself remember why I did things the way I did.
+
+In general, most content should be written with macros, so that the behaviour can be changed later.
+
+## Structure
+All translation keys and LaTeX labels should use a structured approach:
+`<key type>:<partname>:<section name>:<subsection name>:<...>:<name>`
+
+The `<partname>:...:<lowest section name>` will be defined as `\fqname` (fully qualified name) when using the `\Part`, `\Section`, ... commands.
+
+`<key type>` is:
+
+- formula: `f`
+- equation: `eq`
+- table: `tab`
+- figure: `fig`
+- parts, (sub)sections: `sec`
+
+Use `misc` as (sub(sub))section for anything that can not be categorized within its (sub)section/part.
+
+### Files and directories
+Separate parts in different source files named `<partname>.tex`.  
+If a part should be split up in multiple source files itself, use a
+subdirectory named `<partname>` containing `<partname>.tex` and other source files for sections.  
+This way, the `fqname` of a section or formula partially matches the path of the source file it is in.
+
+## `formula` environment
+The main way to display something is the formula environment:
+```tex
+\begin{formula}{<key>}
+    \desc{English name}{English description}{$q$ is some variable, $s$ \qtyRef{some_quantity}}
+    \desc[german]{Deutscher Name}{Deutsche Beschreibung}{$q$ ist eine Variable, $s$ \qtyRef{some_quantity}}
+    <content>
+\end{formula}
+```
+Each formula automatically gets a `f:<section names...>:<key>` label.
+For the content, several macros are available:
+- `\eq{<equation>}` a wrapper for the `align` environment
+- `\fig[width]{<path>}`
+- `\quantity{<symbol>}{<units>}{<vector, scalar, extensive etc.>}` for physical quantites
+- `\constant{<symbol>}{ <values> }` for constants, where `<values>` may contain one or more `\val{value}{unit}` commands.
+
+### References
+**Use references where ever possible.**  
+In equations, reference or explain every variable. Several referencing commands are available for easy referencing:
+- `\fqSecRef{<fqname of section>}` prints the translated title of the section
+- `\fqEqRef{<fqname of formula>}` prints the translated title of the formula (first argument of `\desc`)
+- `\qtyRef{<key>}` prints the translated name of the quantity
+- `\QtyRef{<key>}` prints the symbol and the translated name of the quantity
+- `\constRef{<key>}` prints the translated name of the constant
+- `\ConstRef{<key>}` prints the symbol and the translated name of the constant
+- `\elRef{<symbol>}` prints the symbol of the chemical element
+- `\ElRef{<symbol>}` prints the name of the chemical element
+
+
+## Multilanguage
+All text should be defined as a translation (`translations` package, see `util/translation.tex`).
+Use `\dt` or `\DT` or the the shorthand language commands `\eng`, `\Eng` etc. to define translations.
+These commands also be write the translations to an auxiliary file, which is read after the document begins.
+This means (on subsequent compilations) that the translation can be resolved before they are defined.  
+Use the `gt` or `GT` macros to retrieve translations.
+The english translation of any key must be defined, because it will also be used as fallback.
+
+Lower case macros are relative to the current `fqname`, while upper case macros are absolute.
+
+Never make a macro that would have to be changed if a new language was added, eg dont do
+```tex
+% 1: key, 2: english version, 3: german version
+\newcommand{\mycmd}[3]{
+    \dosomestuff{english}{#1}{#2}
+    \dosomestuff{german}{#1}{#3}
+}
+
+\mycmd{key}{this is english}{das ist deutsch}
+```
+Instead, do
+```tex
+% [1]: lang, 2: key, 2: text
+\newcommand{\mycmd}[3][english]{
+    \dosomestuff{#1}{#2}{#3}
+}
+
+\mycmd{key}{this is english}
+\mycmd[german]{key}{das ist deutsch}
+```

scripts/ch_elchem.py

@@ -0,0 +1,80 @@
+#!/usr/bin env python3
+from formulary import *
+from scipy.constants import gas_constant, Avogadro, elementary_charge
+
+Faraday = Avogadro * elementary_charge
+
+@np.vectorize
+def fbutler_volmer_anode(ac, z, eta, T):
+    return np.exp((1-ac)*z*Faraday*eta/(gas_constant*T))
+
+@np.vectorize
+def fbutler_volmer_cathode(ac, z, eta, T):
+    return -np.exp(-ac*z*Faraday*eta/(gas_constant*T))
+
+def fbutler_volmer(ac, z, eta, T):
+    return fbutler_volmer_anode(ac, z, eta, T) + fbutler_volmer_cathode(ac, z, eta, T)
+
+def butler_volmer():
+    fig, ax = plt.subplots(figsize=size_half_third)
+    ax.set_xlabel("$\\eta$ [V]")
+    ax.set_ylabel("$j/j_0$")
+    etas = np.linspace(-0.1, 0.1, 400)
+    T = 300
+    z = 1.0
+    # other a
+    ac2, ac3 = 0.2, 0.8
+    i2 = fbutler_volmer(0.2, z, etas, T)
+    i3 = fbutler_volmer(0.8, z, etas, T)
+    ax.plot(etas, i2, color="blue", linestyle="dashed", label=f"$\\alpha_\\text{{C}}={ac2}$")
+    ax.plot(etas, i3, color="green", linestyle="dashed", label=f"$\\alpha_\\text{{C}}={ac3}$")
+    # 0.5
+    ac = 0.5
+    irel_anode = fbutler_volmer_anode(ac, z, etas, T)
+    irel_cathode = fbutler_volmer_cathode(ac, z, etas, T)
+    ax.plot(etas, irel_anode,  color="gray")
+    ax.plot(etas, irel_cathode, color="gray")
+    ax.plot(etas, irel_cathode + irel_anode, color="black", label=f"$\\alpha_\\text{{C}}=0.5$")
+    ax.grid()
+    ax.legend()
+    ylim = 6
+    ax.set_ylim(-ylim, ylim)
+    return fig
+
+@np.vectorize
+def ftafel_anode(ac, z, eta, T):
+    return 10**((1-ac)*z*Faraday*eta/(gas_constant*T*np.log(10)))
+
+@np.vectorize
+def ftafel_cathode(ac, z, eta, T):
+    return -10**(-ac*z*Faraday*eta/(gas_constant*T*np.log(10)))
+
+def tafel():
+    i0 = 1
+    ac = 0.2
+    z = 1
+    T = 300
+    eta_max = 0.2
+    etas = np.linspace(-eta_max, eta_max, 400)
+    i = np.abs(fbutler_volmer(ac, z, etas ,T))
+    iright = i0 * np.abs(ftafel_cathode(ac, z, etas, T))
+    ileft = i0 * ftafel_anode(ac, z, etas, T)
+
+    fig, ax = plt.subplots(figsize=size_half_third)
+    ax.set_xlabel("$\\eta$ [V]")
+    ax.set_ylabel("$\\log_{10}\\left(\\frac{|j|}{j_0}\\right)$")
+    # ax.set_ylabel("$\\log_{10}\\left(|j|/j_0\\right)$")
+    ax.set_yscale("log")
+    # ax.plot(etas, linear, label="Tafel slope")
+    ax.plot(etas[etas >= 0], ileft[etas >= 0],  linestyle="dashed", color="gray", label="Tafel Approximation")
+    ax.plot(etas[etas <= 0], iright[etas <= 0], linestyle="dashed", color="gray")
+    ax.plot(etas, i, label=f"Butler-Volmer $\\alpha_\\text{{C}}={ac:.1f}$")
+    ax.legend()
+    ax.grid()
+    return fig
+
+if __name__ == '__main__':
+    export(butler_volmer(), "ch_butler_volmer")
+    export(tafel(), "ch_tafel")
+
+

scripts/cm_phonons.py

@@ -0,0 +1,64 @@
+#!/usr/bin env python3
+from formulary import *
+
+def fone_atom_basis(q, a, M, C1, C2):
+    return np.sqrt(4*C1/M * (np.sin(q*a/2)**2 + C2/C1 * np.sin(q*a)**2))
+
+def one_atom_basis():
+    a = 1.
+    C1 = 0.25
+    C2 = 0
+    M = 1.
+    qs = np.linspace(-2*np.pi/a, 2*np.pi/a, 300)
+    omega = fone_atom_basis(qs, a, M, C1, C2)
+    fig, ax = plt.subplots(figsize=size_half_third)
+    ax.set_xlabel(r"$q$")
+    ax.set_xticks([i * np.pi/a for i in range(-2, 3)])
+    ax.set_xticklabels([f"${i}\\pi/a$" if i != 0 else "0" for i in range(-2, 3)])
+    ax.set_ylabel(r"$\omega$ in $\left[4C_1/M\right]$")
+    yunit = np.sqrt(4*C1/M)
+    ax.set_ylim(0, yunit+0.1)
+    ax.set_yticks([0,yunit])
+    ax.set_yticklabels(["0","1"])
+    ax.plot(qs, omega)
+    ax.text(-1.8*np.pi/a, 0.8, "NN\n$C_2=0$", ha='center')
+    ax.text(0, 0.8, "1. BZ", ha='center')
+    ax.vlines([-np.pi/a, np.pi/a], ymin=-2, ymax=2, color="black")
+    ax.grid()
+    return fig
+
+def ftwo_atom_basis_acoustic(q, a, M1, M2, C):
+    return np.sqrt(C*(1/M1+1/M2) - C * np.sqrt((1/M1+1/M2)**2 - 4/(M1*M2) * np.sin(q*a/2)**2))
+
+def ftwo_atom_basis_optical(q, a, M1, M2, C):
+    return np.sqrt(C*(1/M1+1/M2) + C * np.sqrt((1/M1+1/M2)**2 - 4/(M1*M2) * np.sin(q*a/2)**2))
+
+def two_atom_basis():
+    a = 1.
+    C = 0.25
+    M1 = 1.
+    M2 = 0.7
+    qs = np.linspace(-2*np.pi/a, 2*np.pi/a, 300)
+    omega_a = ftwo_atom_basis_acoustic(qs, a, M1, M2, C)
+    omega_o = ftwo_atom_basis_optical(qs, a, M1, M2, C)
+    fig, ax = plt.subplots(figsize=size_half_third)
+    ax.plot(qs, omega_a, label="acoustic")
+    ax.plot(qs, omega_o, label="optical")
+    ax.text(0, 0.8, "1. BZ", ha='center')
+    ax.vlines([-np.pi/a, np.pi/a], ymin=-2, ymax=2, color="black")
+    ax.set_ylim(-0.03, 1.03)
+    ax.set_ylabel(r"$\omega$ in $\left[\sqrt{2C\mu^{-1}}\right]$")
+    yunit = np.sqrt(2*C*(1/M1+1/M2))
+    ax.set_ylim(0, yunit+0.1)
+    ax.set_yticks([0,yunit])
+    ax.set_yticklabels(["0","1"])
+    ax.set_xlabel(r"$q$")
+    ax.set_xticks([i * np.pi/a for i in range(-2, 3)])
+    ax.set_xticklabels([f"${i}\\pi/a$" if i != 0 else "0" for i in range(-2, 3)])
+    ax.legend()
+    ax.grid()
+
+    return fig
+if __name__ == '__main__':
+    export(one_atom_basis(), "cm_phonon_dispersion_one_atom_basis")
+    export(two_atom_basis(), "cm_phonon_dispersion_two_atom_basis")

scripts/distributions.py

@@ -1,5 +1,6 @@
 from numpy import fmax
-from plot import *
+from formulary import *
+import itertools
 
 
 def get_fig():
@@ -22,7 +23,6 @@ def gauss():
         ax.plot(x, y, label=label)
     ax.legend()
     return fig
-export(gauss(), "distribution_gauss")
 
 # CAUCHY / LORENTZ
 def fcauchy(x, x_0, gamma):
@@ -37,7 +37,6 @@ def cauchy():
         ax.plot(x, y, label=label)
     ax.legend()
     return fig
-export(cauchy(), "distribution_cauchy")
 
 # MAXWELL-BOLTZMANN
 def fmaxwell(x, a):
@@ -53,7 +52,37 @@ def maxwell():
     ax.legend()
     return fig
 
-export(maxwell(), "distribution_maxwell-boltzmann")
+# GAMMA
+@np.vectorize
+def fgamma(x, alpha, lam):
+    return lam**alpha / scp.special.gamma(alpha) * x**(alpha-1) * np.exp(-lam*x)
+def gamma():
+    fig, ax = get_fig()
+    x = np.linspace(0, 20, 300)
+    for (alpha, lam) in itertools.product([1, 2, 5], [1, 2]):
+        y = fgamma(x, alpha, lam)
+        label = f"$\\alpha = {alpha}, \\lambda = {lam}$"
+        ax.plot(x, y, label=label)
+    ax.set_ylim(0, 1.1)
+    ax.set_xlim(0, 10)
+    ax.legend()
+    return fig
+
+# BETA
+@np.vectorize
+def fbeta(x, alpha, beta):
+    return x**(alpha-1) * (1-x)**(beta-1) / scp.special.beta(alpha, beta)
+def beta():
+    fig, ax = get_fig()
+    x = np.linspace(0, 20, 300)
+    for (alpha, lam) in itertools.product([1, 2, 5], [1, 2]):
+        y = fgamma(x, alpha, lam)
+        label = f"$\\alpha = {alpha}, \\beta = {lam}$"
+        ax.plot(x, y, label=label)
+    ax.set_ylim(0, 1.1)
+    ax.set_xlim(0, 10)
+    ax.legend()
+    return fig
 
 
 # POISSON
@@ -73,8 +102,6 @@ def poisson():
     ax.legend()
     return fig
 
-export(poisson(), "distribution_poisson")
-
 # BINOMIAL
 def binom(n, k):
     return scp.special.factorial(n) / (
@@ -98,9 +125,17 @@ def binomial():
     ax.legend()
     return fig
 
-export(binomial(), "distribution_binomial")
+
+if __name__ == '__main__':
+    export(gauss(), "distribution_gauss")
+    export(cauchy(), "distribution_cauchy")
+    export(maxwell(), "distribution_maxwell-boltzmann")
+    export(gamma(), "distribution_gamma")
+    export(beta(), "distribution_beta")
+    export(poisson(), "distribution_poisson")
+    export(binomial(), "distribution_binomial")
+
 
 # FERMI-DIRAC
-
 # BOSE-EINSTEIN
-
+# see stat-mech

scripts/formulary.py

@@ -0,0 +1,81 @@
+#!/usr/bin env python3
+import os
+import matplotlib.pyplot as plt
+import numpy as np
+import math
+import scipy as scp
+
+import matplotlib as mpl
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["mathtext.fontset"] = "stix"
+mpl.rcParams["text.usetex"] = True
+mpl.rcParams['text.latex.preamble'] = r'\usepackage{amsmath}\usepackage{siunitx}'
+
+
+if __name__ == "__main__":  # make relative imports work as described here: https://peps.python.org/pep-0366/#proposed-change
+    if __package__ is None:
+        __package__ = "formulary"
+        import sys
+        filepath = os.path.realpath(os.path.abspath(__file__))
+        sys.path.insert(0, os.path.dirname(os.path.dirname(filepath)))
+
+from util.mpl_colorscheme import set_mpl_colorscheme
+import util.colorschemes as cs
+from util.gen_tex_colorscheme import generate_latex_colorscheme
+# SET THE COLORSCHEME
+# hard white and black
+# cs.p_gruvbox["fg0"] = "#000000"
+# cs.p_gruvbox["bg0"] = "#ffffff"
+# COLORSCHEME = cs.gruvbox_light()
+# COLORSCHEME = cs.gruvbox_dark()
+# cs.p_tum["fg0"] = cs.p_tum["alt-blue"]
+COLORSCHEME = cs.tum()
+# COLORSCHEME = cs.legacy()
+
+tex_src_path = "../src/"
+img_out_dir = os.path.join(tex_src_path, "img")
+filetype = ".pdf"
+skipasserts = False
+
+full = 8
+size_half_half = (full/2, full/2)
+size_third_half = (full/3, full/2)
+size_half_third = (full/2, full/3)
+
+def assert_directory():
+    if not skipasserts:
+        assert os.path.abspath(".").endswith("scripts"), "Please run from the `scripts` directory"
+
+def texvar(var, val, math=True):
+    s = "$" if math else ""
+    s += f"\\{var} = {val}"
+    if math: s += "$"
+    return s
+
+def export(fig, name, tight_layout=True):
+    assert_directory()
+    filename = os.path.join(img_out_dir, name + filetype)
+    if tight_layout:
+        fig.tight_layout()
+    fig.savefig(filename, bbox_inches="tight", pad_inches=0.0)
+
+@np.vectorize
+def smooth_step(x: float, left_edge: float, right_edge: float):
+    x = (x - left_edge) / (right_edge - left_edge)
+    if x <= 0: return 0.
+    elif x >= 1: return 1.
+    else: return 3*(x*2) - 2*(x**3)
+
+
+# run even when imported
+set_mpl_colorscheme(COLORSCHEME)
+
+if __name__ == "__main__":
+    assert_directory()
+    s = \
+    """% This file was generated by scripts/formulary.py\n% Do not edit it directly, changes will be overwritten\n""" + generate_latex_colorscheme(COLORSCHEME)
+    filename = os.path.join(tex_src_path, "util/colorscheme.tex")
+    print(f"Writing tex colorscheme to {filename}")
+    with open(filename, "w") as file:
+        file.write(s)
+

scripts/mpl_colorscheme.py

@@ -0,0 +1,149 @@
+"""
+Set the colorscheme for matplotlib plots and latex.
+
+Calling this script generates util/colorscheme.tex containing xcolor definitions.
+"""
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+from cycler import cycler
+
+skipasserts = False
+
+GRUVBOX = {
+    "bg0":          "#282828",
+    "bg0-hard":     "#1d2021",
+    "bg0-soft":     "#32302f",
+    "bg1":          "#3c3836",
+    "bg2":          "#504945",
+    "bg3":          "#665c54",
+    "bg4":          "#7c6f64",
+    "fg0":          "#fbf1c7",
+    "fg0-hard":     "#f9f5d7",
+    "fg0-soft":     "#f2e5bc",
+    "fg1":          "#ebdbb2",
+    "fg2":          "#d5c4a1",
+    "fg3":          "#bdae93",
+    "fg4":          "#a89984",
+    "dark-red":     "#cc241d",
+    "dark-green":   "#98971a",
+    "dark-yellow":  "#d79921",
+    "dark-blue":    "#458588",
+    "dark-purple":  "#b16286",
+    "dark-aqua":    "#689d6a",
+    "dark-orange":  "#d65d0e",
+    "dark-gray":    "#928374",
+    "light-red":    "#fb4934",
+    "light-green":  "#b8bb26",
+    "light-yellow": "#fabd2f",
+    "light-blue":   "#83a598",
+    "light-purple": "#d3869b",
+    "light-aqua":   "#8ec07c",
+    "light-orange": "#f38019",
+    "light-gray":   "#a89984",
+    "alt-red":      "#9d0006",
+    "alt-green":    "#79740e",
+    "alt-yellow":   "#b57614",
+    "alt-blue":     "#076678",
+    "alt-purple":   "#8f3f71",
+    "alt-aqua":     "#427b58",
+    "alt-orange":   "#af3a03",
+    "alt-gray":     "#7c6f64",
+}
+
+FORMULASHEET_COLORSCHEME = GRUVBOX
+
+colors = ["red", "orange", "yellow", "green", "aqua", "blue", "purple", "gray"]
+
+# default order for matplotlib
+color_order = ["blue", "orange", "green", "red", "purple", "yellow", "aqua", "gray"]
+
+def set_mpl_colorscheme(palette: dict[str, str], variant="dark"):
+    P = palette
+    if variant == "dark":
+        FIG_BG_COLOR =          P["bg0"]
+        PLT_FG_COLOR =          P["fg0"]
+        PLT_BG_COLOR =          P["bg0"]
+        PLT_GRID_COLOR =        P["bg2"]
+        LEGEND_FG_COLOR =       PLT_FG_COLOR
+        LEGEND_BG_COLOR =       P["bg1"]
+        LEGEND_BORDER_COLOR =   P["bg2"]
+    else:
+        FIG_BG_COLOR =          P["fg0"]
+        PLT_FG_COLOR =          P["bg0"]
+        PLT_BG_COLOR =          P["fg0"]
+        PLT_GRID_COLOR =        P["fg2"]
+        LEGEND_FG_COLOR =       PLT_FG_COLOR
+        LEGEND_BG_COLOR =       P["fg1"]
+        LEGEND_BORDER_COLOR =   P["fg2"]
+    COLORS = [P[f"{variant}-{c}"] for c in color_order]
+
+
+    color_rcParams = {
+        'axes.edgecolor': PLT_FG_COLOR,
+        'axes.facecolor': PLT_BG_COLOR,
+        'axes.labelcolor': PLT_FG_COLOR,
+        'axes.titlecolor': 'auto',
+        # 'axes.prop_cycle': cycler('color', ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']),
+        'axes.prop_cycle': cycler('color', COLORS),
+        # 'axes3d.xaxis.panecolor': (0.95, 0.95, 0.95, 0.5),
+        # 'axes3d.yaxis.panecolor': (0.9, 0.9, 0.9, 0.5),
+        # 'axes3d.zaxis.panecolor': (0.925, 0.925, 0.925, 0.5),
+        # 'boxplot.boxprops.color': 'black',
+        # 'boxplot.capprops.color': 'black',
+        # 'boxplot.flierprops.color': 'black',
+        # 'boxplot.flierprops.markeredgecolor': 'black',
+        # 'boxplot.flierprops.markeredgewidth': 1.0,
+        # 'boxplot.flierprops.markerfacecolor': 'none',
+        # 'boxplot.meanprops.color': 'C2',
+        # 'boxplot.meanprops.markeredgecolor': 'C2',
+        # 'boxplot.meanprops.markerfacecolor': 'C2',
+        # 'boxplot.meanprops.markersize': 6.0,
+        # 'boxplot.medianprops.color': 'C1',
+        # 'boxplot.whiskerprops.color': 'black',
+        'figure.edgecolor': PLT_BG_COLOR,
+        'figure.facecolor': PLT_BG_COLOR,
+        # 'figure.figsize': [6.4, 4.8],
+        # 'figure.frameon': True,
+        # 'figure.labelsize': 'large',
+        'grid.color': PLT_GRID_COLOR,
+        # 'hatch.color': 'black',
+        'legend.edgecolor': LEGEND_BORDER_COLOR,
+        'legend.facecolor': LEGEND_BG_COLOR,
+        'xtick.color': PLT_FG_COLOR,
+        'ytick.color': PLT_FG_COLOR,
+        'xtick.labelcolor': PLT_FG_COLOR,
+        'ytick.labelcolor': PLT_FG_COLOR,
+        # 'lines.color': 'C0',
+        'text.color': PLT_FG_COLOR,
+    }
+
+    for k, v in color_rcParams.items():
+        plt.rcParams[k] = v
+
+    # override single char codes
+    # TODO: use color name with variant from palette instead of order
+    mpl.colors.get_named_colors_mapping()["b"] = COLORS[0]
+    mpl.colors.get_named_colors_mapping()["o"] = COLORS[1]
+    mpl.colors.get_named_colors_mapping()["g"] = COLORS[2]
+    mpl.colors.get_named_colors_mapping()["r"] = COLORS[3]
+    mpl.colors.get_named_colors_mapping()["m"] = COLORS[4]
+    mpl.colors.get_named_colors_mapping()["y"] = COLORS[5]
+    mpl.colors.get_named_colors_mapping()["c"] = COLORS[6]
+    mpl.colors.get_named_colors_mapping()["k"] = P["fg0"]
+    mpl.colors.get_named_colors_mapping()["w"] = P["bg0"]
+
+
+
+def color_latex_def(name, color):
+    name = "{" + name.replace("-", "_") + "}"
+    color = "{" + color.strip("#") + "}"
+    return f"\\definecolor{name:10}{{HTML}}{color}"
+
+def generate_latex_colorscheme(palette, variant="light"):
+    s = ""
+    for n, c in palette.items():
+        s += color_latex_def(n, c) + "\n"
+    return s
+
+
+

scripts/other/Untitled.ipynb

@@ -0,0 +1,55 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "790c45a0-a10a-411d-bfc0-bdd52e2c2492",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import tikz as t"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "6c5d640f-c287-4e8d-a0c8-8a8d801b6fae",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pic = t.Picture()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9b7f8347-1619-40cd-b864-24840901e7a1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pic.draw(t.node("
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "conda",
+   "language": "python",
+   "name": "conda"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

scripts/periodic_table.py

@@ -0,0 +1,79 @@
+#!/usr/bin env python3
+"""
+Script to process the periodic table as json into latex stuff
+Source for `elements.json` is this amazing project:
+https://pse-info.de/de/data
+
+Copyright Matthias Quintern 2025
+"""
+import json
+import os
+import re
+
+outdir = "../src/ch"
+
+
+def gen_periodic_table():
+    with open("other/elements.json") as file:
+        ptab = json.load(file)
+    # print(ptab["elements"][1])
+    s = "% This file was created by the periodic_table.py script.\n% Do not edit manually. Any changes might get lost.\n"
+    for i, el_key in enumerate(ptab):
+        el = ptab[el_key]
+        def get(*keys):
+            """get keys or return empty string"""
+            val = el
+            for key in keys:
+                if not key in val: return ""
+                val = val[key]
+            return val
+        # print(i, el)
+        el_s = f"\\begin{{element}}{{{el['symbol']}}}{{{el['number']}}}{{{el['period']}}}{{{el['column']}}}"
+        # description
+        el_s += f"\n\t\\desc[english]{{{el['names']['en']}}}{{{get('appearance', 'en')}}}{{}}"
+        el_s += f"\n\t\\desc[german]{{{el['names']['de']}}}{{English: {get('names', 'en')}\\\\{get('appearance', 'de')}}}{{}}"
+
+        # simple properties
+        for field in ["crystal_structure", "set", "magnetic_ordering"]:
+            if field in el:
+                el_s += f"\n\t\\property{{{field}}}{{{el[field]}}}"
+        # mass
+        m = get("atomic_mass", "value")
+        if m:
+            assert(get("atomic_mass", "unit") == "u")
+            el_s += f"\n\t\\property{{{'atomic_mass'}}}{{{m}}}"
+
+        # refractive indices
+        temp = ""
+        add_refractive_index = lambda idx: f"\\GT{{{idx['label']}}}: ${idx['value']}$, "
+        idxs = get("optical", "refractive_index")
+        # print(idxs)
+        if type(idxs) == list:
+            for idx in idxs: add_refractive_index(idx)
+        elif type(idxs) == dict: add_refractive_index(idxs)
+        elif type(idxs) == float: temp += f"${idxs}$, "
+        if temp:
+            el_s += f"\n\t\\property{{{'refractive_index'}}}{{{temp[:-2]}}}"
+
+
+        # electron configuration
+        match = re.fullmatch(r"([A-Z][a-z]*)? ?(.+?)", el["electron_config"])
+        if match:
+            el_s += f"\n\t\\property{{{'electron_config'}}}{{"
+            if match.groups()[0]:
+                el_s += f"\\elRef{{{match.groups()[0]}}} "
+            el_s += f"{match.groups()[1]}}}"
+
+        el_s += "\n\\end{element}"
+        # print(el_s)
+        s += el_s + "\n"
+    # print(s)
+    return s
+
+
+if __name__ == "__main__":
+    ptable = gen_periodic_table()
+    assert os.path.abspath(".").endswith("scripts"), "Please run from the `scripts` directory"
+    with open(f"{outdir}/periodic_table.tex", "w") as file:
+        file.write(ptable)
+

scripts/qubits.py

@@ -1,4 +1,4 @@
-from plot import *
+from formulary import *
 import scqubits as scq
 import qutip as qt
 
@@ -23,33 +23,36 @@ def _plot_transmon_n_wavefunctions(qubit: scq.Transmon, fig_ax, which=[0,1]):
     ax.set_xlim(*xlim)
     ax.set_xticks(np.arange(xlim[0], xlim[1]+1))
 
-def _plot_transmon(qubit: scq.Transmon, ngs, fig, axs):
+def _plot_transmon(qubit: scq.Transmon, ngs, fig, axs, wavefunction=True):
     _,_ = qubit.plot_evals_vs_paramvals("ng", ngs, fig_ax=(fig, axs[0]), evals_count=5, subtract_ground=False)
-    _,_ = qubit.plot_wavefunction(fig_ax=(fig, axs[1]), which=[0, 1, 2], mode="abs_sqr")
+    if wavefunction:
-    _plot_transmon_n_wavefunctions(qubit, (fig, axs[2]), which=[0, 1, 2])
+        _,_ = qubit.plot_wavefunction(fig_ax=(fig, axs[1]), which=[0, 1, 2], mode="abs_sqr")
-    qubit.ng = 0.5
+        _plot_transmon_n_wavefunctions(qubit, (fig, axs[2]), which=[0, 1, 2])
-    _plot_transmon_n_wavefunctions(qubit, (fig, axs[3]), which=[0, 1, 2])
+        qubit.ng = 0.5
-    qubit.ng = 0
+        _plot_transmon_n_wavefunctions(qubit, (fig, axs[3]), which=[0, 1, 2])
+        qubit.ng = 0
 
 
-def transmon_cpb():
+def transmon_cpb(wavefunction=True):
     EC = 1
     qubit = scq.Transmon(EJ=30, EC=EC, ng=0, ncut=30)
     ngs = np.linspace(-2, 2, 200)
-    fig, axs = plt.subplots(4, 3, squeeze=True, figsize=(full,full))
+    nrows = 4 if wavefunction else 1
+
+    fig, axs = plt.subplots(nrows, 3, squeeze=False, figsize=(full,full/3))
     axs = axs.T
     qubit.ng = 0
     qubit.EJ = 0.1 * EC
     title = lambda x: f"$E_J/E_C = {x}$"
-    _plot_transmon(qubit, ngs, fig, axs[0])
+    _plot_transmon(qubit, ngs, fig, axs[0], wavefunction=wavefunction)
     axs[0][0].set_title("Cooper-Pair-Box\n"+title(qubit.EJ))
 
     qubit.EJ = EC
-    _plot_transmon(qubit, ngs,  fig, axs[1])
+    _plot_transmon(qubit, ngs,  fig, axs[1], wavefunction=wavefunction)
     axs[1][0].set_title("Quantronium\n"+title(qubit.EJ))
 
     qubit.EJ = 20 * EC
-    _plot_transmon(qubit, ngs, fig, axs[2])
+    _plot_transmon(qubit, ngs, fig, axs[2], wavefunction=wavefunction)
     axs[2][0].set_title("Transmon\n"+title(qubit.EJ))
 
     for ax in axs[1:,:].flatten(): ax.set_ylabel("")
@@ -58,15 +61,14 @@ def transmon_cpb():
         ax.set_xticklabels(["-2", "-1", "", "0", "", "1", "2"])
         ylim = ax.get_ylim()
         ax.vlines([-1, -0.5], ymin=ylim[0], ymax=ylim[1], color="#aaa", linestyle="dotted")
-    axs[0][2].legend()
+    # axs[0][2].legend()
     fig.tight_layout()
     return fig
 
-export(transmon_cpb(), "qubit_transmon")
 
 
 def flux_onium():
-    fig, axs = plt.subplots(1, 3, squeeze=True, figsize=(full,full/2))
+    fig, axs = plt.subplots(1, 3, squeeze=True, figsize=(full,full/3))
     fluxs = np.linspace(0.4, 0.6, 50)
     EJ = 35.0
     alpha = 0.3
@@ -100,4 +102,6 @@ def flux_onium():
     axs[2].set_title("Fluxonium")
     return fig
 
-export(flux_onium(), "qubit_flux_onium")
+if __name__ == "__main__":
+    export(transmon_cpb(wavefunction=False), "qubit_transmon")
+    export(flux_onium(), "qubit_flux_onium")

scripts/readme.md

@@ -0,0 +1,16 @@
+# Scripts
+Put all scripts that generate plots or tex files here.
+You can run all files at once using `make scripts`
+
+## Plots
+For plots with `matplotlib`:
+1. import `formulary.py` 
+2. use one of the preset figsizes
+3. save the image using the `export` function in the `if __name__ == '__main__'` part
+
+## Colorscheme
+To ensure a uniform look of the tex source and the python plots, 
+the tex and matplotlib colorschemes are both handled in `formulary.py`.
+Set the `COLORSCHEME` variable to the desired colors.
+Importing `formulary.py`  will automatically apply the colors to matplotlib,
+and running it will generate `util/colorscheme.tex` for LaTeX.

scripts/requirements.txt

@@ -1,4 +1,5 @@
 numpy
+scipy
 matplotlib
 scqubits
 qutip

scripts/stat-mech.py

@@ -1,4 +1,5 @@
-from plot import *
+#!/usr/bin env python3
+from formulary import *
 
 def flennard_jones(r, epsilon, sigma):
     return 4 * epsilon * ((sigma/r)**12 - (sigma/r)**6)
@@ -17,7 +18,6 @@ def lennard_jones():
     ax.legend()
     ax.set_ylim(-1.1, 1.1)
     return fig
-export(lennard_jones(), "potential_lennard_jones")
 
 # BOLTZMANN / FERMI-DIRAC / BOSE-EINSTEN DISTRIBUTIONS
 def fboltzmann(x):
@@ -45,7 +45,6 @@ def id_qgas():
     ax.legend()
     ax.set_ylim(-0.1, 4)
     return fig
-export(id_qgas(), "td_id_qgas_distributions")
 
 @np.vectorize
 def fstep(x):
@@ -67,7 +66,6 @@ def fermi_occupation():
     ax.legend()
     ax.set_ylim(-0.1, 1.1)
     return fig
-export(fermi_occupation(), "td_fermi_occupation")
 
 def fermi_heat_capacity():
     fig, ax = plt.subplots(figsize=size_half_third)
@@ -83,8 +81,8 @@ def fermi_heat_capacity():
 
 
     low_temp_Cv = linear(x)
-    ax.plot(x, low_temp_Cv, color="orange", linestyle="dashed", label=r"${\pi^2}/{2}\,{T}/{T_\text{F}}$")
+    ax.plot(x, low_temp_Cv, color="o", linestyle="dashed", label=r"${\pi^2}/{2}\,{T}/{T_\text{F}}$")
-    ax.hlines([3/2], xmin=0, xmax=10, color="blue", linestyle="dashed", label="Petit-Dulong")
+    ax.hlines([3/2], xmin=0, xmax=10, color="b", linestyle="dashed", label="Petit-Dulong")
     @np.vectorize
     def unphysical_f(x):
         # exponential 
@@ -104,7 +102,7 @@ def fermi_heat_capacity():
         else: return a * x
     # ax.plot(x, smoothing, label="smooth")
     y = unphysical_f(x)
-    ax.plot(x, y, color="black")
+    ax.plot(x, y, color="k")
     ax.legend(loc="lower right")
 
 
@@ -116,5 +114,9 @@ def fermi_heat_capacity():
     ax.set_xlim(0, 1.4 * T_F)
     ax.set_ylim(0, 2)
     return fig
-export(fermi_heat_capacity(), "td_fermi_heat_capacity")
 
+if __name__ == '__main__':
+    export(lennard_jones(), "potential_lennard_jones")
+    export(fermi_heat_capacity(), "td_fermi_heat_capacity")
+    export(fermi_occupation(), "td_fermi_occupation")
+    export(id_qgas(), "td_id_qgas_distributions")

scripts/util/colorschemes.py

@@ -0,0 +1,179 @@
+"""
+A colorscheme for this project needs:
+fg and bg 0-4, where 0 is used as default font / background
+fg-<color> and bg-<color> where <color> is  "red", "orange", "yellow", "green", "aqua", "blue", "purple", "gray"
+"""
+
+from math import floor
+
+
+colors = ["red", "orange", "yellow", "green", "aqua", "blue", "purple", "gray"]
+
+def brightness(color:str, percent:float):
+    if color.startswith("#"):
+        color = color.strip("#")
+        newcolor = "#"
+    else:
+        newcolor = ""
+    for i in range(3):
+        c = float(int(color[i*2:i*2+2], 16))
+        c = int(round(max(0, min(c*percent, 0xff)), 0))
+        newcolor += f"{c:02x}"
+    return newcolor
+
+#
+# GRUVBOX
+#
+p_gruvbox = {
+    "fg0":          "#282828",
+    "fg0-hard":     "#1d2021",
+    "fg0-soft":     "#32302f",
+    "fg1":          "#3c3836",
+    "fg2":          "#504945",
+    "fg3":          "#665c54",
+    "fg4":          "#7c6f64",
+    "bg0":          "#fbf1c7",
+    "bg0-hard":     "#f9f5d7",
+    "bg0-soft":     "#f2e5bc",
+    "bg1":          "#ebdbb2",
+    "bg2":          "#d5c4a1",
+    "bg3":          "#bdae93",
+    "bg4":          "#a89984",
+    "dark-red":     "#cc241d",
+    "dark-green":   "#98971a",
+    "dark-yellow":  "#d79921",
+    "dark-blue":    "#458588",
+    "dark-purple":  "#b16286",
+    "dark-aqua":    "#689d6a",
+    "dark-orange":  "#d65d0e",
+    "dark-gray":    "#928374",
+    "light-red":    "#fb4934",
+    "light-green":  "#b8bb26",
+    "light-yellow": "#fabd2f",
+    "light-blue":   "#83a598",
+    "light-purple": "#d3869b",
+    "light-aqua":   "#8ec07c",
+    "light-orange": "#f38019",
+    "light-gray":   "#a89984",
+    "alt-red":      "#9d0006",
+    "alt-green":    "#79740e",
+    "alt-yellow":   "#b57614",
+    "alt-blue":     "#076678",
+    "alt-purple":   "#8f3f71",
+    "alt-aqua":     "#427b58",
+    "alt-orange":   "#af3a03",
+    "alt-gray":     "#7c6f64",
+}
+
+def gruvbox_light():
+    GRUVBOX_LIGHT = { "fg0": p_gruvbox["fg0-hard"], "bg0": p_gruvbox["bg0-hard"] } \
+        | {f"fg{n}": p_gruvbox[f"fg{n}"] for n in range(1,5)} \
+        | {f"bg{n}": p_gruvbox[f"bg{n}"] for n in range(1,5)} \
+        | {f"fg-{n}": p_gruvbox[f"alt-{n}"] for n in colors} \
+        | {f"bg-{n}": p_gruvbox[f"light-{n}"] for n in colors}
+    return GRUVBOX_LIGHT
+
+def gruvbox_dark():
+    GRUVBOX_DARK = { "fg0": p_gruvbox["bg0-hard"], "bg0": p_gruvbox["fg0-hard"] } \
+        | {f"fg{n}": p_gruvbox[f"bg{n}"] for n in range(1,5)} \
+        | {f"bg{n}": p_gruvbox[f"fg{n}"] for n in range(1,5)} \
+        | {f"fg-{n}": p_gruvbox[f"light-{n}"] for n in colors} \
+        | {f"bg-{n}": p_gruvbox[f"dark-{n}"] for n in colors}
+    return GRUVBOX_DARK
+
+#
+# LEGACY
+#
+p_legacy = {
+    "fg0":              "#fcfcfc",
+    "bg0":              "#333333",
+    "red":              "#d12229",
+    "green":            "#007940",
+    "yellow":           "#ffc615",
+    "blue":             "#2440fe",
+    "purple":           "#4D1037",
+    "aqua":             "#008585",
+    "orange":           "#f68a1e",
+    "gray":             "#928374",
+}
+
+def legacy():
+    LEGACY = \
+        { f"fg{n}": brightness(p_legacy["fg0"], 1-n/8) for n in range(5)} \
+        | { f"bg{n}": brightness(p_legacy["bg0"], 1+n/8) for n in range(5)} \
+        | { f"bg-{n}": c for n,c in p_legacy.items() } \
+        | { f"fg-{n}": brightness(c, 2.0) for n,c in p_legacy.items() }
+    return LEGACY
+
+#
+# TUM
+#
+p_tum = {
+    "dark-blue":		"#072140",
+    "light-blue":	    "#5E94D4",
+    "alt-blue":	        "#3070B3",
+    "light-yellow":	    "#FED702",
+    "dark-yellow":	    "#CBAB01",
+    "alt-yellow":	    "#FEDE34",
+    "light-orange":	    "#F7811E",
+    "dark-orange":	    "#D99208",
+    "alt-orange":	    "#F9BF4E",
+    "light-purple":	    "#B55CA5",
+    "dark-purple":		"#9B468D",
+    "alt-purple":		"#C680BB",
+    "light-red":	    "#EA7237",
+    "dark-red":	        "#D95117",
+    "alt-red":	        "#EF9067",
+    "light-green":      "#9FBA36",
+    "dark-green":       "#7D922A",
+    "alt-green":	    "#B6CE55",
+    "light-gray":	    "#475058",
+    "dark-gray":	    "#20252A",
+    "alt-gray":	        "#333A41",
+    "light-aqua":       "#689d6a",
+    "dark-aqua":        "#427b58",  # taken aquas from gruvbox
+    "fg0-hard":	        "#000000",
+    "fg0":		        "#000000",
+    "fg0-soft":	        "#20252A",
+    "fg1":               "#072140",
+    "fg2":	            "#333A41",
+    "fg3":	            "#475058",
+    "fg4":	            "#6A757E",
+    "bg0-hard":	        "#FFFFFF",
+    "bg0":		        "#FBF9FA",
+    "bg0-soft":	        "#EBECEF",
+    "bg1":	            "#DDE2E6",
+    "bg2":	            "#E3EEFA",
+    "bg3":	            "#F0F5FA",
+}
+
+def tum():
+    TUM = {}
+    for n,c in p_tum.items():
+        n2 = n.replace("light", "bg").replace("dark", "fg")
+        TUM[n2] = c
+    return TUM
+
+#
+# STUPID
+#
+p_stupid = {
+    "bg0":              "#0505aa",
+    "fg0":              "#ffffff",
+    "red":              "#ff0000",
+    "green":            "#23ff81",
+    "yellow":           "#ffff00",
+    "blue":             "#5555ff",
+    "purple":           "#b00b69",
+    "aqua":             "#00ffff",
+    "orange":           "#ffa500",
+    "gray":             "#444444",
+}
+def stupid():
+    LEGACY = \
+        { f"fg{n}": brightness(p_stupid["fg0"], 1-n/8) for n in range(5)} \
+        | { f"bg{n}": brightness(p_stupid["bg0"], 1+n/8) for n in range(5)} \
+        | { f"bg-{n}": c for n,c in p_stupid.items() } \
+        | { f"fg-{n}": brightness(c, 2.0) for n,c in p_stupid.items() }
+    return LEGACY
+

scripts/util/gen_tex_colorscheme.py

@@ -0,0 +1,10 @@
+def color_latex_def(name, color):
+    # name = name.replace("-", "_")
+    color = color.strip("#")
+    return "\\definecolor{" + name + "}{HTML}{" + color + "}"
+
+def generate_latex_colorscheme(palette):
+    s = ""
+    for n, c in palette.items():
+        s += color_latex_def(n, c) + "\n"
+    return s

scripts/util/mpl_colorscheme.py

@@ -0,0 +1,84 @@
+"""
+Set the colorscheme for matplotlib plots and latex.
+
+Calling this script generates util/colorscheme.tex containing xcolor definitions.
+"""
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+from cycler import cycler
+
+# default order for matplotlib
+color_order = ["blue", "orange", "green", "red", "purple", "yellow", "aqua", "gray"]
+
+def set_mpl_colorscheme(palette: dict[str, str]):
+    P = palette
+    FIG_BG_COLOR =          P["bg0"]
+    PLT_FG_COLOR =          P["fg0"]
+    PLT_BG_COLOR =          P["bg0"]
+    PLT_GRID_COLOR =        P["bg2"]
+    LEGEND_FG_COLOR =       PLT_FG_COLOR
+    LEGEND_BG_COLOR =       P["bg1"]
+    LEGEND_BORDER_COLOR =   P["bg2"]
+    COLORS = [P[f"fg-{c}"] for c in color_order]
+
+
+    color_rcParams = {
+        'axes.edgecolor': PLT_FG_COLOR,
+        'axes.facecolor': PLT_BG_COLOR,
+        'axes.labelcolor': PLT_FG_COLOR,
+        'axes.titlecolor': 'auto',
+        # 'axes.prop_cycle': cycler('color', ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']),
+        'axes.prop_cycle': cycler('color', COLORS),
+        # 'axes3d.xaxis.panecolor': (0.95, 0.95, 0.95, 0.5),
+        # 'axes3d.yaxis.panecolor': (0.9, 0.9, 0.9, 0.5),
+        # 'axes3d.zaxis.panecolor': (0.925, 0.925, 0.925, 0.5),
+        # 'boxplot.boxprops.color': 'black',
+        # 'boxplot.capprops.color': 'black',
+        # 'boxplot.flierprops.color': 'black',
+        # 'boxplot.flierprops.markeredgecolor': 'black',
+        # 'boxplot.flierprops.markeredgewidth': 1.0,
+        # 'boxplot.flierprops.markerfacecolor': 'none',
+        # 'boxplot.meanprops.color': 'C2',
+        # 'boxplot.meanprops.markeredgecolor': 'C2',
+        # 'boxplot.meanprops.markerfacecolor': 'C2',
+        # 'boxplot.meanprops.markersize': 6.0,
+        # 'boxplot.medianprops.color': 'C1',
+        # 'boxplot.whiskerprops.color': 'black',
+        'figure.edgecolor': PLT_BG_COLOR,
+        'figure.facecolor': PLT_BG_COLOR,
+        # 'figure.figsize': [6.4, 4.8],
+        # 'figure.frameon': True,
+        # 'figure.labelsize': 'large',
+        'grid.color': PLT_GRID_COLOR,
+        # 'hatch.color': 'black',
+        'legend.edgecolor': LEGEND_BORDER_COLOR,
+        'legend.facecolor': LEGEND_BG_COLOR,
+        'xtick.color': PLT_FG_COLOR,
+        'ytick.color': PLT_FG_COLOR,
+        'xtick.labelcolor': PLT_FG_COLOR,
+        'ytick.labelcolor': PLT_FG_COLOR,
+        # 'lines.color': 'C0',
+        'text.color': PLT_FG_COLOR,
+    }
+
+    for k, v in color_rcParams.items():
+        plt.rcParams[k] = v
+
+    # override single char codes
+    # TODO: use color name with variant from palette instead of order
+    mpl.colors.get_named_colors_mapping()["b"] = COLORS[0]
+    mpl.colors.get_named_colors_mapping()["o"] = COLORS[1]
+    mpl.colors.get_named_colors_mapping()["g"] = COLORS[2]
+    mpl.colors.get_named_colors_mapping()["r"] = COLORS[3]
+    mpl.colors.get_named_colors_mapping()["m"] = COLORS[4]
+    mpl.colors.get_named_colors_mapping()["y"] = COLORS[5]
+    mpl.colors.get_named_colors_mapping()["c"] = COLORS[6]
+    mpl.colors.get_named_colors_mapping()["k"] = P["fg0"]
+    mpl.colors.get_named_colors_mapping()["w"] = P["bg0"]
+    mpl.colors.get_named_colors_mapping()["black"] = P["fg0"]
+    for color in color_order:
+        mpl.colors.get_named_colors_mapping()[color] = P[f"fg-{color}"]
+
+
+
+

src/.latexmkrc

@@ -0,0 +1,31 @@
+# Specify the auxiliary and output directories
+$aux_dir = '../.aux';
+$out_dir = '../out';
+
+# Set lualatex as the default engine
+$pdf_mode = 1; # Enable PDF generation mode
+# $pdflatex = 'lualatex --interaction=nonstopmode --shell-escape'
+$lualatex = 'lualatex %O --interaction=nonstopmode --shell-escape %S'
+
+# Additional options for compilation
+    # '-verbose',
+    # '-file-line-error',
+
+# Quickfix-like filtering (warnings to ignore)
+# @warnings_to_filter = (
+#     qr/Underfull \\hbox/,
+#     qr/Overfull \\hbox/,
+#     qr/LaTeX Warning: .+ float specifier changed to/,
+#     qr/LaTeX hooks Warning/,
+#     qr/Package siunitx Warning: Detected the "physics" package:/,
+#     qr/Package hyperref Warning: Token not allowed in a PDF string/
+# );
+
+# # Filter function for warnings
+# sub filter_warnings {
+#     my $warning = shift;
+#     foreach my $filter (@warnings_to_filter) {
+#         return 0 if $warning =~ $filter;
+#     }
+#     return 1;
+# }

src/analysis.tex

@@ -1,125 +0,0 @@
-\Part[
-    \eng{Calculus}
-    \ger{Analysis}
-    ]{cal}
-
-    \Subsection[
-        \eng{Convolution}
-        \ger{Faltung / Konvolution}
-        ]{conv}
-        \begin{ttext}
-            \eng{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}
-            \ger{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}
-        \end{ttext}
-        \begin{formula}{def}
-            \desc{Definition}{}{}
-            \desc[german]{Definition}{}{}
-            \eq{(f*g)(t) = f(t) * g(t) = int_{-\infty}^\infty f(\tau) g(t-\tau) \d \tau}
-        \end{formula}
-        \begin{formula}{notation}
-            \desc{Notation}{}{}
-            \desc[german]{Notation}{}{}
-            \eq{
-                f(t) * g(t-t_0) &= (f*g)(t-t_0) \\
-                f(t-t_0) * g(t-t_0) &= (f*g)(t-2t_0)
-            }
-        \end{formula}
-        \begin{formula}{commutativity}
-            \desc{Commutativity}{}{}
-            \desc[german]{Kommutativität}{}{}
-            \eq{f * g = g * f}
-        \end{formula}
-
-        \begin{formula}{associativity}
-            \desc{Associativity}{}{}
-            \desc[german]{Assoziativität]}{}{}
-            \eq{(f*g)*h = f*(g*h)}
-        \end{formula}
-
-        \begin{formula}{distributivity}
-            \desc{Distributivity}{}{}
-            \desc[german]{Distributivität}{}{}
-            \eq{f * (g + h) = f*g + f*h}
-        \end{formula}
-
-        \begin{formula}{complex_conjugate}
-            \desc{Complex conjugate}{}{}
-            \desc[german]{Komplexe konjugation}{}{}
-            \eq{(f*g)^* = f^* * g^*}
-        \end{formula}
-        
-    \Subsection[
-        \eng{Fourier analysis}
-        \ger{Fourieranalyse}
-        ]{fourier}
-        \Subsubsection[
-            \eng{Fourier series}
-            \ger{Fourierreihe}
-            ]{series}
-            \begin{formula}{series}
-                \desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
-                \desc[german]{Fourierreihe}{Komplexe Darstellung}{}
-                \eq{f(t) = \sum_{k=-\infty}^{\infty} c_k \Exp{\frac{2\pi \I kt}{T}}}
-            \end{formula}
-            \Eng[real]{real}
-            \Ger[real]{reellwertig}
-            \begin{formula}{coefficient}
-                \desc{Fourier coefficients}{Complex representation}{}
-                \desc[german]{Fourierkoeffizienten}{Komplexe Darstellung}{}
-                \eq{
-                    c_k &= \frac{1}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Exp{-\frac{2\pi \I}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
-                    c_{-k} &= \overline{c_k} \quad \text{\GT{if} $f$ \GT{real}}
-                }
-            \end{formula}
-
-            \begin{formula}{series_sincos}
-                \desc{Fourier series}{Sine and cosine representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
-                \desc[german]{Fourierreihe}{Sinus und Kosinus Darstellung}{}
-                \eq{f(t) = \frac{a_0}{2} + \sum_{k=1}^{\infty} \left(a_k \Cos{\frac{2\pi}{T}kt} + b_k\Sin{\frac{2\pi}{T}kt}\right)}
-            \end{formula}
-            \begin{formula}{coefficient}
-                \desc{Fourier coefficients}{Sine and cosine representation\\If $f$ has point symmetry: $a_{k>0}=0$, if $f$ has axial symmetry: $b_k=0$}{}
-                \desc[german]{Fourierkoeffizienten}{Sinus und Kosinus Darstellung\\Wenn $f$ punktsymmetrisch: $a_{k>0}=0$, wenn $f$ achsensymmetrisch: $b_k=0$}{}
-                \eq{
-                    a_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Cos{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
-                    b_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Sin{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge1\\
-                    a_k &= c_k + c_{-k}      \quad\text{\GT{for}}\,k\ge0\\
-                    b_k &= \I(c_k - c_{-k})  \quad\text{\GT{for}}\,k\ge1
-                }
-            \end{formula}
-        \TODO{cleanup}
-        
-
-
-        \Subsubsection[
-            \eng{Fourier transformation}
-            \ger{Fouriertransformation}
-            ]{trafo}
-            \begin{formula}{transform}
-                \desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
-                \desc[german]{Fouriertransformierte}{}{}
-                \eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
-            \end{formula}
-
-            \Eng[linear_in]{linear in}
-            \Ger[linear_in]{linear in}
-            \GT{for} $f\in L^1(\R^n)$:
-            \begin{enumerate}[i)]
-                \item $f \mapsto \hat{f}$ \GT{linear_in} $f$
-                \item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
-                \item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
-                \item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
-            \end{enumerate}
-
-
-\Section[
-    \eng{List of common integrals}
-    \ger{Liste nützlicher Integrale}
-    ]{integrals}
-
-    \begin{formula}{riemann_zeta}
-        \desc{Riemann Zeta Function}{}{}
-        \desc[german]{Riemannsche Zeta-Funktion}{}{}
-        \eq{\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \frac{1}{(1-2^{(1-s)})\Gamma(s)} \int_0^\infty \d\eta \frac{\eta^{(s-1)}}{\e^\eta + 1}}
-    \end{formula}
-

src/calculus.tex

@@ -1,55 +0,0 @@
-\Part[
-    \eng{Analysis}
-    \ger{Analysis}
-    ]{ana}
-
-    \Subsection[
-        \eng{Convolution}
-        \ger{Faltung / Konvolution}
-        ]{conv}
-        \begin{ttext}
-            \eng{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}
-            \ger{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}
-        \end{ttext}
-        \begin{formula}{def}
-            \desc{Definition}{}{}
-            \desc[german]{Definition}{}{}
-            \eq{(f*g)(t) = f(t) * g(t) = int_{-\infty}^\infty f(\tau) g(t-\tau) \d \tau}
-        \end{formula}
-        \begin{formula}{notation}
-            \desc{Notation}{}{}
-            \desc[german]{Notation}{}{}
-            \eq{
-                f(t) * g(t-t_0) &= (f*g)(t-t_0) \\
-                f(t-t_0) * g(t-t_0) &= (f*g)(t-2t_0)
-            }
-        \end{formula}
-        \begin{formula}{commutativity}
-            \desc{Commutativity}{}{}
-            \desc[german]{Kommutativität}{}{}
-            \eq{f * g = g * f}
-        \end{formula}
-
-        \begin{formula}{associativity}
-            \desc{Associativity}{}{}
-            \desc[german]{Assoziativität]}{}{}
-            \eq{(f*g)*h = f*(g*h)}
-        \end{formula}
-
-        \begin{formula}{distributivity}
-            \desc{Distributivity}{}{}
-            \desc[german]{Distributivität}{}{}
-            \eq{f * (g + h) = f*g + f*h}
-        \end{formula}
-
-        \begin{formula}{complex_conjugate}
-            \desc{Complex conjugate}{}{}
-            \desc[german]{Komplexe konjugation}{}{}
-            \eq{(f*g)^* = f^* * g^*}
-        \end{formula}
-        
-    \Subsection[
-        \eng{Fourier analysis}
-        \ger{Fourieranalyse}
-        ]{fourier}
-

src/ch/ch.tex

@@ -0,0 +1,9 @@
+\Part[
+    \eng{Chemistry}
+    \ger{Chemie}
+]{ch}
+\Section[
+    \eng{Periodic table}
+    \ger{Periodensystem}
+]{ptable}
+    \drawPeriodicTable

src/ch/el.tex

@@ -0,0 +1,583 @@
+\Section[
+    \eng{Electrochemistry}
+    \ger{Elektrochemie}
+]{el}
+\begin{formula}{chemical_potential}
+    \desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{gibbs_free_energy}, \QtyRef{amount}}
+    \desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
+    \quantity{\mu}{\joule\per\mol;\joule}{is}
+    \eq{
+        \mu_i \equiv \pdv{G}{n_i}_{n_j\neq n_i,p,T}
+    }
+\end{formula}
+
+\begin{formula}{standard_chemical_potential}
+    \desc{Standard chemical potential}{In equilibrium}{\QtyRef{chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}, \QtyRef{activity}}
+    \desc[german]{Standard chemisches Potential}{}{}
+    \eq{\mu_i = \mu_i^\theta + RT \Ln{a_i}}
+\end{formula}
+
+\begin{formula}{chemical_equilibrium}
+    \desc{Chemical equilibrium}{}{\QtyRef{chemical_potential}, \QtyRef{stoichiometric_coefficient}}
+    \desc[german]{Chemisches Gleichgewicht}{}{}
+    \eq{\sum_\text{\GT{products}} \nu_i \mu_i = \sum_\text{\GT{educts}} \nu_i \mu_i}
+\end{formula}
+
+\begin{formula}{activity}
+    \desc{Activity}{relative activity}{\QtyRef{chemical_potential}, \QtyRef{standard_chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}}
+    \desc[german]{Aktivität}{Relative Aktivität}{}
+    \quantity{a}{}{s}
+    \eq{a_i = \Exp{\frac{\mu_i-\mu_i^\theta}{RT}}}
+\end{formula}
+
+\begin{formula}{electrochemical_potential}
+    \desc{Electrochemical potential}{Chemical potential with electrostatic contributions}{\QtyRef{chemical_potential}, $z$ valency (charge), \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvani Potential)}
+    \desc[german]{Elektrochemisches Potential}{Chemisches Potential mit elektrostatischen Enegiebeiträgen}{\QtyRef{chemical_potential}, $z$ Ladungszahl, \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvanisches Potential)}
+    \quantity{\muecp}{\joule\per\mol;\joule}{is}
+    \eq{\muecp_i \equiv \mu_i + z_i F \phi}
+\end{formula}
+
+
+\Subsection[
+    \eng{Electrochemical cell}
+    \ger{Elektrochemische Zelle}
+]{cell}
+    \eng[galvanic]{galvanic}
+    \ger[galvanic]{galvanisch}
+    \eng[electrolytic]{electrolytic}
+    \ger[electrolytic]{electrolytisch}
+
+    \Eng[working_electrode]{Working electrode}
+    \Eng[counter_electrode]{Counter electrode}
+    \Eng[reference_electrode]{Reference electrode}
+    \Ger[working_electrode]{Working electrode}
+    \Ger[counter_electrode]{Gegenelektrode}
+    \Ger[reference_electrode]{Referenzelektrode}
+    \Eng[potentiostat]{Potentiostat}
+    \Ger[potentiostat]{Potentiostat}
+
+    \begin{formula}{schematic}
+        \desc{Schematic}{}{}
+        \desc[german]{Aufbau}{}{}
+        \begin{tikzpicture}[scale=1.0,transform shape]
+            \pgfmathsetmacro{\W}{6}
+            \pgfmathsetmacro{\H}{3}
+            \pgfmathsetmacro{\elW}{\W/20}
+
+            \pgfmathsetmacro{\CEx}{1/6*\W}
+            \pgfmathsetmacro{\WEx}{3/6*\W}
+            \pgfmathsetmacro{\REx}{5/6*\W}
+
+            \fill[bg-blue] (0,0) rectangle (\W, \H/2);
+            \draw[ultra thick] (0,0) rectangle (\W,\H);
+            % Electrodes
+            \draw[thick, fill=bg-gray]   (\CEx-\elW,\H/5) rectangle (\CEx+\elW,\H);
+            \draw[thick, fill=bg-purple] (\WEx-\elW,\H/5) rectangle (\WEx+\elW,\H);
+            \draw[thick, fill=bg-yellow] (\REx-\elW,\H/5) rectangle (\REx+\elW,\H);
+            \node at (\CEx,3*\H/5) {C};
+            \node at (\WEx,3*\H/5) {W};
+            \node at (\REx,3*\H/5) {R};
+
+            % potentiostat
+            \pgfmathsetmacro{\potH}{\H+0.5+2}
+            \pgfmathsetmacro{\potM}{\H+0.5+1}
+            \draw[thick] (0,\H+0.5) rectangle (\W,\potH);
+            % Wires
+            \draw (\CEx,\H) -- (\CEx,\potM) to[voltmeter,-o] (\WEx,\potM) to[european voltage source] (\WEx+1/6*\W,\potM) to[ammeter] (\REx,\potM);
+            \draw (\WEx,\H) -- (\WEx,\H+1.5);
+            \draw (\REx,\H) -- (\REx,\H+1.5);
+
+            % labels
+            \node[anchor=west, align=left] at (\W+0.2, 1*\H/4) {{\color{bg-gray}  \blacksquare} \GT{counter_electrode}};
+            \node[anchor=west, align=left] at (\W+0.2, 2*\H/4) {{\color{bg-purple}\blacksquare} \GT{working_electrode}};
+            \node[anchor=west, align=left] at (\W+0.2, 3*\H/4) {{\color{bg-yellow}\blacksquare} \GT{reference_electrode}};
+            \node[anchor=west, align=left] at (\W+0.2, \potM) {\GT{potentiostat}};
+    \end{tikzpicture}
+    \end{formula}
+
+    \begin{formula}{cell}
+        \desc{Electrochemical cell types}{}{}
+        \desc[german]{Arten der Elektrochemische Zelle}{}{}
+        \ttxt{
+            \eng{
+                \begin{itemize}
+                    \item Electrolytic cell: Uses electrical energy to force a chemical reaction
+                    \item Galvanic cell: Produces electrical energy through a chemical reaction
+                \end{itemize}
+            }
+            \ger{
+                \begin{itemize}
+                    \item Elektrolytische Zelle: Nutzt elektrische Energie um eine Reaktion zu erzwingen
+                    \item Galvanische Zelle: Produziert elektrische Energie durch eine chemische Reaktion 
+                \end{itemize}
+            }
+        }
+    \end{formula}
+
+    % todo group together
+    \begin{formula}{faradaic}
+        \desc{Faradaic process}{}{}
+        \desc[german]{Faradäischer Prozess}{}{}
+        \ttxt{
+            \eng{Charge transfers between the electrode bulk and the electrolyte.}
+            \ger{Ladung wird zwischen Elektrode und dem Elektrolyten transferiert.}
+        }
+    \end{formula}
+    \begin{formula}{non-faradaic}
+        \desc{Non-Faradaic (capacitive) process}{}{}
+        \desc[german]{Nicht-Faradäischer (kapazitiver) Prozess}{}{}
+        \ttxt{
+            \eng{Charge is stored at the electrode-electrolyte interface.}
+            \ger{Ladung lagert sich am Elektrode-Elektrolyt Interface an.}
+        }
+    \end{formula}
+
+
+    \begin{formula}{electrode_potential}
+        \desc{Electrode potential}{}{}
+        \desc[german]{Elektrodenpotential}{}{}
+        \quantity{E}{\volt}{s}
+    \end{formula}
+
+    \begin{formula}{standard_cell_potential}
+        \desc{Standard cell potential}{}{$\Delta_\txR G^\theta$ standard \qtyRef{gibbs_free_energy} of reaction, $n$ number of electrons, \ConstRef{faraday}}
+        \desc[german]{Standard Zellpotential}{}{$\Delta_\txR G^\theta$ Standard \qtyRef{gibbs_free_energy} der Reaktion, $n$ Anzahl der Elektronen, \ConstRef{faraday}}
+        \eq{E^\theta_\text{rev} = \frac{-\Delta_\txR G^\theta}{nF}}
+    \end{formula}
+
+
+    \begin{formula}{nernst_equation}
+        \desc{Nernst equation}{Electrode potential for a half-cell reaction}{\QtyRef{electrode_potential}, $E^\theta$ \secEqRef{standard_cell_potential}, \ConstRef{universal_gas}, \ConstRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \QtyRef{activity}, \QtyRef{stoichiometric_coefficient}}
+        \desc[german]{Nernst-Gleichung}{Elektrodenpotential für eine Halbzellenreaktion}{}
+        \eq{E = E^\theta + \frac{RT}{zF} \Ln{\frac{ \left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{oxidized}}{\left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{reduced}}}}
+    \end{formula}
+
+    \begin{formula}{cell_efficiency}
+        \desc{Thermodynamic cell efficiency}{}{$P$ \fqEqRef{ed:el:power}}
+        \desc[german]{Thermodynamische Zelleffizienz}{}{}
+        \eq{
+            \eta_\text{cell} &= \frac{P_\text{obtained}}{P_\text{maximum}} = \frac{E_\text{cell}}{E_\text{cell,rev}} & & \text{\gt{galvanic}} \\
+            \eta_\text{cell} &= \frac{P_\text{minimum}}{P_\text{applied}} = \frac{E_\text{cell,rev}}{E_\text{cell}} & & \text{\gt{electrolytic}}
+        }
+    \end{formula}
+
+
+\Subsection[
+    \eng{Ionic conduction in electrolytes}
+    \ger{Ionische Leitung in Elektrolyten}
+]{ion_cond}
+    \eng[z]{charge number}
+    \ger[z]{Ladungszahl}
+    \eng[of_i]{of ion $i$}
+    \ger[of_i]{des Ions $i$}
+     
+    \begin{formula}{diffusion}
+        \desc{Diffusion}{caused by concentration gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{diffusion_constant} \gt{of_i}, \QtyRef{concentration} \gt{of_i}}
+        \desc[german]{Diffusion}{durch Konzentrationsgradienten}{}
+        \eq{ i_\text{diff} = \sum_i -z_i F D_i \left(\odv{c_i}{x}\right) }
+    \end{formula}
+
+    \begin{formula}{migration}
+        \desc{Migration}{caused by potential gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ potential gradient in the solution}
+        \desc[german]{Migration}{durch Potentialgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ Potentialgradient in der Lösung}
+        \eq{ i_\text{mig} = \sum_i -z_i^2 F^2 \, c_i \, \mu_i \, \nabla\Phi_\txs }
+    \end{formula}
+
+    \begin{formula}{convection}
+        \desc{Convection}{caused by pressure gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} in flowing electrolyte}
+        \desc[german]{Convection}{durch Druckgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} im fliessenden Elektrolyt}
+        \eq{ i_\text{conv} = \sum_i -z_i F \, c_i \, v_i^\text{flow} }
+    \end{formula}
+
+    \begin{formula}{ionic_conductivity}
+        \desc{Ionic conductivity}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ charge number, \qtyRef{concentration} and \qtyRef{mobility} of the positive (+) and negative (-) ions}
+        \desc[german]{Ionische Leitfähigkeit}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ Ladungszahl, \qtyRef{concentration} und \qtyRef{mobility} der positiv (+) und negativ geladenen Ionen}
+        \quantity{\kappa}{\per\ohm\cm=\siemens\per\cm}{}
+        \eq{\kappa = F^2 \left(z_+^2 \, c_+  \, \mu_+ + z_-^2 \, c_- \, \mu_-\right)}
+    \end{formula}
+
+    \begin{formula}{ionic_resistance}
+        \desc{Ohmic resistance of ionic current flow}{}{$L$ \qtyRef{length}, $A$ \qtyRef{area}, \QtyRef{ionic_conductivity}}
+        \desc[german]{Ohmscher Widerstand für Ionen-Strom}{}{}
+        \eq{R_\Omega = \frac{L}{A\,\kappa}}
+    \end{formula}
+
+    \begin{formula}{ionic_mobility}
+        \desc{Ionic  mobility}{}{$v_\pm$ steady state drift \qtyRef{velocity}, $\phi$ \qtyRef{electric_scalar_potential}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{charge}, \QtyRef{viscosity}, $r_\pm$ ion radius}
+        \desc[german]{Ionische Moblilität}{}{}
+        \quantity{u_\pm}{\cm^2\mol\per\joule\s}{}
+        \eq{u_\pm = - \frac{v_\pm}{\nabla \phi \,z_\pm F} = \frac{e}{6\pi F \eta_\text{dyn} r_\pm}}
+    \end{formula}
+
+    \begin{formula}{stokes_friction}
+        \desc{Stokes's law}{Frictional force exerted on spherical objects moving in a viscous fluid at low Reynolds numbers}{$r$ particle radius, \QtyRef{viscosity}, $v$ particle \qtyRef{velocity}}
+        \desc[german]{Gesetz von Stokes}{Reibungskraft auf ein sphärisches Objekt in einer Flüssigkeit bei niedriger Reynolds-Zahl}{$r$ Teilchenradius, \QtyRef{viscosity}, $v$ Teilchengeschwindigkeit}
+        \eq{F_\txR = 6\pi\,r \eta v}
+    \end{formula}
+
+    \begin{formula}{transference}
+        \desc{Transference number}{Ion transport number \\Fraction of the current carried by positive / negative ions}{$i_{+/-}$ current through positive/negative charges}
+        \desc[german]{Überführungszahl}{Anteil der positiv / negativ geladenen Ionen am Gesamtstrom}{$i_{+/-}$ Strom durch positive / negative Ladungn}
+        \eq{t_{+/-} = \frac{i_{+/-}}{i_+ + i_-}}
+    \end{formula}
+
+    \eng[csalt]{electrolyte \qtyRef{concentration}}
+    \eng[csalt]{\qtyRef{concentration} des Elektrolyts}
+    \begin{formula}{molar_conductivity}
+        \desc{Molar conductivity}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{csalt}}
+        \desc[german]{Molare Leitfähigkeit}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{salt}}
+        \quantity{\Lambda_\txM}{\siemens\cm^2\per\mol=\ampere\cm^2\per\volt\mol}{ievs}
+        \eq{\Lambda_\txM = \frac{\kappa}{c_\text{salt}}}
+    \end{formula}
+
+    \begin{formula}{kohlrausch_law}
+        \desc{Kohlrausch's law}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} at infinite dilution, $c_\text{salt}$ \gt{csalt}, $K$ \GT{constant}}
+        \desc[german]{}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} bei unendlicher Verdünnung, $\text{salt}$ \gt{csalt} $K$ \GT{constant}}
+        \eq{\Lambda_\txM = \Lambda_\txM^0 - K \sqrt{c_\text{salt}}}
+    \end{formula}
+    
+% Electrolyte conductivity
+    \begin{formula}{molality}
+        \desc{Molality}{}{\QtyRef{amount} of the solute, \QtyRef{mass} of the solvent}
+        \desc[german]{Molalität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{mass} des Lösungsmittels}
+        \quantity{b}{\mol\per\kg}{}
+        \eq{b = \frac{n}{m}}
+    \end{formula}
+
+    \begin{formula}{molarity}
+        \desc{Molarity}{\GT{see} \qtyRef{concentration}}{\QtyRef{amount} of the solute, \QtyRef{volume} of the solvent}
+        \desc[german]{Molarität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{volume} des Lösungsmittels}
+        \quantity{c}{\mol\per\litre}{}
+        \eq{c = \frac{n}{V}}
+    \end{formula}
+
+    \begin{formula}{ionic_strength}
+        \desc{Ionic strength}{Measure of the electric field in a solution through solved ions}{\QtyRef{molality}, \QtyRef{molarity}, $z$ \qtyRef{charge_number}}
+        \desc[german]{Ionenstärke}{Maß eienr Lösung für die elektrische Feldstärke durch gelöste Ionen}{}
+        \quantity{I}{\mol\per\kg;\mol\per\litre}{}
+        \eq{I_b &= \frac{1}{2} \sum_i b_i z_i^2 \\ I_c &= \frac{1}{2} \sum_i c_i z_i^2}
+    \end{formula}
+
+    \begin{formula}{debye_screening_length}
+        \desc{Debye screening length}{}{\ConstRef{avogadro}, \ConstRef{charge}, \QtyRef{ionic_strength}, \QtyRef{permittivity}, \ConstRef{boltzmann}, \QtyRef{temperature}}
+        \desc[german]{Debye-Länge / Abschirmlänge}{}{}
+        \eq{\lambda_\txD = \sqrt{\frac{\epsilon \kB T}{2\NA e^2 I_C}}}
+    \end{formula}
+
+    \begin{formula}{mean_ionic_activity}
+        \desc{Mean ionic activity coefficient}{Accounts for decreased reactivity because ions must divest themselves of their ion cloud before reacting}{}
+        \desc[german]{Mittlerer ionischer Aktivitätskoeffizient}{Berücksichtigt dass Ionen sich erst von ihrer Ionenwolke lösen müssen, bevor sie reagieren können}{}
+        \quantity{\gamma}{}{s}
+        \eq{\gamma_\pm = \left(\gamma_+^{\nu_+} \, \gamma_-^{\nu_-}\right)^{\frac{1}{\nu_+ + \nu_-}}}
+    \end{formula}
+
+    \begin{formula}{debye_hueckel_law}
+        \desc{Debye-Hückel limiting law}{For an infinitely dilute solution}{\QtyRef{mean_ionic_activity}, $A$ solvent dependant constant, $z$ \qtyRef{charge_number}, \QtyRef{ionic_strength} in [\si{\mol\per\kg}]}
+        \desc[german]{Debye-Hückel Gesetz}{Für eine unendlich verdünnte Lösung}{}
+        \eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
+    \end{formula} 
+
+\Subsection[
+    \eng{Kinetics}
+    \ger{Kinetik}
+]{kin}
+    \begin{formula}{transfer_coefficient}
+        \desc{Transfer coefficient}{}{}
+        \desc[german]{Durchtrittsfaktor}{Transferkoeffizient\\Anteil des Potentials der sich auf die freie Reaktionsenthalpie des anodischen Prozesses auswirkt}{}
+        \eq{
+            \alpha_\txA &= \alpha \\
+            \alpha_\txC &= 1-\alpha
+        }
+    \end{formula}
+
+    \begin{formula}{overpotential}
+        \desc{Overpotential}{}{}
+        \desc[german]{Überspannung}{}{}
+        \ttxt{
+            \eng{Potential deviation from the equilibrium cell potential}
+            \ger{Abweichung der Spannung von der Zellspannung im Gleichgewicht}
+        }
+    \end{formula}
+    \begin{formula}{activation_overpotential}
+        \desc{Activation verpotential}{}{$E_\text{electrode}$ potential at which the reaction starts $E_\text{ref}$ thermodynamic potential of the reaction}
+        \desc[german]{Aktivierungsüberspannung}{}{$E_\text{electrode}$ Potential bei der die Reaktion beginnt, $E_\text{ref}$ thermodynamisches Potential der Reaktion}
+        \eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
+    \end{formula}
+
+    \Subsubsection[
+        \eng{Mass transport}
+        \ger{Massentransport}
+    ]{mass}
+        \begin{formula}{concentration_overpotential}
+            \desc{Concentration overpotential}{Due to concentration gradient near the electrode, the ions need to \hyperref[f:ch:el:ion_cond:diffusion]{diffuse} to the electrode before reacting}{\ConstRef{universal_gas}, \QtyRef{temperature}, $\c_{0/\txS}$ ion concentration in the electrolyte / at the double layer, $z$ \qtyRef{charge_number}, \ConstRef{faraday}}
+            \desc[german]{Konzentrationsüberspannung}{Durch einen Konzentrationsgradienten an der Elektrode müssen Ionen erst zur Elektrode \hyperref[f:ch:el:ion_cond:diffusion]{diffundieren}, bevor sie reagieren können}{}
+            \eq{
+                \eta_\text{conc,anodic} &= -\frac{RT}{\alpha \,zF} \ln \left(\frac{c_\text{red}^0}{c_\text{red}^\txS}\right) \\
+                \eta_\text{conc,cathodic} &= -\frac{RT}{(1-\alpha) zF} \ln \left(\frac{c_\text{ox}^0}{c_\text{ox}^\txS}\right)
+            }
+        \end{formula}
+
+        \begin{formula}{diffusion_overpotential}
+            \desc{Diffusion overpotential}{Due to mass transport limitations}{$j_\infty$ \secEqRef{limiting_current}, $j_\text{meas}$ measured \qtyRef{current_density}, \ConstRef{universal_gas}, \QtyRef{temperature}, $n$ \qtyRef{charge_number}, \ConstRef{faraday}}
+            \desc[german]{Diffusionsüberspannung}{Durch Limit des Massentransports}{}
+            % \eq{\eta_\text{diff} = \frac{RT}{nF} \ln \left( \frac{\cfrac{c^\txs_\text{ox}}{c^0_\text{ox}}}{\cfrac{c^\txs_\text{red}}{c^0_\text{red}}} \right)}
+            \eq{\eta_\text{diff} = \frac{RT}{nF} \Ln{\frac{j_\infty}{j_\infty - j_\text{meas}}}}
+        \end{formula}
+
+        \begin{formula}{diffusion_layer}
+            \desc{Cell layers}{}{}
+            \desc[german]{Zellschichten}{}{}
+            \begin{tikzpicture}
+                \tikzset{
+                    label/.style={color=fg1,anchor=center,rotate=90},
+                }
+                \pgfmathsetmacro{\tkW}{8}               % Total width
+                \pgfmathsetmacro{\tkH}{4}               % Total height
+                \pgfmathsetmacro{\edW}{1}               % electrode width              
+                \pgfmathsetmacro{\hhW}{1}               % helmholtz width
+                \pgfmathsetmacro{\ndW}{2}               % nernst diffusion with
+                \pgfmathsetmacro{\eyW}{\tkW-\edW-\hhW-\ndW}     % electrolyte width
+                \pgfmathsetmacro{\edX}{0}               % electrode width              
+                \pgfmathsetmacro{\hhX}{\edW}            % helmholtz width
+                \pgfmathsetmacro{\ndX}{\edW+\hhW}       % nernst diffusion with
+                \pgfmathsetmacro{\eyX}{\tkW-\eyW}       % electrolyte width
+
+                \path[fill=bg-orange]        (\edX,0) rectangle (\edX+\edW,\tkH); \node[label] at (\edX+\edW/2,\tkH/2) {\GT{electrode}};
+                \path[fill=bg-green!90!bg0]  (\hhX,0) rectangle (\hhX+\hhW,\tkH); \node[label] at (\hhX+\hhW/2,\tkH/2) {\GT{helmholtz_layer}};
+                \path[fill=bg-green!60!bg0]  (\ndX,0) rectangle (\ndX+\ndW,\tkH); \node[label] at (\ndX+\ndW/2,\tkH/2) {\GT{nernst_layer}};
+                \path[fill=bg-green!20!bg0]  (\eyX,0) rectangle (\eyX+\eyW,\tkH); \node[label] at (\eyX+\eyW/2,\tkH/2) {\GT{electrolyte}};
+                \draw (\hhX,2) -- (\ndX,3) -- (\tkW,3);
+                % axes
+                \draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
+                \draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east]  {$c$};
+                \tkYTick{2}{$c^\txS$};
+                \tkYTick{3}{$c^0$};
+            \end{tikzpicture}
+        \end{formula}
+        \Eng[c_surface]{surface \qtyRef{concentration}}
+        \Eng[c_bulk]{bulk \qtyRef{concentration}}
+        \Ger[c_surface]{Oberflächen-\qtyRef{concentration}}
+        \Ger[c_bulk]{Bulk-\qtyRef{concentration}}
+
+
+        \begin{formula}{diffusion_layer_thickness}
+            \desc{Nerst Diffusion layer thickness}{}{$c^0$ \GT{c_bulk}, $c^\txS$ \GT{c_surface}}
+            \desc[german]{Dicke der Nernstschen Diffusionsschicht}{}{}
+            \eq{\delta_\txN = \frac{c^0 - c^\txS}{\odv{c}{x}_{x=0}}}
+        \end{formula}
+        
+        \begin{formula}{limiting_current}
+            \desc{(Limiting) current density}{}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \secEqRef{diffusion_layer_thickness}}
+            % \desc[german]{Limitierender Strom}{}{}
+            \eq{
+                \abs{j} &= nFD \frac{c^0-c^\txS}{\delta_\text{diff}}
+                \shortintertext{\GT{for} $c^\txS \to 0$}
+                \abs{j_\infty} &= nFD \frac{c^0}{\delta_\text{diff}}
+            }
+        \end{formula}
+
+        \begin{formula}{relation?}
+            \desc{Current - concentration relation}{}{$c^0$ \GT{c_bulk}, $c^\txS$ \GT{c_surface}, $j$ \secEqRef{limiting_current}}
+            \desc[german]{Strom - Konzentrationsbeziehung}{}{}
+            \eq{\frac{j}{j_\infty} = 1 - \frac{c^\txS}{c^0}}
+        \end{formula}
+
+        \begin{formula}{kinetic_current}
+            \desc{Kinetic current density}{}{$j_\text{meas}$ measured \qtyRef{current_density}, $j_\infty$ \secEqRef{limiting_current}}
+            \desc[german]{Kinetische Stromdichte}{}{$j_\text{meas}$ gemessene \qtyRef{current_density}, $j_\infty$ \secEqRef{limiting_current}}
+            \eq{j_\text{kin} = \frac{j_\text{meas} j_\infty}{j_\infty - j_\text{meas}}}
+        \end{formula}
+
+    \begin{formula}{roughness_factor}
+        \desc{Roughness factor}{Surface area related to electrode geometry}{}
+        \eq{\rfactor}
+    \end{formula}   
+
+    \begin{formula}{butler_volmer}
+        \desc{Butler-Volmer equation}{Reaction kinetics near the equilibrium potentential}
+        {$j$ \qtyRef{current_density}, $j_0$ exchange current density, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txC/\txA}$ cathodic/anodic charge transfer coefficient, $\text{rf}$ \secEqRef{roughness_factor}}
+        %Current through an electrode iof a unimolecular redox reaction with both anodic and cathodic reaction occuring on the same electrode
+        \desc[german]{Butler-Volmer-Gleichung}{Reaktionskinetik in der Nähe des Gleichgewichtspotentials}
+        {$j$ \qtyRef{current_density}, $j_0$ Austauschstromdichte, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txC/\txA}$ Ladungstransferkoeffizient an der Kathode/Anode, $\text{rf}$ \secEqRef{roughness_factor}}
+        \begin{gather}
+            j = j_0 \,\rfactor\, \left[ \Exp{\frac{(1-a_\txC) z F \eta}{RT}} - \Exp{-\frac{\alpha_\txC z F \eta}{RT}}\right]
+            \intertext{\GT{with}}
+            \alpha_\txA = 1 - \alpha_\txC
+        \end{gather}
+        \separateEntries
+        \fig{img/ch_butler_volmer.pdf}
+    \end{formula}
+
+    % \Subsubsection[
+    %     \eng{Tafel approximation}
+    %     \ger{Tafel Näherung}
+    % ]{tafel}
+
+    % \begin{formula}{slope}
+    %     \desc{Tafel slope}{}{}
+    %     \desc[german]{Tafel Steigung}{}{}
+    %     \eq{}
+    % \end{formula}
+
+    \begin{formula}{equation}
+        \desc{Tafel approximation}{For slow kinetics: $\abs{\eta} > \SI{0.1}{\volt}$}{}
+        \desc[german]{Tafel Näherung}{Für langsame Kinetik: $\abs{\eta} > \SI{0.1}{\volt}$}{}
+        \eq{
+            \Log{j} &\approx \Log{j_0} + \frac{\alpha_\txC zF \eta}{RT\ln(10)} && \eta \gg \SI{0.1}{\volt}\\
+            \Log{\abs{j}} &\approx \Log{j_0} - \frac{(1-\alpha_\txC) zF \eta}{RT\ln(10)} && \eta \ll -\SI{0.1}{\volt}
+        }
+        \fig{img/ch_tafel.pdf}
+    \end{formula}
+
+
+
+\Subsection[
+    \eng{Techniques}
+    \ger{Techniken}
+]{tech}
+
+    \Subsubsection[
+        \eng{Reference electrodes}
+        \ger{Referenzelektroden}
+    ]{ref}
+        \begin{ttext}
+            \eng{Defined as reference for measuring half-cell potententials}
+            \ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
+        \end{ttext}
+
+        \begin{formula}{she}
+            \desc{Standard hydrogen elektrode (SHE)}{}{$p=\SI{e5}{\pascal}$, $a_{\ce{H+}}=\SI{1}{\mol\per\litre}$ (\Rightarrow $\pH=0$)}
+            \desc[german]{Standardwasserstoffelektrode (SHE)}{}{}
+            \ttxt{
+                \eng{Potential of the reaction: \ce{2H^+ +2e^- <--> H2}}
+                \ger{Potential der Reaktion: \ce{2H^+ +2e^- <--> H2}}
+            }
+        \end{formula}
+
+        \begin{formula}{rhe}
+            \desc{Reversible hydrogen electrode (RHE)}{RHE Potential does not change with the pH value}{$E^0\equiv \SI{0}{\volt}$, \QtyRef{activity}, \QtyRef{pressure}, \GT{see} \fqEqRef{ch:el:cell:nernst_equation}}
+            \desc[german]{Reversible Wasserstoffelektrode (RHE)}{Potential ändert sich nicht mit dem pH-Wert}{}
+            \eq{
+                E_\text{RHE} &= E^0 + \frac{RT}{F} \Ln{\frac{a_{\ce{H^+}}}{p_{\ce{H2}}}} \\
+                             &= \SI{0}{\volt} - \SI{0.059}{\volt}
+            }
+        \end{formula}
+    
+    
+
+    \Subsubsection[
+        \eng{Cyclic voltammetry}
+        \ger{Zyklische Voltammetrie}
+    ]{cv}
+        \begin{bigformula}{duck}
+            \desc{Cyclic voltammogram}{}{}
+            % \desc[german]{}{}{}
+
+            \begin{minipage}{0.44\textwidth}
+                
+                \begin{tikzpicture}
+                    \pgfmathsetmacro{\Ax}{-2.3}
+                    \pgfmathsetmacro{\Ay}{ 0.0}
+                    \pgfmathsetmacro{\Bx}{ 0.0}
+                    \pgfmathsetmacro{\By}{ 1.0}
+                    \pgfmathsetmacro{\Cx}{ 0.4}
+                    \pgfmathsetmacro{\Cy}{ 1.5}
+                    \pgfmathsetmacro{\Dx}{ 2.0}
+                    \pgfmathsetmacro{\Dy}{ 0.5}
+                    \pgfmathsetmacro{\Ex}{ 0.0}
+                    \pgfmathsetmacro{\Ey}{-1.5}
+                    \pgfmathsetmacro{\Fx}{-0.4}
+                    \pgfmathsetmacro{\Fy}{-2.0}
+                    \pgfmathsetmacro{\Gx}{-2.3}
+                    \pgfmathsetmacro{\Gy}{-0.3}
+                    \pgfmathsetmacro{\x}{3}
+                    \pgfmathsetmacro{\y}{3}
+                    \begin{axis}[ymin=-\y,ymax=\y,xmax=\x,xmin=-\x,
+                        % equal axis,
+                        minor tick num=1,
+                        xlabel={$E$}, xlabel style={at={(axis description cs:0.5,-0.06)}},
+                        ylabel={$j$}, ylabel style={at={(axis description cs:-0.06,0.5)}},
+                        anchor=center, at={(0,0)},
+                        axis equal image,clip=false,
+                    ]
+                        % CV with beziers
+                        \draw[thick, fg-blue]                                                       (axis cs:\Ax,\Ay) coordinate (A) node[left]  {A}
+                            ..controls (axis cs:\Ax+1.8, \Ay+0.0) and (axis cs:\Bx-0.2, \By-0.4) .. (axis cs:\Bx,\By) coordinate (B) node[left]  {B}
+                            ..controls (axis cs:\Bx+0.1, \By+0.2) and (axis cs:\Cx-0.3, \Cy+0.0) .. (axis cs:\Cx,\Cy) coordinate (C) node[above] {C}
+                            ..controls (axis cs:\Cx+0.5, \Cy+0.0) and (axis cs:\Dx-1.3, \Dy+0.1) .. (axis cs:\Dx,\Dy) coordinate (D) node[right] {D}
+                            ..controls (axis cs:\Dx-2.0, \Dy-0.1) and (axis cs:\Ex+0.3, \Ey+0.8) .. (axis cs:\Ex,\Ey) coordinate (E) node[right] {E}
+                            ..controls (axis cs:\Ex-0.1, \Ey-0.2) and (axis cs:\Fx+0.2, \Fy+0.0) .. (axis cs:\Fx,\Fy) coordinate (F) node[below] {F}
+                            ..controls (axis cs:\Fx-0.2, \Fy+0.0) and (axis cs:\Gx+1.5, \Gy-0.2) .. (axis cs:\Gx,\Gy) coordinate (G) node[left]  {G};
+                        \node[above] at (A) {\rightarrow};
+
+                        \draw[dashed, fg2] (axis cs: \Bx,\By) -- (axis cs: \Ex, \Ey);
+
+                        \draw[->] (axis cs:-\x-0.6, 0.4) -- (axis cs:-\x-0.6, \y) node[left=0.3cm, anchor=east, rotate=90] {Cath / Red};
+                        \draw[->] (axis cs:-\x-0.6,-0.4) -- (axis cs:-\x-0.6,-\y) node[left=0.3cm, anchor=west, rotate=90] {An / Ox};
+                    \end{axis}
+                \end{tikzpicture}
+            \end{minipage}
+            \begin{minipage}{0.55\textwidth}
+                \begin{ttext}
+                    \eng{\begin{itemize}
+                        \item {\color{fg-blue}A-D}: Diffusion layer growth \rightarrow decreased current after peak
+                        \item {\color{fg-blue}D}: Switching potential
+                        \item {\color{fg-blue}B,E}: Equal concentrations of reactants
+                        \item {\color{fg-blue}C,F}: Formal potential of redox pair: $E \approx \frac{E_\txC - E_\txF}{2}$
+                        \item {\color{fg-blue}C,F}: Peak separation for reverisble processes: $\Delta E_\text{rev} = E_\txC - E_\txF = n\,\SI{59}{\milli\volt}$
+                        \item Information about surface chemistry
+                        \item Double-layer capacity (horizontal lines): $I = C v$
+                    \end{itemize}}
+                \end{ttext}
+            \end{minipage}
+        \end{bigformula}
+
+        \begin{formula}{peak_current}
+            \desc{Randles-Sevcik equation}{For reversible reaction.\\Peak current depends on square root of the scan rate}{$n$ \qtyRef{charge_number}, \ConstRef{faraday}, $A$ electrode surface area, $c^0$ bulk \qtyRef{concentration}, $v$ \qtyRef{scan_rate}, $D_\text{ox}$ \qtyRef{diffusion_coefficient} of oxidized analyte, \ConstRef{universal_gas}, \QtyRef{temperature}}
+            \desc[german]{Randles-Sevcik Gleichung}{Spitzenstrom}{}
+            \eq{i_\text{peak} = 0.446\,nFAc^0 \sqrt{\frac{nFvD_\text{ox}}{RT}}}
+        \end{formula}
+
+        \begin{hiddenformula}{scan_rate}
+            \desc{Scan rate}{}{}
+            \desc[german]{Scanrate}{}{}
+            \quantity{v}{\volt\per\s}{s}
+        \end{hiddenformula}
+        
+
+        \begin{formula}{upd}
+            \desc{Underpotential deposition (UPD)}{}{}
+            \desc[german]{}{}{}
+            \ttxt{Reversible deposition of metal onto a foreign metal electrode at potentials positive of the Nernst potential \TODO{clarify}}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Rotating disk electrodes}
+        % \ger{}
+    ]{rde} \abbrLink{rde}{RDE}
+        \begin{formula}{viscosity}
+            \desc{Dynamic viscosity}{}{}
+            \desc[german]{Dynamisch Viskosität}{}{}
+            \quantity{\eta,\mu}{\pascal\s=\newton\s\per\m^2=\kg\per\m\s}{}
+        \end{formula}
+
+        \begin{formula}{kinematic_viscosity}
+            \desc{Kinematic viscosity}{\qtyRef{viscosity} related to density of a fluid}{\QtyRef{viscosity}, \QtyRef{density}}
+            \desc[german]{Kinematische Viskosität}{\qtyRef{viscosity} im Verhältnis zur Dichte der Flüssigkeit}{}
+            \quantity{\nu}{\cm^2\per\s}{}
+            \eq{\nu = \frac{\eta}{\rho}}
+        \end{formula}
+
+        \begin{formula}{diffusion_layer_thickness}
+            \desc{Diffusion layer thickness}{\TODO{Where does 1.61 come from}}{$D$ \qtyRef{diffusion_coefficient}, $\nu$ \qtyRef{kinematic_viscosity}, \QtyRef{angular_frequency}}
+            \desc[german]{Diffusionsshichtdicke}{}{}
+            \eq{\delta_\text{diff}= 1.61 D{^\frac{1}{3}} \nu^{\frac{1}{6}} \omega^{-\frac{1}{2}}}
+        \end{formula}
+
+        \begin{formula}{limiting_current}
+            \desc{Limiting current density}{for a \abbrRef{rde}}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \secEqRef{diffusion_layer_thickness}, $\nu$ \qtyRef{kinematic_viscosity}, \QtyRef{angular_frequency}}
+            % \desc[german]{Limitierender Strom}{}{}
+            \eq{j_\infty = nFD \frac{c^0}{\delta_\text{diff}} = \frac{1}{1.61} nFD^{\frac{2}{3}}  v^{\frac{-1}{6}} c^0 \sqrt{\omega}}
+        \end{formula}
+
+

src/ch/misc.tex

@@ -0,0 +1,115 @@
+\Section[
+    \eng{Thermoelectricity}
+    \ger{Thermoelektrizität}
+]{thermo}
+    \begin{formula}{seebeck}
+        \desc{Seebeck coefficient}{}{$V$ voltage, \QtyRef{temperature}}
+        \desc[german]{Seebeck-Koeffizient}{}{}
+        \quantity{S}{\micro\volt\per\kelvin}{s}
+        \eq{S = -\frac{\Delta V}{\Delta T}}
+    \end{formula}
+    \begin{formula}{seebeck_effect}
+        \desc{Seebeck effect}{Elecromotive force across two points of a material with a temperature difference}{\QtyRef{conductivity}, $V$ local voltage, \QtyRef{seebeck}, \QtyRef{temperature}}
+        \desc[german]{Seebeck-Effekt}{}{}
+        \eq{\vec{j} = \sigma(-\Grad V - S \Grad T)}
+    \end{formula}
+
+    \begin{formula}{thermal_conductivity}
+        \desc{Thermal conductivity}{Conduction of heat, without mass transport}{\QtyRef{heat}, \QtyRef{length}, \QtyRef{area}, \QtyRef{temperature}}
+        \desc[german]{Wärmeleitfähigkeit}{Leitung von Wärme, ohne Stofftransport}{}
+        \quantity{\kappa,\lambda,k}{\watt\per\m\K=\kg\m\per\s^3\kelvin}{s}
+        \eq{\kappa = \frac{\dot{Q} l}{A\,\Delta T}}
+        \eq{\kappa_\text{tot} = \kappa_\text{lattice} + \kappa_\text{electric}}
+    \end{formula}
+
+    \begin{formula}{wiedemann-franz}
+        \desc{Wiedemann-Franz law}{}{Electric \QtyRef{thermal_conductivity}, $L$ in \si{\watt\ohm\per\kelvin} Lorentz number, \QtyRef{conductivity}}
+        \desc[german]{Wiedemann-Franz Gesetz}{}{Elektrische \QtyRef{thermal_conductivity}, $L$ in \si{\watt\ohm\per\kelvin} Lorentzzahl, \QtyRef{conductivity}}
+        \eq{\kappa = L\sigma T}
+    \end{formula}
+
+    \begin{formula}{zt}
+        \desc{Thermoelectric figure of merit}{Dimensionless quantity for comparing different materials}{\QtyRef{seebeck}, \QtyRef{conductivity}, }
+        \desc[german]{Thermoelektrische Gütezahl}{Dimensionsoser Wert zum Vergleichen von Materialien}{}
+        \eq{zT = \frac{S^2\sigma}{\lambda} T}
+    \end{formula}
+
+
+\Section[
+    \eng{misc}
+    \ger{misc}
+]{misc}
+
+    % TODO: hide
+    \begin{formula}{stoichiometric_coefficient}
+        \desc{Stoichiometric coefficient}{}{}
+        \desc[german]{Stöchiometrischer Koeffizient}{}{}
+        \quantity{\nu}{}{s}
+    \end{formula}
+
+    \begin{formula}{std_condition}
+        \desc{Standard temperature and pressure}{}{}
+        \desc[german]{Standardbedingungen}{}{}
+        \eq{
+            T &= \SI{273.15}{\kelvin} = \SI{0}{\celsius} \\
+            p &= \SI{100000}{\pascal} = \SI{1.000}{\bar}
+        }
+    \end{formula}
+    \begin{formula}{ph}
+        \desc{pH definition}{}{$a_{\ce{H+}}$ hyrdrogen ion \qtyRef{activity}}
+        \desc[german]{pH-Wert definition}{}{$a_{\ce{H+}}$ Wasserstoffionen-\qtyRef{activity}}
+        \eq{\pH = -\log_{10}(a_{\ce{H+}})}
+    \end{formula}
+
+    \begin{formula}{ph_rt}
+        \desc{pH}{At room temperature \SI{25}{\celsius}}{}
+        \desc[german]{pH-Wert}{Bei Raumtemperatur \SI{25}{\celsius}}{}
+        \eq{
+            \pH > 7 &\quad\tGT{basic} \\
+            \pH < 7 &\quad\tGT{acidic} \\
+            \pH = 7 &\quad\tGT{neutral}
+        }
+    \end{formula}
+
+    \begin{formula}{covalent_bond}
+        \desc{Covalent bond}{}{}
+        \desc[german]{Kolvalente Bindung}{}{}
+        \ttxt{
+            \eng{Bonds that involve sharing of electrons to form electron pairs between atoms.}
+            \ger{Bindungen zwischen Atomen die durch geteilte Elektronen, welche Elektronenpaare bilden, gebildet werden.}
+        }
+    \end{formula}
+
+    \begin{formula}{grotthuss}
+        \desc{Grotthuß-mechanism}{}{}
+        \desc[german]{Grotthuß-Mechanismus}{}{}
+        \ttxt{
+            \eng{The mobility of protons in aqueous solutions is much higher than that of other ions because they can "move" by breaking and reforming covalent bonds of water molecules.}
+            \ger{The Moblilität von Protononen in wässrigen Lösungen ist wesentlich größer als die anderer Ionen, da sie sich "bewegen" können indem die Wassertsoffbrückenbindungen gelöst und neu gebildet werden.}
+        }
+    \end{formula}
+
+
+    \begin{formula}{common_chemicals}
+        \desc{Common chemicals}{}{}
+        \desc[german]{Häufige Chemikalien}{}{}
+        \begin{tabular}{l|c}
+            \GT{name}                                                                                           & \GT{formula} \\ \hline\hline
+            \begin{ttext}[cyanide]\eng{Cyanide}\ger{Zyanid}\end{ttext}                                          & \ce{CN} \\ \hline
+            \begin{ttext}[ammonia]\eng{Ammonia}\ger{Ammoniak}\end{ttext}                                        & \ce{NH3} \\ \hline
+            \begin{ttext}[hydrogen peroxide]\eng{Hydrogen Peroxide}\ger{Wasserstoffperoxid}\end{ttext}          & \ce{H2O2} \\ \hline
+            \begin{ttext}[sulfuric acid]\eng{Sulfuric Acid}\ger{Schwefelsäure}\end{ttext}                       & \ce{H2SO4} \\ \hline
+            \begin{ttext}[ethanol]\eng{Ethanol}\ger{Ethanol}\end{ttext}                                         & \ce{C2H5OH} \\ \hline
+            \begin{ttext}[acetic acid]\eng{Acetic Acid}\ger{Essigsäure}\end{ttext}                              & \ce{CH3COOH} \\ \hline
+            \begin{ttext}[methane]\eng{Methane}\ger{Methan}\end{ttext}                                          & \ce{CH4} \\ \hline
+            \begin{ttext}[hydrochloric acid]\eng{Hydrochloric Acid}\ger{Salzsäure}\end{ttext}                   & \ce{HCl} \\ \hline
+            \begin{ttext}[sodium hydroxide]\eng{Sodium Hydroxide}\ger{Natriumhydroxid}\end{ttext}               & \ce{NaOH} \\ \hline
+            \begin{ttext}[nitric acid]\eng{Nitric Acid}\ger{Salpetersäure}\end{ttext}                           & \ce{HNO3} \\ \hline
+            \begin{ttext}[calcium carbonate]\eng{Calcium Carbonate}\ger{Calciumcarbonat}\end{ttext}             & \ce{CaCO3} \\ \hline
+            \begin{ttext}[glucose]\eng{Glucose}\ger{Glukose}\end{ttext}                                         & \ce{C6H12O6} \\ \hline
+            \begin{ttext}[benzene]\eng{Benzene}\ger{Benzol}\end{ttext}                                          & \ce{C6H6} \\ \hline
+            \begin{ttext}[acetone]\eng{Acetone}\ger{Aceton}\end{ttext}                                          & \ce{C3H6O} \\ \hline
+            \begin{ttext}[ethylene]\eng{Ethylene}\ger{Ethylen}\end{ttext}                                       & \ce{C2H4} \\ \hline
+            \begin{ttext}[potassium permanganate]\eng{Potassium Permanganate}\ger{Kaliumpermanganat}\end{ttext} & \ce{KMnO4} \\ \hline
+        \end{tabular}
+    \end{formula}

src/cm/charge_transport.tex

@@ -0,0 +1,95 @@
+\Section[
+    \eng{Charge transport}
+    \ger{Ladungstransport}
+]{charge_transport}
+\Subsection[
+    \eng{Drude model}
+    \ger{Drude-Modell}
+]{drude}
+    \begin{ttext}
+        \eng{Classical model describing the transport properties of electrons in materials (metals):
+            The material is assumed to be an ion lattice and with freely moving electrons (electron gas). The electrons are 
+            accelerated by an electric field and decelerated through collisions with the lattice ions.
+            The model disregards the Fermi-Dirac partition of the conducting electrons.
+        }
+        \ger{Ein klassisches Model zur Beschreibung der Transporteigenschaften von Elektronen in (v.a.) Metallen:
+            Der Festkörper wird als Ionenkristall mit frei beweglichen Elektronen (Elektronengas). 
+            Die Elektronen werden durch ein Elektrisches Feld $E$ beschleunigt und durch Stöße mit den Gitterionen gebremst.
+            Das Modell vernachlässigt die Fermi-Dirac Verteilung der Leitungselektronen.
+        }
+    \end{ttext}
+    \begin{formula}{motion}
+        \desc{Equation of motion}{}{$v$ electron speed, $\vec{v}_\text{D}$ drift velocity, $\tau$ mean free time between collisions}
+        \desc[german]{Bewegungsgleichung}{}{$v$ Elektronengeschwindigkeit, $\vec{v}_\text{D}$ Driftgeschwindigkeit, $\tau$ Stoßzeit}
+        \eq{\masse \odv{\vec{v}}{t} + \frac{\masse}{\tau} \vec{v}_\text{D} = -e \vec{\E}}
+    \end{formula}
+    \begin{formula}{scattering_time}
+        \desc{Scattering time}{Momentum relaxation time}{}
+        \desc[german]{Streuzeit}{}{}
+        \quantity{\tau}{\s}{s}
+        \ttxt{
+            \eng{$\tau$\\ the average time between scattering events weighted by the characteristic momentum change cause by the scattering process.}
+        }
+    \end{formula}
+    \begin{formula}{current_density}
+        \desc{Current density}{Ohm's law}{$n$ charge particle density}
+        \desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte}
+        \quantity{\vec{j}}{\ampere\per\m^2}{v}
+        \eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{\E}}
+    \end{formula}
+    \begin{formula}{conductivity}
+        \desc{Drude-conductivity}{}{}
+        \desc[german]{Drude-Leitfähigkeit}{}{}
+        \eq{\sigma = \frac{\vec{j}}{\vec{\E}} = \frac{e^2 \tau n}{\masse} = n e \mu}
+    \end{formula}
+
+\Subsection[
+    \eng{Sommerfeld model}
+    \ger{Sommerfeld-Modell}
+]{sommerfeld}
+    \begin{ttext}
+        \eng{Assumes a gas of free fermions underlying the pauli-exclusion principle. Only electrons in an energy range of $\kB T$ around the Fermi energy $\EFermi$ participate in scattering processes.}
+        \ger{Annahme eines freien Fermionengases, welches dem Pauli-Prinzip unterliegt. Nur Elektronen in einem Energiebereich von $\kB T$ um die Fermi Energe $\EFermi$ nehmen an Streuprozessen teil.}
+    \end{ttext}
+    \begin{formula}{current_density}
+        \desc{Electrical current density}{}{}
+        \desc[german]{Elektrische Stromdichte}{}{}
+        \eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
+    \end{formula}
+    \TODO{The formula for the conductivity is the same as in the drude model?}
+
+\Subsection[
+    \eng{Boltzmann-transport}
+    \ger{Boltzmann-Transport}
+]{boltzmann}
+    \begin{ttext}
+        \eng{Semiclassical description using a probability distribution (\fqEqRef{stat:todo:fermi_dirac}) to describe the particles.}
+        \ger{Semiklassische Beschreibung, benutzt eine Wahrscheinlichkeitsverteilung (\fqEqRef{stat:todo:fermi_dirac}).}
+    \end{ttext}
+    \begin{formula}{boltzmann_transport}
+        \desc{Boltzmann Transport equation}{for charge transport}{$f$ \ref{stat:todo:fermi-dirac}}
+        \desc[german]{Boltzmann-Transportgleichung}{für Ladungstransport}{}
+        \eq{
+            \pdv{f(\vec{r},\vec{k},t)}{t} = -\vec{v} \cdot \Grad_{\vec{r}} f - \frac{e}{\hbar}(\vec{\mathcal{E}} + \vec{v} \times \vec{B}) \cdot \Grad_{\vec{k}} f + \left(\pdv{f(\vec{r},\vec{k},t)}{t}\right)_{\text{\GT{scatter}}}
+        }
+    \end{formula}
+
+\Subsection[
+    \eng{misc}
+    \ger{misc}
+    ]{misc}
+    \begin{formula}{tsu_esaki}
+        \desc{Tsu-Esaki tunneling current}{Describes the current $I_{\txL \leftrightarrow \txR}$ through a barrier}{$\mu_i$ \qtyRef{chemical_pot} at left/right side, $U_i$ voltage on left/right side. Electrons occupy region between $U_i$ and $\mu_i$}
+        \desc[german]{Tsu-Esaki Tunnelstrom}{Beschreibt den Strom $I_{\txL \leftrightarrow \txR}$ durch eine Barriere }{$\mu_i$ \qtyRef{chemical_pot} links/rechts, $U_i$ Spannung links/rechts. Elektronen besetzen Bereich zwischen $U_i$ und $\mu_i$}
+        \eq{
+            I_\text{T} = \frac{2e}{h} \int_{U_\txL}^\infty \left(f(E, \mu_\txL) -f(E, \mu_\txR)\right) T(E) \d E
+        }
+    \end{formula}
+
+    \begin{formula}{continuity}
+        \desc{Charge continuity equation}{Electric charge can only change by the amount of electric current}{\QtyRef{charge_density}, \QtyRef{current_density}}
+        \desc[german]{Kontinuitätsgleichung der Ladung}{Elektrische Ladung kann sich nur durch die Stärke des Stromes ändern}{}
+        \eq{
+            \pdv{\rho}{t} = - \nabla \vec{j}
+        }
+    \end{formula}

src/cm/cm.tex

@@ -0,0 +1,60 @@
+\Part[
+    \eng{Condensed matter physics}
+    \ger{Festkörperphysik}
+]{cm}
+    \TODO{Bonds, hybridized orbitals}
+    \TODO{Lattice vibrations, van hove singularities, debye frequency}
+
+    \begin{formula}{dos}
+        \desc{Density of states (DOS)}{}{\QtyRef{volume}, $N$ number of energy levels, \QtyRef{energy}}
+        \desc[german]{Zustandsdichte (DOS)}{}{\QtyRef{volume}, $N$ Anzahl der Energieniveaus, \QtyRef{energy}}
+        \eq{D(E) = \frac{1}{V}\sum_{i=1}^{N} \delta(E-E(\vec{k_i}))}
+    \end{formula}
+    \begin{formula}{dos_parabolic}
+        \desc{Density of states for parabolic dispersion}{Applies to \fqSecRef{cm:egas}}{}
+        \desc[german]{Zustandsdichte für parabolische Dispersion}{Bei \fqSecRef{cm:egas}}{}
+        \eq{
+            D_1(E) &= \frac{1}{2\sqrt{c_k(E-E_0)}}  && (\text{1D}) \\
+            D_2(E) &= \frac{\pi}{2c_k}              && (\text{2D}) \\
+            D_3(E) &= \pi \sqrt{\frac{E-E_0}{c_k^3}}&& (\text{3D})
+        }
+    \end{formula}
+
+    \Section[
+        \eng{Lattice vibrations}
+        \ger{Gitterschwingungen}
+    ]{vib}
+
+        \begin{formula}{dispersion_1atom_basis}
+            \desc{Phonon dispersion of a lattice with a one-atom basis}{same as the dispersion of a linear chain}{$C_n$ force constants between layer $s$ and $s+n$, $M$ \qtyRef{mass} of the reference atom, $a$ \qtyRef{lattice_constant}, $q$ phonon \qtyRef{wavevector}, $u$ Ansatz for the atom displacement}
+            \desc[german]{Phonondispersion eines Gitters mit zweiatomiger Basis}{gleich der Dispersion einer linearen Kette}{$C_n$ Kraftkonstanten zwischen Ebene $s$ und $s+n$, $M$ \qtyRef{mass} des Referenzatoms, $a$ \qtyRef{lattice_constant}, $q$ Phonon \qtyRef{wavevector}, $u$ Ansatz für die Atomauslenkung}
+            \eq{
+                \omega^2 = \frac{4C_1}{M}\left[\sin^2 \left(\frac{qa}{2}\right) + \frac{C2}{C1} \sin^2(qa)\right] \\
+                \intertext{\GT{with}}
+                u_{s+n} = U\e^{-i \left[\omega t - q(s+n)a \right]}
+            }
+            \fig{img/cm_phonon_dispersion_one_atom_basis.pdf}
+        \end{formula}
+        \TODO{Plots}
+        \begin{formula}{dispersion_2atom_basis}
+            \desc{Phonon dispersion of a lattice with a two-atom basis}{}{$C$ force constant between layers, $M_i$ \qtyRef{mass} of the basis atoms, $a$ \qtyRef{lattice_constant}, $q$ phonon \qtyRef{wavevector}, $u, v$ Ansatz for the displacement of basis atom 1 and 2, respectively}
+            \desc[german]{Phonondispersion eines Gitters mit einatomiger Basis}{}{$C$ Kraftkonstanten zwischen Ebene $s$ und $s+n$, $M_i$ \qtyRef{mass} der Basisatome, $a$ \qtyRef{lattice_constant}, $q$ Phonon \qtyRef{wavevector}, $u, v$ jeweils Ansatz für die Atomauslenkung des Basisatoms 1 und 2}
+            \eq{
+                \omega^2_{\txa,\txo} = C \left(\frac{1}{M_1}+\frac{1}{M_2}\right) \mp C \sqrt{\left(\frac{1}{M_1}+\frac{1}{M_2}\right)^2 - \frac{4}{M_1M_2} \sin^2 \left(\frac{qa}{2}\right)}
+                \intertext{\GT{with}}
+                u_{s} = U\e^{-i \left(\omega t - qsa \right)}, \quad
+                v_{s} = V\e^{-i \left(\omega t - qsa \right)}
+            }
+            \fig{img/cm_phonon_dispersion_two_atom_basis.pdf}
+        \end{formula}
+
+        \Subsection[
+            \eng{Debye model}
+            \ger{Debye-Modell}
+            ]{debye}
+            \begin{ttext}
+                \eng{Atoms behave like coupled \hyperref[sec:qm:hosc]{quantum harmonic oscillators}. The finite sample size leads to periodic boundary conditio. The finite sample size leads to periodic boundary conditions for the vibrations.}
+                \ger{Atome verhalten sich wie gekoppelte \hyperref[sec:qm:hosc]{quantenmechanische harmonische Oszillatoren}. Die endliche Ausdehnung des Körpers führt zu periodischen Randbedingungen. }
+            \end{ttext}
+
+

src/cm/crystal.tex

@@ -0,0 +1,182 @@
+\Section[
+    \eng{Crystals}
+    \ger{Kristalle}
+]{crystal}
+\Subsection[
+    \eng{Bravais lattice}
+    \ger{Bravais-Gitter}
+]{bravais}
+
+
+    \Eng[lattice_system]{Lattice system}
+    \Ger[lattice_system]{Gittersystem}
+    \Eng[crystal_family]{Crystal system}
+    \Ger[crystal_family]{Kristall-system}
+    \Eng[point_group]{Point group}
+    \Ger[point_group]{Punktgruppe}
+    \eng[bravais_lattices]{Bravais lattices}
+    \ger[bravais_lattices]{Bravais Gitter}
+
+    \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
+    \renewcommand\tabularxcolumn[1]{m{#1}}
+    \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
+
+    \begin{bigformula}{2d}
+        \desc{2D}{In 2D, there are 5 different Bravais lattices}{}
+        \desc[german]{2D}{In 2D gibt es 5 verschiedene Bravais-Gitter}{}
+        \begin{adjustbox}{width=\textwidth}
+            \begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
+                \hline
+                \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
+                                                     & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
+                \GT{monoclinic} (m) & $\text{C}_\text{2}$   & \bvimg{mp} & \\ \hline
+                \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
+                \GT{tetragonal} (t) & $\text{D}_\text{4}$   & \bvimg{tp} & \\ \hline
+                \GT{hexagonal} (h) & $\text{D}_\text{6}$    & \bvimg{hp} & \\ \hline
+            \end{tabularx}
+        \end{adjustbox}
+    \end{bigformula}
+    
+
+    \begin{bigformula}{3d}
+        \desc{3D}{In 3D, there are 14 different Bravais lattices}{}
+        \desc[german]{3D}{In 3D gibt es 14 verschiedene Bravais-Gitter}{}
+        % \newcolumntype{g}{>{\columncolor[]{0.8}}}
+        \begin{adjustbox}{width=\textwidth}
+            \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
+                \hline
+                \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
+                                                     & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
+                \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP}  &  &  &  \\  \hline
+                \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS}  &  &  \\ \hline
+                \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
+                \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} &  & \bvimg{tI} & \\ \hline
+                \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} &  &  & \\ \cline{2-7}
+                 & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} &  &  & \\ \hline
+                \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} &  & \bvimg{cI} & \bvimg{cF} \\ \hline
+            \end{tabularx}
+        \end{adjustbox}
+    \end{bigformula}
+
+    \begin{formula}{lattice_constant}
+        \desc{Lattice constant}{Parameter (length or angle) describing the smallest unit cell}{}
+        \desc[german]{Gitterkonstante}{Parameter (Länge oder Winkel) der die Einheitszelle beschreibt}{}
+        \quantity{a}{}{s}
+    \end{formula}
+
+    \begin{formula}{lattice_vector}
+        \desc{Lattice vector}{}{$n_i \in \Z$}
+        \desc[german]{Gittervektor}{}{}
+        \quantity{\vec{R}}{}{\angstrom}
+        \eq{\vec{R} = n_1 \vec{a_1} + n_2 \vec{a_2} + n_3 \vec{a_3}}
+    \end{formula}
+
+    \TODO{primitive unit cell: contains one lattice point}\\
+    \begin{formula}{miller}
+        \desc{Miller index}{}{Miller family: planes that are equivalent due to crystal symmetry}
+        \desc[german]{Millersche Indizes}{}{}
+        \eq{
+            (hkl) & \text{\GT{plane}}\\
+            [hkl] & \text{\GT{direction}}\\
+            \{hkl\} & \text{\GT{millerFamily}}
+        }
+    \end{formula}
+    
+
+\Subsection[
+    \eng{Reciprocal lattice}
+    \ger{Reziprokes Gitter}
+]{reci}
+    \begin{ttext}
+        \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
+        \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
+    \end{ttext}
+
+    \begin{formula}{vectors}
+        \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
+        \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
+        \eq{
+            \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
+            \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
+            \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
+        }
+    \end{formula}
+    \begin{formula}{reciprocal_lattice_vector}
+        \desc{Reciprokal attice vector}{}{$n_i \in \Z$}
+        \desc[german]{Reziproker Gittervektor}{}{}
+        \quantity{\vec{G}}{}{\angstrom}
+        \eq{\vec{G}_{{hkl}} = h \vec{b_1} + k \vec{b_2} + l \vec{b_3}}
+    \end{formula}
+
+    \Subsection[
+        \eng{Scattering processes}
+        \ger{Streuprozesse}
+    ]{scatter}
+        \begin{formula}{matthiessen}
+            \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{\QtyRef{mobility}, \QtyRef{scattering_time}}
+            \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{}
+            \eq{
+                \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
+                \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
+            }
+        \end{formula}
+
+\Subsection[
+    \eng{Lattices}
+    \ger{Gitter}
+]{lat}
+    \begin{formula}{sc}
+        \desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}}
+        \desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{}
+        \eq{
+            \vec{a}_{1}=a \begin{pmatrix} 1\\0\\0 \end{pmatrix},\, 
+            \vec{a}_{2}=a \begin{pmatrix} 0\\1\\0 \end{pmatrix},\, 
+            \vec{a}_{3}=a \begin{pmatrix} 0\\0\\1 \end{pmatrix} 
+        }
+    \end{formula}
+    \begin{formula}{bcc}
+        \desc{Body centered cubic (BCC)}{Reciprocal: \fqEqRef{cm:bravais:fcc}}{\QtyRef{lattice_constant}}
+        \desc[german]{Kubisch raumzentriert (BCC)}{Reziprok: \fqEqRef{cm:bravais:fcc}}{}
+        \eq{
+            \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} -1\\1\\1 \end{pmatrix},\, 
+            \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\-1\\1 \end{pmatrix},\, 
+            \vec{a}_{3}=\frac{a}{2} \begin{pmatrix} 1\\1\\-1 \end{pmatrix} 
+        }
+    \end{formula}
+
+    \begin{formula}{fcc}
+        \desc{Face centered cubic (FCC)}{Reciprocal: \fqEqRef{cm:bravais:bcc}}{\QtyRef{lattice_constant}}
+        \desc[german]{Kubisch flächenzentriert (FCC)}{Reziprok: \fqEqRef{cm:bravais:bcc}}{}
+        \eq{
+            \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} 0\\1\\1 \end{pmatrix},\,
+            \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\0\\1 \end{pmatrix},\, 
+            \vec{a}_{3}=\frac{a}{2} \begin{pmatrix} 1\\1\\0 \end{pmatrix}
+        }
+    \end{formula}
+
+    \begin{formula}{diamond}
+        \desc{Diamond lattice}{}{}
+        \desc[german]{Diamantstruktur}{}{}
+        \ttxt{
+            \eng{\fqEqRef{cm:bravais:fcc} with basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ and $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$}
+            \ger{\fqEqRef{cm:bravais:fcc} mit Basis  $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ und $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$}
+        }
+    \end{formula}
+    \begin{formula}{zincblende}
+        \desc{Zincblende lattice}{}{}
+        \desc[german]{Zinkblende-Struktur}{}{}
+        \ttxt{
+            \includegraphics[width=0.5\textwidth]{img/cm_zincblende.png}
+            \eng{Like \fqEqRef{cm:bravais:diamond} but with different species on each basis}
+            \ger{Wie  \fqEqRef{cm:bravais:diamond} aber mit unterschiedlichen Spezies auf den Basen}
+        }
+    \end{formula}
+    \begin{formula}{wurtzite}
+        \desc{Wurtzite structure}{hP4}{}
+        \desc[german]{Wurtzite-Struktur}{hP4}{}
+        \ttxt{
+            \includegraphics[width=0.5\textwidth]{img/cm_wurtzite.png}
+            Placeholder
+        }
+    \end{formula}
+

src/cm/egas.tex

@@ -0,0 +1,72 @@
+\Section[
+    \eng{Free electron gas}
+    \ger{Freies Elektronengase}
+]{egas}
+\begin{ttext}
+    \eng{Assumptions: electrons can move freely and independent of each other.}
+    \ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.}
+\end{ttext}
+
+\begin{formula}{drift_velocity}
+    \desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity}
+    \desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit}
+    \eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}}
+\end{formula}
+
+\begin{formula}{mean_free_path}
+    \desc{Mean free path}{}{}
+    \desc[german]{Mittlere freie Weglänge}{}{}
+    \eq{\ell = \braket{v} \tau}
+\end{formula}
+
+\begin{formula}{mobility}
+    \desc{Electrical mobility}{How quickly a particle moves through a material when moved by an electric field}{$q$ \qtyRef{charge}, $m$ \qtyRef{mass}, $\tau$ \qtyRef{scattering_time}}
+    \desc[german]{Elektrische Mobilität / Beweglichkeit}{Leichtigkeit mit der sich durch ein Elektrisches Feld beeinflusstes Teilchen im Material bewegt}{}
+    \quantity{\mu}{\centi\m^2\per\volt\s}{s}
+    \eq{\mu = \frac{q \tau}{m}}
+\end{formula}
+
+\Subsection[
+    \eng{2D electron gas}
+    \ger{2D Elektronengas}
+]{2deg}
+
+    \begin{ttext}
+        \eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
+        \ger{
+            Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird.
+        }
+    \end{ttext}
+    \begin{formula}{confinement_energy}
+        \desc{Confinement energy}{Raises ground state energy}{}
+        \desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{}
+        \eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}}
+    \end{formula}
+
+    \Eng[plain_wave]{plain wave}
+    \Ger[plain_wave]{ebene Welle}
+    \begin{formula}{energy}
+        \desc{Energy}{}{}
+        \desc[german]{Energie}{}{}
+        \eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}}
+    \end{formula}
+
+\Subsection[
+    \eng{1D electron gas / quantum wire}
+    \ger{1D Eleltronengas / Quantendraht}
+]{1deg}
+
+    \begin{formula}{energy}
+        \desc{Energy}{}{}
+        \desc[german]{Energie}{}{}
+        \eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2}
+    \end{formula}
+    \TODO{condunctance}
+    
+\Subsection[
+    \eng{0D electron gas / quantum dot}
+    \ger{0D Elektronengase / Quantenpunkt}
+]{0deg}
+
+    \TODO{TODO}
+

src/cm/low_temp.tex

@@ -0,0 +1,198 @@
+\def\L{\text{L}}
+\def\gl{\text{GL}}
+\def\GL{Ginzburg-Landau }
+\def\Tcrit{T_\text{c}}
+\def\Bcrit{B_\text{c}}
+\def\ssc{\text{s}}
+\def\ssn{\text{n}}
+
+\Section[
+    \eng{Superconductivity}
+    \ger{Supraleitung}
+]{sc}
+    \begin{ttext}
+        \eng{
+            Materials for which the electric resistance jumps to 0 under a critical temperature $\Tcrit$.
+            Below $\Tcrit$ they have perfect conductivity and perfect diamagnetism, up until a critical magnetic field $\Bcrit$.
+            \\\textbf{Type I}: Has a single critical magnetic field at which the superconuctor becomes a normal conductor.
+            \\\textbf{Type II}: Has two critical 
+        }
+        \ger{
+            Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur $\Tcrit$ auf 0 springt.
+            Sie verhalten sich dann wie ideale Leiter und ideale Diamagnete, bis zu einem kritischen Feld $\Bcrit$.
+
+        }
+    \end{ttext}
+
+    \begin{formula}{perfect_conductor}
+        \desc{Perfect conductor}{}{}
+        \desc[german]{Ideale Leiter}{}{}
+        \ttxt{
+            \eng{
+                In contrast to a superconductor, perfect conductors become diamagnetic only when the external magnetic field is turned on \textbf{after} the material was cooled below the critical temperature.
+                (\fqEqRef{ed:fields:mag:induction:lenz})
+            }
+            \ger{
+                Im Gegensatz zu einem Supraleiter werden ideale Leiter nur dann diamagnetisch, wenn das externe magnetische Feld \textbf{nach} dem Abkühlen unter die kritische Temperatur eingeschaltet wird.
+                (\fqEqRef{ed:fields:mag:induction:lenz})
+            }
+        }
+    \end{formula}
+
+    \begin{formula}{meissner_effect}
+        \desc{Meißner-Ochsenfeld effect}{Perfect diamagnetism}{}
+        \desc[german]{Meißner-Ochsenfeld Effekt}{Idealer Diamagnetismus}{}
+        \ttxt{
+            \eng{External magnetic field decays exponetially inside the superconductor below a critical temperature and a critical magnetic field.} 
+            \ger{Externes Magnetfeld fällt im Supraleiter exponentiell unterhalb einer kritischen Temperatur und unterhalb einer kritischen Feldstärke ab.} 
+        }
+    \end{formula}
+    \Subsection[
+        \eng{London equations}
+        \ger{London-Gleichungen}
+    ]{london}
+        \begin{ttext}
+            \eng{
+                Quantitative description of the \fqEqRef{cm:sc:meissner_effect}.
+            }
+            \ger{
+                Quantitative Beschreibung des \fqEqRef{cm:sc:meissner_effect}s.
+            }
+            
+        \end{ttext}
+        % \begin{formula}{coefficient}
+        %     \desc{London-coefficient}{}{}
+        %     \desc[german]{London-Koeffizient}{}{}
+        %     \eq{\Lambda = \frac{m_\ssc}{n_\ssc q_\ssc^2}}
+        % \end{formula}
+        \begin{formula}{first}
+            % \vec{j} = \frac{nq\hbar}{m}\Grad S - \frac{nq^2}{m}\vec{A}
+            \desc{First London Equation}{}{$\vec{j}$ current density, $n_\ssc$, $m_\ssc$, $q_\ssc$  density, mass and charge of superconduticng particles}
+            \desc[german]{Erste London-Gleichun-}{}{$\vec{j}$ Stromdichte, $n_\ssc$, $m_\ssc$, $q_\ssc$ Dichte, Masse und Ladung der supraleitenden Teilchen}
+            \eq{
+                \pdv{\vec{j}_{\ssc}}{t} = \frac{n_\ssc q_\ssc^2}{m_\ssc}\vec{E} {\color{gray}- \Order{\vec{j}_\ssc^2}}
+                % \\{\color{gray} = \frac{q}{m}\Grad \left(\frac{1}{2} \TODO{FActor} \vec{j}^2\right)}
+            }
+        \end{formula}
+        \begin{formula}{second}
+            \desc{Second London Equation}{Describes the \fqEqRef{cm:sc:meissner_effect}}{$\vec{j}$ current density, $n_\ssc$, $m_\ssc$, $q_\ssc$ density, mass and charge of superconduticng particles}
+            \desc[german]{Zweite London-Gleichung}{Beschreibt den \fqEqRef{cm:sc:meissner_effect}}{$\vec{j}$ Stromdichte, $n_\ssc$, $m_\ssc$, $q_\ssc$ Dichte, Masse und Ladung der supraleitenden Teilchen}
+            \eq{
+                \Rot \vec{j_\ssc} = -\frac{n_\ssc q_\ssc^2}{m_\ssc} \vec{B}
+            }
+        \end{formula}
+        \begin{formula}{penetration_depth}
+            \desc{London penetration depth}{}{}
+            \desc[german]{London Eindringtiefe}{}{}
+            \eq{\lambda_\L = \sqrt{\frac{m_\ssc}{\mu_0 n_\ssc q_\ssc^2}}}
+        \end{formula}
+
+
+
+    \Subsection[
+        \eng{\GL Theory (GLAG)}
+        \ger{\GL Theorie (GLAG)}
+    ]{gl}
+        \begin{ttext}
+            \eng{
+                \TODO{TODO}
+            }
+            
+        \end{ttext}
+        \begin{formula}{coherence_length}
+            \desc{\GL Coherence Length}{}{}
+            \desc[german]{\GL Kohärenzlänge}{}{}
+            \eq{
+                \xi_\gl &= \frac{\hbar}{\sqrt{2m \abs{\alpha}}} \\
+                \xi_\gl(T) &= \xi_\gl(0) \frac{1}{\sqrt{1-\frac{T}{\Tcrit}}}
+            }
+        \end{formula}
+        \begin{formula}{penetration_depth}
+            \desc{\GL Penetration Depth / Field screening length}{}{}
+            \desc[german]{\GL Eindringtiefe}{}{}
+            \eq{
+                \lambda_\gl &= \sqrt{\frac{m_\ssc\beta}{\mu_0 \abs{\alpha} q_s^2}} \\
+                \lambda_\gl(T) &= \lambda_\gl(0) \frac{1}{\sqrt{1-\frac{T}{\Tcrit}}}
+            }
+        \end{formula}
+        \begin{formula}{first}
+            \desc{First Ginzburg-Landau Equation}{}{$\xi_\gl$ \fqEqRef{cm:sc:gl:coherence_length}, $\lambda_\gl$ \fqEqRef{cm:sc:gl:penetration_depth}}
+            \desc[german]{Erste Ginzburg-Landau Gleichung}{}{}
+            \eq{\alpha\Psi + \beta\abs{\Psi}^2 \Psi + \frac{1}{2m} (-i\hbar \Grad + 2e\vec{A})^2\Psi = 0}
+        \end{formula}
+        \begin{formula}{second}
+            \desc{Second Ginzburg-Landau Equation}{}{}
+            \desc[german]{Zweite Ginzburg-Landau Gleichung}{}{}
+            \eq{\vec{j_\ssc} = \frac{ie\hbar}{m}(\Psi^*\Grad\Psi - \Psi\Grad\Psi^*) - \frac{4e^2}{m}\abs{\Psi}^2 \vec{A}}
+        \end{formula}
+
+        \TODO{proximity effect}
+
+    \Subsection[
+        \eng{Microscopic theory}
+        \ger{Mikroskopische Theorie}
+    ]{micro}
+
+        \begin{formula}{isotop_effect}
+            \desc{Isotope effect}{Superconducting behaviour depends on atomic mass and thereby of the lattice \Rightarrow Microscopic origin}{$\Tcrit$ critial temperature, $M$ isotope mass, $\omega_\text{ph}$}
+            \desc[german]{Isotopeneffekt}{Supraleitung hängt von der Atommasse und daher von den Gittereigenschaften ab \Rightarrow Mikroskopischer Ursprung}{$\Tcrit$ kritische Temperatur, $M$ Isotopen-Masse, $\omega_\text{ph}$}
+            \eq{
+                \Tcrit \propto \frac{1}{\sqrt{M}} \\
+                \omega_\text{ph} \propto \frac{1}{\sqrt{M}} \Rightarrow \Tcrit \propto \omega_\text{ph}
+            }
+        \end{formula}
+
+        \begin{formula}{cooper_pairs}
+            \desc{Cooper pairs}{}{}
+            \desc[german]{Cooper-Paars}{}{}
+            \ttxt{
+                \eng{Conduction electrons reduce their energy through an attractive interaction: One electron passing by atoms attracts the these, which creats a positive charge region behind the electron, which in turn attracts another electron. }
+            }
+        \end{formula}
+    
+        \Subsubsection[
+            \eng{BCS-Theory}
+            \ger{BCS-Theorie}
+        ]{bcs}
+            \begin{ttext}
+                \eng{
+                    Electron pairs form bosonic quasi-particles called Cooper pairs which can condensate into the ground state. 
+                    The wave function spans the whole material, which makes it conduct without resistance.
+                    The exchange bosons between the electrons are phonons.
+                }
+                \ger{
+                    Elektronenpaar bilden bosonische Quasipartikel (Cooper Paare) welche in den Grundzustand kondensieren können. 
+                    Die Wellenfunktion übersoannt den gesamten Festkörper, was einen widerstandslosen Ladungstransport garantiert.
+                    Die Austauschbosononen zwischen den Elektronen sind Bosonen.
+                }
+            \end{ttext}
+            \def\BCS{{\text{BCS}}}
+            \begin{formula}{hamiltonian}
+                \desc{BCS Hamiltonian}{for $N$ interacting electrons}{
+                    $c_{\veck\sigma}$ creation/annihilation operators create/destroy at $\veck$ with spin $\sigma$ \\
+                    First term: non-interacting free electron gas\\
+                    Second term: interaction energy
+                }
+                \desc[german]{BCS Hamiltonian}{}{}
+                \eq{
+                    \hat{H}_\BCS = 
+                    \sum_{\sigma} \sum_\veck \epsilon_\veck \hat{c}_{\veck\sigma}^\dagger \hat{c}_{\veck\sigma}
+                    + \sum_{\veck,\veck^\prime} V_{\veck,\veck^\prime} 
+                        \hat{c}_{\veck\uparrow}^\dagger \hat{c}_{-\veck\downarrow}^\dagger
+                        \hat{c}_{-\veck^\prime\downarrow} \hat{c}_{\veck^\prime,\uparrow}
+                }
+            \end{formula}
+
+            \begin{formula}{bogoliubov-valatin}
+                \desc{Bogoliubov-Valatin transformation}{Diagonalization of the \fqEqRef{cm:sc:micro:bcs:hamiltonian} to derive excitation energies}{}
+                \desc[german]{Bogoliubov-Valatin transformation}{}{}
+                \eq{
+                    \hat{H}_\BCS  - N\mu = \sum_\veck \big[\xi_\veck - E_\veck + \Delta_\veck g_\veck^*\big] + \sum_\veck \big[E_\veck a_\veck^\dagger a_\veck + E_\veck \beta_{-\veck}^\dagger \beta_{-\veck}\big]
+                }
+            \end{formula}
+
+            \begin{formula}{gap_equation}
+                \desc{BCS-gap equation}{}{}
+                \desc[german]{}{}{}
+                \eq{\Delta_\veck^* = -\sum_\veck^+\prime V_{\veck,\veck^\prime} \frac{\Delta_{\veck^\prime}}{2E_\veck} \tanh \left(\frac{E_{\veck^\prime}}{2\kB T}\right)}
+            \end{formula}

src/cm/mat.tex

@@ -0,0 +1,28 @@
+\Section[
+    \eng{Material physics}
+    \ger{Materialphysik}
+]{mat}
+
+\begin{formula}{tortuosity}
+    \desc{Tortuosity}{Degree of the winding of  a transport path through a porous material. \\ Multiple definitions exist}{$l$ path length, $L$ distance of the end points}
+    \desc[german]{Toruosität}{Grad der Gewundenheit eines Transportweges in einem porösen Material. \\ Mehrere Definitionen existieren}{$l$ Weglänge, $L$ Distanz der Endpunkte}
+    \quantity{\tau}{}{}
+    \eq{
+        \tau &= \left(\frac{l}{L}\right)^2 \\
+        \tau &= \frac{l}{L}
+    }
+\end{formula}
+
+\begin{formula}{stress}
+    \desc{Stress}{Force per area}{\QtyRef{force}, \QtyRef{area}}
+    \desc[german]{Spannung}{(Engl. "stress") Kraft pro Fläche}{}
+    \quantity{\sigma}{\newton\per\m^2}{v}
+    \eq{\ten{\sigma}_{ij} = \frac{F_i}{A_j}}
+\end{formula}
+
+\begin{formula}{strain}
+    \desc{Strain}{}{$\Delta x$ distance from reference position $x_0$}
+    \desc[german]{Dehnung}{(Engl. "strain")}{$\Delta x$ Auslenkung aus der Referenzposition $x_0$}
+    \quantity{\epsilon}{}{s}
+    \eq{\epsilon = \frac{\Delta x}{x_0}}
+\end{formula}

src/cm/misc.tex

@@ -0,0 +1,110 @@
+\Section[
+    \eng{Band theory}
+    \ger{Bändermodell}
+]{band}
+    \Subsection[
+        \eng{Hybrid orbitals}
+        \ger{Hybridorbitale}
+    ]{hybrid_orbitals}  
+    \begin{ttext}
+        \eng{Hybrid orbitals are linear combinations of other atomic orbitals.}
+        \ger{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.}
+    \end{ttext}
+
+    % chemmacros package
+    \begin{formula}{sp3}
+        \desc{sp3 Orbital}{\GT{eg} \ce{CH4}}{}
+        \desc[german]{sp3 Orbital}{}{}
+        \eq{
+            1\text{s} + 3\text{p} = \text{sp3}
+            \orbital{sp3}
+        }
+    \end{formula}
+    \begin{formula}{sp2}
+        \desc{sp2 Orbital}{}{}
+        \desc[german]{sp2 Orbital}{}{}
+        \eq{
+            1\text{s} + 2\text{p} = \text{sp2}
+            \orbital{sp2}
+        }
+    \end{formula}
+    \begin{formula}{sp}
+        \desc{sp Orbital}{}{}
+        \desc[german]{sp Orbital}{}{}
+        \eq{
+            1\text{s} + 1\text{p} = \text{sp}
+            \orbital{sp}
+        }
+    \end{formula}
+
+
+
+\Section[
+    \eng{Diffusion}
+    \ger{Diffusion}
+]{diffusion}    
+    \begin{formula}{diffusion_coefficient}
+        \desc{Diffusion coefficient}{}{}
+        \desc[german]{Diffusionskoeffizient}{}{}
+        \quantity{D}{\m^2\per\s}{s}
+    \end{formula}
+
+    \begin{formula}{particle_current_density}
+        \desc{Particle current density}{Number of particles through an area}{}
+        \desc[german]{Teilchenstromdichte}{Anzahl der Teilchen durch eine Fläche}{}
+        \quantity{J}{1\per\s^2}{s}
+    \end{formula}
+
+    \begin{formula}{einstein_relation}
+        \desc{Einstein relation}{Classical}{\QtyRef{diffusion_coefficient}, \mu \qtyRef{mobility}, \QtyRef{temperature}, $q$ \qtyRef{charge}}
+        \desc[german]{Einsteinrelation}{Klassisch}{}
+        \eq{D = \frac{\mu \kB T}{q}}
+    \end{formula}   
+
+    \begin{formula}{concentration}
+        \desc{Concentration}{A quantity per volume}{}
+        \desc[german]{Konzentration}{Eine Größe pro Volumen}{}
+        \quantity{c}{x\per\m^3}{s}
+    \end{formula}
+
+    \begin{formula}{fick_law_1}
+        \desc{Fick's first law}{Particle movement is proportional to concentration gradient}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}}
+        \desc[german]{Erstes Ficksches Gesetz}{Teilchenbewegung ist proportional zum Konzentrationsgradienten}{}
+        \eq{J = -D\frac{c}{x}}
+    \end{formula}
+
+    \begin{formula}{fick_law_2}
+        \desc{Fick's second law}{}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}}
+        \desc[german]{Zweites Ficksches Gesetz}{}{}
+        \eq{\pdv{c}{t} = D \pdv[2]{c}{x}}
+    \end{formula}
+
+\Section[
+    \eng{\GT{misc}}
+    \ger{\GT{misc}}
+]{misc}
+
+
+
+    \begin{formula}{work_function}
+        \desc{Work function}{Lowest energy required to remove an electron into the vacuum}{}
+        \desc[german]{Austrittsarbeit}{eng. "Work function"; minimale Energie um ein Elektron aus dem Festkörper zu lösen}{}
+        \quantity{W}{\eV}{s}
+        \eq{W = \Evac - \EFermi}
+    \end{formula}
+
+    \begin{formula}{electron_affinity}
+        \desc{Electron affinity}{Energy required to remove one electron from an anion with one negative charge.\\Energy difference between vacuum level and conduction band}{}
+        \desc[german]{Elektronenaffinität}{Energie, die benötigt wird um ein Elektron aus einem einfach-negativ geladenen Anion zu entfernen. Entspricht der Energiedifferenz zwischen Vakuum-Niveau und dem Leitungsband}{}
+        \quantity{\chi}{\eV}{s}
+        \eq{\chi = \left(\Evac - \Econd\right)}
+    \end{formula}
+
+
+    \begin{formula}{laser}
+        \desc{Laser}{Light amplification by stimulated emission of radiation}{}
+        \desc[german]{Laser}{}{}
+        \ttxt{
+            \eng{\textit{Gain medium} is energized \textit{pumping energy} (electric current or light), light of certain wavelength is amplified in the gain medium}
+        }
+    \end{formula}

src/cm/semiconductors.tex

@@ -0,0 +1,160 @@
+\Section[
+    \eng{Semiconductors}
+    \ger{Halbleiter}
+]{semic}
+\begin{formula}{types}
+    \desc{Intrinsic/extrinsic}{}{$n,p$ \fqEqRef{cm:semic:charge_density_eq}}
+    \desc[german]{Intrinsisch/Extrinsisch}{}{}
+    \ttxt{
+        \eng{
+            Intrinsic: pure, electron density determiend only by thermal excitation and $n_i^2 = n_0 p_0$\\
+            Extrinsic: doped
+        }
+        \ger{
+            Intrirnsisch: Pur, Elektronendichte gegeben durch thermische Anregung und $n_i^2 = n_0 p_0$ \\
+            Extrinsisch: gedoped
+        }
+    }
+\end{formula}
+
+\begin{formula}{charge_density_eq}
+    \desc{Equilibrium charge densitites}{Holds when $\frac{\Econd-\EFermi}{\kB T}>3.6$ and $\frac{\EFermi-\Evalence}{\kB T} > 3.6$}{}
+    \desc[german]{Ladungsträgerdichte im Equilibrium}{Gilt wenn $\frac{\Econd-\EFermi}{\kB T}>3.6$ und $\frac{\EFermi-\Evalence}{\kB T} > 3.6$}{}
+    \eq{
+        n_0 &\approx N_\text{c}(T) \Exp{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
+        p_0 &\approx N_\text{v}(T) \Exp{-\frac{\EFermi - E_\text{v}}{\kB T}} 
+    }
+\end{formula}
+\begin{formula}{charge_density_intrinsic}
+    \desc{Intrinsic charge density}{}{}
+    \desc[german]{Intrinsische Ladungsträgerdichte}{}{}
+    \eq{
+        n_\text{i} \approx \sqrt{n_0 p_0} = \sqrt{N_\text{c}(T) N_\text{v}(T)} \Exp{-\frac{E_\text{gap}}{2\kB T}}
+    }
+\end{formula}
+
+\begin{formula}{mass_action}
+    \desc{Mass action law}{Charge densities at thermal equilibrium, independent of doping}{}
+    \desc[german]{Massenwirkungsgesetz}{Ladungsträgerdichten im Equilibrium, unabhängig der Dotierung }{}
+    \eq{np = n_i^2}
+\end{formula}
+
+
+\begin{formula}{bandgaps}
+    \desc{Bandgaps of common semiconductors}{}{}
+    \desc[german]{Bandlücken wichtiger Halbleiter}{}{}
+    \begin{tabular}{l|CCc}
+        & \Egap(\SI{0}{\kelvin}) [\si{\eV}] & \Egap(\SI{300}{\kelvin}) [\si{\eV}] & \\ \hline
+        \GT{diamond} & 5,48 & 5,47 & \GT{indirect} \\
+        Si      & 1,17 & 1,12 & \GT{indirect} \\
+        Ge      & 0,75 & 0,66 & \GT{indirect} \\
+        GaP     & 2,32 & 2,26 & \GT{indirect} \\
+        GaAs    & 1,52 & 1,43 & \GT{direct}   \\
+        InSb    & 0,24 & 0,18 & \GT{direct}   \\
+        InP     & 1,42 & 1,35 & \GT{direct}   \\
+        CdS     & 2.58 & 2.42 & \GT{direct}
+    \end{tabular}
+\end{formula}
+
+
+\begin{formula}{min_maj}
+    \desc{Minority / Majority charge carriers}{}{}
+    \desc[german]{Minoritäts- / Majoritätsladungstraäger}{}{}
+    \ttxt{
+        \eng{
+            Majority carriers: higher number of particles ($e^-$ in n-type, $h^+$ in p-type)\\
+            Minority carriers: lower number of particles  ($h^+$ in n-type, $e^-$ in p-type)
+        }
+        \ger{
+            Majoritätsladungstraäger: höhere Teilchenzahl ($e^-$ in n-Typ, $h^+$ in p-Typ)\\
+            Minoritätsladungsträger: niedrigere Teilchenzahl  ($h^+$ in n-Typ, $e^-$ in p-Typ)
+        }
+    }
+\end{formula}   
+\TODO{effective mass approx}
+
+
+\Subsection[
+    \eng{Devices and junctions}
+    \ger{Bauelemente und Kontakte}
+]{junctions}
+    \begin{formula}{metal-sc}
+        \desc{Metal-semiconductor junction}{}{}
+        \desc[german]{Metall-Halbleiter Kontakt}{}{}
+        % \ttxt{
+        %     \eng{
+
+        %     }
+        % }
+    \end{formula}
+
+    \begin{bigformula}{schottky_barrier}
+        \desc{Schottky barrier}{Rectifying \fqEqRef{cm:sc:junctions:metal-sc}}{}
+        % \desc[german]{}{}{}
+        \centering
+        \resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_metal_n_sc_separate.tex}}
+        \resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_metal_n_sc.tex}}
+        \TODO{Work function electron affinity sind doch Energien und keine Potentiale, warum wird also immer $q$ davor geschrieben?}
+    \end{bigformula}
+    \begin{formula}{schottky-mott_rule}
+        \desc{Schottky-Mott rule}{}{$\Phi_\txB$ barrier potential, $\Phi_\txM$ \GT{metal}  \qtyRef{work_function}, $\chi_\text{sc}$ \qtyRef{electron_affinity}}
+        % \desc[german]{}{}{}
+        \eq{\Phi_\txB \approx \Phi_\txM - \chi_\text{sc}}
+    \end{formula}
+    \TODO{work function verhältnisse, wann ist es ohmisch wann depleted?}
+    \begin{bigformula}{ohmic}
+        \desc{Ohmic contact}{}{}
+        \desc[german]{Ohmscher Kontakt}{}{}
+        \centering
+        \resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_ohmic_separate.tex}}
+        \resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_ohmic.tex}}
+    \end{bigformula}
+
+    \begin{bigformula}{pn}
+        \desc{p-n junction}{}{}
+        \desc[german]{p-n Übergang}{}{}
+        \centering
+        \input{img/cm/sc_junction_pn.tex}
+        \resizebox{0.49\textwidth}{!}{\tikzPnJunction{1/3}{0}{0}{1/3}{0}{0}{}}          
+        \resizebox{0.49\textwidth}{!}{\tikzPnJunction{1/2}{0.4}{-0.4}{1/2}{-0.4}{0.4}{}}
+    \end{bigformula}
+    
+
+
+\Subsection[
+    \eng{Excitons}
+    \ger{Exzitons}
+]{exciton}
+    \begin{formula}{desc}
+        \desc{Exciton}{}{}
+        \desc[german]{Exziton}{}{}
+        \ttxt{
+            \eng{
+                Quasi particle, excitation in condensed matter as bound electron-hole pair.
+                \\ Free (Wannier) excitons:  delocalised over many lattice sites
+                \\ Bound (Frenkel) excitonsi: localised in single unit cell
+            }
+
+            \ger{
+                Quasiteilchen, Anregung im Festkörper als gebundenes Elektron-Loch-Paar
+                \\ Freie (Wannier) Exzitons: delokalisiert, über mehrere Einheitszellen
+                \\ Gebundene (Frenkel) Exzitons: lokalisiert in einer Einheitszelle
+            }
+        }
+    \end{formula}
+    \eng[free_X]{for free Excitons}
+    \ger[free_X]{für freie Exzitons}
+    \begin{formula}{rydberg}
+        \desc{Exciton Rydberg energy}{\gt{free_X}}{$R_\txH$ \fqEqRef{qm:h:rydberg_energy}}
+        \desc[german]{}{}{}
+        \eq{
+            E(n) = - \left(\frac{\mu}{m_0\epsilon_r^2}\right) R_\txH \frac{1}{n^2}
+        }
+    \end{formula}
+    \begin{formula}{bohr_radius}
+        \desc{Exciton Bohr radius}{\gt{free_X}}{\QtyRef{relative_permittivity}, \ConstRef{bohr_radius}, \ConstRef{electron_mass}, $mu$ \GT{reduced_mass}}
+        \desc[german]{Exziton-Bohr Radius}{}{}
+        \eq{
+            r_n = \left(\frac{m_\txe\epsilon_r a_\txB}{mu}\right) n^2
+        }
+    \end{formula}

src/cm/techniques.tex

@@ -0,0 +1,212 @@
+\Section[
+    \eng{Measurement techniques}
+    \ger{Messtechniken}
+]{meas}
+
+\newcommand\newTechnique{\hline}
+    \Eng[name]{Name}
+    \Ger[name]{Name}
+    \Eng[application]{Application}
+    \Ger[application]{Anwendung}
+
+    \Subsection[
+        \eng{Raman spectroscopy}
+        \ger{Raman Spektroskopie}
+    ]{raman}
+
+    % TODO remove fqname from minipagetable?
+
+    \begin{bigformula}{raman}
+        \desc{Raman spectroscopy}{}{}
+        \desc[german]{Raman-Spektroskopie}{}{}
+        \begin{minipagetable}{raman}
+            \tentry{application}{
+                \eng{Vibrational modes, Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqRef{cm:misc:vdw_material}}
+                \ger{Vibrationsmoden, Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqRef{cm:misc:vdw_material}}
+            }
+            \tentry{how}{
+                \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, inelastic scattering because of rotation-, vibration-, phonon and spinflip-processes, plot spectrum as shift of the laser light (in \si{\per\cm})}
+                \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, inelastische Streuung durch Rotations-, Schwingungs-, Phonon und Spin-Flip-Prozesse, plotte Spektrum als Verschiebung gegen das Laser Licht (in \si{\per\cm}) }
+            }
+        \end{minipagetable}
+        \begin{minipage}{0.45\textwidth}
+            \begin{figure}[H]
+                \centering
+                % \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
+                % \caption{\cite{Bian2021}}
+            \end{figure}
+        \end{minipage}
+    \end{bigformula}
+
+
+    \begin{bigformula}{pl}
+        \desc{Photoluminescence spectroscopy}{}{}
+        \desc[german]{Photolumeszenz-Spektroskopie}{}{}
+        \begin{minipagetable}{pl}
+            \tentry{application}{
+                \eng{Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqRef{cm:misc:vdw_material}}
+                \ger{Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqRef{cm:misc:vdw_material}}
+            }
+            \tentry{how}{
+                \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, electrons are excited, relax to the conduction band minimum and finally accross the band gap under photon emission}
+                \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, Elektronen werden angeregt und relaxieren in das Leitungsband-Minimum und schließlich über die Bandlücke unter Photonemission}
+            }
+        \end{minipagetable}
+        \begin{minipage}{0.45\textwidth}
+            \begin{figure}[H]
+                \centering
+                % \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
+                % \caption{\cite{Bian2021}}
+            \end{figure}
+        \end{minipage}
+    \end{bigformula}
+
+
+    \Subsection[
+        \eng{ARPES}
+        \ger{ARPES}
+    ]{arpes}
+        what?
+        in?
+        how?
+        plot
+
+    \Subsection[
+        \eng{Scanning probe microscopy SPM}
+        \ger{Rastersondenmikroskopie (SPM)}
+        ]{spm}
+        \begin{ttext}
+            \eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
+            \ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
+        \end{ttext}
+
+
+    \begin{bigformula}{amf}
+        \desc{Atomic force microscopy (AMF)}{}{}
+        \desc[german]{Atomare Rasterkraftmikroskopie (AMF)}{}{}
+        \begin{minipagetable}{amf}
+            \tentry{application}{
+                \eng{Surface stuff}
+                \ger{Oberflächenzeug}
+            }
+            \tentry{how}{
+                \eng{With needle}
+                \ger{Mit Nadel}
+            }
+        \end{minipagetable}
+        \begin{minipage}{0.45\textwidth}
+            \begin{figure}[H]
+                \centering
+                \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
+                \caption{\cite{Bian2021}}
+            \end{figure}
+        \end{minipage}
+    \end{bigformula}
+
+
+
+
+    \begin{bigformula}{stm}
+        \desc{Scanning tunneling microscopy (STM)}{}{}
+        \desc[german]{Rastertunnelmikroskop (STM)}{}{}
+        \begin{minipagetable}{stm}
+            \tentry{application}{
+                \eng{Surface stuff}
+                \ger{Oberflächenzeug}
+            }
+            \tentry{how}{
+                \eng{With TUnnel}
+                \ger{Mit TUnnel}
+            }
+        \end{minipagetable}
+        \begin{minipage}{0.45\textwidth}
+            \begin{figure}[H]
+                \centering
+                \includegraphics[width=0.8\textwidth]{img/cm_stm.pdf}
+                \caption{\cite{Bian2021}}
+            \end{figure}
+        \end{minipage}
+    \end{bigformula}
+
+\Section[
+    \eng{Fabrication techniques}
+    \ger{Herstellungsmethoden}
+]{fab}
+
+    \begin{bigformula}{cvd}
+    \desc{Chemical vapor deposition (CVD)}{}{}
+    \desc[german]{Chemische Gasphasenabscheidung (CVD)}{}{}
+    \begin{minipagetable}{cvd}
+        \tentry{how}{
+            \eng{
+                A substrate is exposed to volatile precursors, which react and/or decompose on the heated substrate surface to produce the desired deposit.
+                By-products are removed by gas flow through the chamber.
+            }
+            \ger{
+                An der erhitzten Oberfläche eines Substrates wird aufgrund einer chemischen Reaktion mit einem Gas eine Feststoffkomponente abgeschieden.
+                Nebenprodukte werden durch den Gasfluss durch die Kammer entfernt.
+            }
+        }
+        \tentry{application}{
+            \eng{
+                \begin{itemize}
+                    \item Polysilicon \ce{Si}
+                    \item Silicon dioxide \ce{SiO_2}     
+                    \item Graphene
+                    \item Diamond
+                \end{itemize}
+            }
+            \ger{
+                \begin{itemize}
+                    \item Poly-silicon \ce{Si}
+                    \item Siliziumdioxid \ce{SiO_2}     
+                    \item Graphen
+                    \item Diamant
+                \end{itemize}
+            }
+        }
+    \end{minipagetable}
+    \begin{minipage}{0.45\textwidth}
+        \centering
+        \includegraphics[width=\textwidth]{img/cm_cvd_english.pdf}
+    \end{minipage}
+\end{bigformula}
+
+
+    \Subsection[
+        \eng{Epitaxy}
+        \ger{Epitaxie}
+        ]{epitaxy}
+        \begin{ttext}
+            \eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
+            \ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
+        \end{ttext}
+
+        \begin{bigformula}{mbe}
+            \desc{Molecular Beam Epitaxy (MBE)}{}{}
+            \desc[german]{Molekularstrahlepitaxie (MBE)}{}{}
+            \begin{minipagetable}{mbe}
+                \tentry{how}{
+                    \eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
+                    \ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
+                }
+                \tentry{application}{
+                    \eng{
+                        \begin{itemize}
+                            \item Gallium arsenide \ce{GaAs}
+                        \end{itemize}
+                        \TODO{Link to GaAs}
+                    }
+                    \ger{
+                        \begin{itemize}
+                            \item Galliumarsenid \ce{GaAs}
+                        \end{itemize}
+                    }
+                }
+            \end{minipagetable}
+            \begin{minipage}{0.45\textwidth}
+                \centering
+                \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
+            \end{minipage}
+        \end{bigformula}
+

src/cm/topo.tex

@@ -1,8 +1,11 @@
-\Part{Topo}
 \Section[
+    \eng{Topological Materials}
+    \ger{Topologische Materialien}
+]{topo}
+\Subsection[
     \eng{Berry phase / Geometric phase}
     \ger{Berry-Phase / Geometrische Phase}
-     ]{berry_phase}
+]{berry_phase}
 
     \begin{ttext}[desc]
         \eng{
@@ -53,28 +56,34 @@
         \eq{\gamma_n = \oint_C \d \vec{R} \cdot A_n(\vec{R}) = \int_S \d\vec{S} \cdot \vec{\Omega}_n(\vec{R})}
     \end{formula}
 
-    \begin{ttext}[chern_number_desc]
-        \eng{The Berry flux through any 2D closed surface is quantized by the \textbf{Chern number}.
-            If there is time-reversal symmetry, the Chern-number is 0.
-        }
-        \ger{Der Berry-Fluß durch eine geschlossene 2D Fl[cher is quantisiert durch die \textbf{Chernzahl}
-            Bei erhaltener Zeitumkehrungssymmetrie ist die Chernzahl 0.
-        }
-    \end{ttext}
     \begin{formula}{chern_number}
         \desc{Chern number}{Eg. number of Berry curvature monopoles in the Brillouin zone (then $\vec{R} = \vec{k}$)}{$\vec{S}$ closed surface in $\vec{R}$-space. A \textit{Chern insulator} is a 2D insulator with $C_n \neq 0$}
         \desc[german]{Chernuzahl}{Z.B. Anzahl der Berry-Krümmungs-Monopole in der Brilouinzone (dann ist $\vec{R} = \vec{k}$). Ein \textit{Chern-Isolator} ist ein 2D Isolator mit $C_n\neq0$}{$\vec{S}$ geschlossene Fläche im $\vec{R}$-Raum}
+        \ttxt{
+            \eng{The Berry flux through any 2D closed surface is quantized by the \textbf{Chern number}.
+                If there is time-reversal symmetry, the Chern-number is 0.
+            }
+            \ger{Der Berry-Fluß durch eine geschlossene 2D Fl[cher is quantisiert durch die \textbf{Chernzahl}
+                Bei erhaltener Zeitumkehrungssymmetrie ist die Chernzahl 0.
+            }
+        }
         \eq{C_n = \frac{1}{2\pi} \oint \d \vec{S}\ \cdot \vec{\Omega}_n(\vec{R})}
     \end{formula}
 
-    \TODO{Hall conductance of 2D band insulator (lecture 4 revision)}
     \begin{formula}{hall_conductance}
         \desc{Hall conductance of a 2D band insulator}{}{}
         \desc[german]{Hall-Leitfähigkeit eines 2D Band-Isolators}{}{}
         \eq{\vec{\sigma}_{xy} = \sum_n \frac{e^2}{h} \int_\text{\GT{occupied}} \d^2k\, \frac{\Omega_{xy}^n}{2\pi} = \sum_n C_n \frac{e^2}{h}}
     \end{formula}
 
-    \begin{ttext}
+    \begin{formula}{topological_insulator}
-        \eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}}
+        \desc{Topological insulator}{}{}
-        
+        \desc[german]{Topologischer Isolator}{}{}
-    \end{ttext}
+        \ttxt{
+            \eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}.}
+            \ger{Ein 2D Isolator mit einer Chernzahl ungleich 0 wird \textbf{topologischer Isolator} genannt.}
+        }
+    \end{formula}
+
+
+

src/comp/ad.tex

@@ -0,0 +1,374 @@
+\Section[
+    \eng{Atomic dynamics}
+    % \ger{}
+]{ad}
+\begin{formula}{hamiltonian}
+    \desc{Electron Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:est:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
+    \desc[german]{Hamiltonian der Elektronen}{}{}
+    \eq{\hat{H}_\txe = \hat{T}_\txe + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe}}
+\end{formula}
+\begin{formula}{ansatz}
+    \desc{Wave function ansatz}{}{$\psi_\text{en}^n$ eigenstate $n$ of \fqEqRef{comp:est:hamiltonian}, $\psi_\txe^i$ eigenstate $i$ of \fqEqRef{comp:ad:bo:hamiltonian}, $\vecr,\vecR$ electron/nucleus positions, $\sigma$ electron spin, $c^{ni}$ coefficients}
+    \desc[german]{Wellenfunktion Ansatz}{}{}
+    \eq{\psi_\text{en}^n\big(\{\vecr,\sigma\},\{\vecR\}\big) = \sum_i c^{ni}\big(\{\vecR\}\big)\, \psi_\txe^i\big(\{\vecr,\sigma\},\{\vecR\}\big)}
+\end{formula}
+\begin{formula}{equation}
+    \desc{Equation}{}{}
+    % \desc[german]{}{}{}
+    \eq{
+        \label{eq:\fqname}
+        \left[E_\txe^j\big(\{\vecR\}\big) + \hat{T}_\txn + V_{\txn \leftrightarrow \txn} - E^n \right]c^{nj} = -\sum_i \Lambda_{ij} c^{ni}\big(\{\vecR\}\big)
+    }
+\end{formula}
+\begin{formula}{coupling_operator}
+    \desc{Exact nonadiabtic coupling operator}{Electron-phonon couplings / electron-vibrational couplings}{$\psi^i_\txe$ electronic states, $\vecR$ nucleus position, $M$ nucleus \qtyRef{mass}}
+    % \desc[german]{}{}{}
+    \begin{multline}
+        \Lambda_{ij} = \int \d^3r (\psi_\txe^j)^* \left(-\sum_I \frac{\hbar^2\nabla_{\vecR_I}^2}{2M_I}\right) \psi_\txe^i \\
+        + \sum_I \frac{1}{M_I} \int\d^3r \left[(\psi_\txe^j)^* (-i\hbar\nabla_{\vecR_I})\psi_\txe^i\right](-i\hbar\nabla_{\vecR_I})
+    \end{multline}
+\end{formula}
+
+\Subsection[
+    \eng{Born-Oppenheimer Approximation}
+    \ger{Born-Oppenheimer Näherung}
+]{bo}
+    \begin{formula}{adiabatic_approx}
+        \desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move (\absRef{adiabatic_theorem})}{$\Lambda_{ij}$ \fqEqRef{comp:ad:coupling_operator}} 
+        \desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{}
+        \eq{\Lambda_{ij} = 0 \quad \text{\GT{for} } i\neq j}
+    \end{formula}
+    \begin{formula}{approx}
+        \desc{Born-Oppenheimer approximation}{Electrons are not influenced by the movement of the atoms}{\GT{see} \fqEqRef{comp:ad:equation}, $V_{\txn \leftrightarrow \txn} = \const$ absorbed into $E_\txe^j$}
+        \desc[german]{Born-Oppenheimer Näherung}{Elektronen werden nicht durch die Bewegung der Atome beeinflusst}{}
+        \begin{gather}
+            \Lambda_{ij} = 0
+            \shortintertext{\fqEqRef{comp:ad:bo:equation} \Rightarrow}
+            \left[E_e^i\big(\{\vecR\}\big) + \hat{T}_\txn - E^n\right]c^{ni}\big(\{\vecR\}\big) = 0
+        \end{gather}
+    \end{formula}
+    \begin{formula}{surface}
+        \desc{Born-Oppenheimer surface}{Potential energy surface (PES)\\ The nuclei follow Newtons equations of motion on the BO surface if the system is in the electronic ground state}{$E_\txe^0, \psi_\txe^0$ lowest eigenvalue/eigenstate of \fqEqRef{comp:ad:bo:hamiltonian}}
+        \desc[german]{Born-Oppenheimer Potentialhyperfläche}{Die Nukleonen Newtons klassichen Bewegungsgleichungen auf der BO Hyperfläche wenn das System im elektronischen Grundzustand ist}{$E_\txe^0, \psi_\txe^0$ niedrigster Eigenwert/Eigenzustand vom \fqEqRef{comp:ad:bo:hamiltonian}}
+        \begin{gather}
+            V_\text{BO}\big(\{\vecR\}\big) = E_\txe^0\big(\{\vecR\}\big) \\
+            M_I \ddot{\vecR}_I(t) = - \Grad_{\vecR_I} V_\text{BO}\big(\{\vecR(t)\}\big)
+        \end{gather}
+    \end{formula}
+    \begin{formula}{ansatz}
+        \desc{Ansatz for \secEqRef{approx}}{Product of single electronic and single nuclear state}{}
+        \desc[german]{Ansatz für \secEqRef{approx}}{Produkt aus einem einzelnen elektronischen Zustand und einem Nukleus-Zustand}{}
+        \eq{
+            \psi_\text{BO} = c^{n0} \big(\{\vecR\}\big) \,\psi_\txe^0 \big(\{\vecr,\sigma\},\{\vecR\}\big)
+        }
+    \end{formula}
+
+    \begin{formula}{limitations}
+        \desc{Limitations}{}{$\tau$ passage of time for electrons/nuclei, $L$ characteristic length scale of atomic dynamics, $\dot{\vec{R}}$ nuclear velocity, $\Delta E$ difference between two electronic states}
+        \desc[german]{Limitationen}{}{}
+        \ttxt{
+            \eng{ 
+                \begin{itemize}
+                    \item Nuclei velocities must be small and electron energy state differences large
+                    \item Nuclei need spin for effects like spin-orbit coupling
+                    \item Nonadiabitc effects in photochemistry, proteins
+                \end{itemize}
+                Valid when Massey parameter $\xi \gg 1$
+            }
+        }
+        \eq{
+            \xi = \frac{\tau_\txn}{\tau_\txe} = \frac{L \Delta E}{\hbar \abs{\dot{\vecR}}}
+        }
+    \end{formula}   
+
+\Subsection[
+    \eng{Structure optimization}
+    \ger{Strukturoptimierung}
+]{opt}
+    \begin{formula}{forces}
+        \desc{Forces}{}{}
+        \desc[german]{Kräfte}{}{}
+        \eq{\vec{F}_I = -\Grad_{\vecR_I} E \explOverEq{\fqEqRef{qm:se:hellmann_feynmann}} -\Braket{\psi(\vecR_I) | \left(\Grad_{\vecR_I} \hat{H}(\vecR_I)\right) | \psi(\vecR) }}
+    \end{formula}
+    \begin{formula}{ionic_cycle}
+        \desc{Ionic cycle}{\fqEqRef{comp:est:dft:ks:scf} for geometry optimization}{}
+        \desc[german]{}{}{}
+        \ttxt{
+            \eng{
+                \begin{enumerate}
+                    \item Initial guess for $n(\vecr)$
+                    \begin{enumerate}
+                        \item Calculate effective potential $V_\text{eff}$
+                        \item Solve \fqEqRef{comp:est:dft:ks:equation}
+                        \item Calculate density $n(\vecr)$
+                        \item Repeat b-d until self consistent
+                    \end{enumerate}
+                    \item Calculate \secEqRef{forces}
+                    \item If $F\neq0$, get new geometry by interpolating $R$ and restart
+                \end{enumerate}
+            }
+        }
+    \end{formula}
+
+    \begin{formula}{transformation}
+        \desc{Transformation of atomic positions under stress}{}{$\alpha,\beta=1,2,3$ position components, $R$ position, $R(0)$ zero-strain position, $\ten{\epsilon}$ \qtyRef{strain} tensor}
+        \desc[german]{Transformation der Atompositionen unter Spannung}{}{$\alpha,\beta=1,2,3$ Positionskomponenten, $R$ Position, $R(0)$ Position ohne Dehnung, $\ten{\epsilon}$ \qtyRef{strain} Tensor}
+        \eq{R_\alpha(\ten{\epsilon}_{\alpha\beta}) = \sum_\beta \big(\delta_{\alpha\beta} + \ten{\epsilon}_{\alpha\beta}\big)R_\beta(0)}
+    \end{formula}
+
+    \begin{formula}{stress_tensor}
+        \desc{Stress tensor}{}{$\Omega$ unit cell volume, \ten{\epsilon} \qtyRef{strain} tensor}
+        \desc[german]{Spannungstensor}{}{}
+        \eq{\ten{\sigma}_{\alpha,\beta} = \frac{1}{\Omega} \pdv{E_\text{total}}{\ten{\epsilon}_{\alpha\beta}}_{\ten{\epsilon}=0}}
+    \end{formula}
+
+    \begin{formula}{pulay_stress}
+        \desc{Pulay stress}{}{}
+        \desc[german]{Pulay-Spannung}{}{}
+        \eq{
+            N_\text{PW} \propto E_\text{cut}^\frac{3}{2} \propto \abs{\vec{G}_\text{max}}^3
+        }
+        \ttxt{\eng{
+            Number of plane waves $N_\text{PW}$ depends on $E_\text{cut}$.
+            If $G$ changes during optimization, $N_\text{PW}$ may change, thus the basis set can change.
+            This typically leads to too small volumes.
+        }}
+    \end{formula}
+
+\Subsection[
+    \eng{Lattice vibrations}
+    \ger{Gitterschwingungen}
+]{latvib}
+    \begin{formula}{force_constant_matrix}
+        \desc{Force constant matrix}{}{}
+        % \desc[german]{}{}{}
+        \eq{\Phi_{IJ}^{\mu\nu} = \pdv{V(\{\vecR\})}{R_I^\mu,R_J^\nu}_{\{\vecR_I\}=\{\vecR_I^0\}}}
+    \end{formula}
+
+    \begin{formula}{harmonic_approx}
+        \desc{Harmonic approximation}{Hessian matrix, 2nd order Taylor expansion of the \fqEqRef{comp:ad:bo:surface} around every nucleus position $\vecR_I^0$}{$\Phi_{IJ}^{\mu\nu}$ \secEqRef{force_constant_matrix}, $s$ displacement}
+        \desc[german]{Harmonische Näherung}{Hesse matrix, Taylor Entwicklung der \fqEqRef{comp:ad:bo:surface} in zweiter Oddnung um Atomposition $\vecR_I^0$}{}
+        \eq{ V^\text{BO}(\{\vecR_I\}) \approx V^\text{BO}(\{\vecR_I^0\}) + \frac{1}{2} \sum_{I,J}^N \sum_{\mu,\nu}^3 s_I^\mu s_J^\nu \Phi_{IJ}^{\mu\nu} }
+    \end{formula}
+    
+    % solving difficult becaus we need to calculate (3N)^2 derivatives, Hellmann-Feynman cant be applied directly
+    % -> DFPT
+
+    % finite-difference method
+    \Subsubsection[
+        \eng{Finite difference method}
+        % \ger{}
+    ]{fin_diff}
+
+        \begin{formula}{approx}
+            \desc{Approximation}{Assume forces in equilibrium structure vanish}{$\Delta s$ displacement of atom $J$}
+            % \desc[german]{}{}{}
+            \eq{\Phi_{IJ}^{\mu\nu} \approx \frac{\vecF_I^\mu(\vecR_1^0, \dots, \vecR_J^0+\Delta s_J^\nu,\dots, \vecR_N^0)}{\Delta s_J^\nu}}
+        \end{formula}
+        \begin{formula}{dynamical_matrix}
+            \desc{Dynamical matrix}{Mass reduced \absRef[fourier transform]{fourier_transform} of the \fqEqRef{comp:ad:latvib:force_constant_matrix}}{$\vec{L}$ vector from origin to unit cell $n$, $\alpha/\beta$ atom index in th unit cell, $\vecq$ \qtyRef{wave_vector}, $\Phi$ \fqEqRef{comp:ad:latvib:force_constant_matrix}, $M$ \qtyRef{mass}}
+            % \desc[german]{}{}{}
+            \eq{D_{\alpha\beta}^{\mu\nu} = \frac{1}{\sqrt{M_\alpha M_\beta}} \sum_{n^\prime} \Phi_{\alpha\beta}^{\mu\nu}(n-n^\prime) \e^{\I \vec{q}(\vec{L}_n - \vec{L}_{n^\prime})}}
+        \end{formula}
+
+        \begin{formula}{eigenvalue_equation}
+            \desc{Eigenvalue equation}{For a periodic crystal, reduces number of equations from $3N_p\times N$ to $3N_p$. Eigenvalues represent phonon band structure.}{$N_p$ number of atoms per unit cell, $\vecc$ displacement amplitudes, $\vecq$ \qtyRef{wave_vector}, $\mat{D}$ \secEqRef{dynamical_matrix}}
+            \desc[german]{Eigenwertgleichung}{}{}
+            \eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) }
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Anharmonic approaches}
+        \ger{Anharmonische Ansätze}
+    ]{anharmonic}
+
+        \begin{formula}{qha}
+            \desc{Quasi-harmonic approximation}{}{}
+            \desc[german]{}{}{}
+            \ttxt{\eng{
+                Include thermal expansion by assuming \fqEqRef{comp:ad:bo:surface} is volume dependant.
+            }}
+        \end{formula}
+
+        \begin{formula}{pertubative}
+            \desc{Pertubative approaches}{}{}
+            % \desc[german]{Störungs}{}{}
+            \ttxt{\eng{
+                Expand \fqEqRef{comp:ad:latvib:force_constant_matrix} to third order.
+            }}
+        \end{formula}
+
+    
+
+
+\Subsection[
+    \eng{Molecular Dynamics}
+    \ger{Molekulardynamik}
+]{md} \abbrLink{md}{MD}
+    \begin{formula}{desc}
+        \desc{Description}{}{}
+        \desc[german]{Beschreibung}{}{}
+        \ttxt{\eng{
+            \begin{itemize}
+                \item Exact (within previous approximations) approach to treat anharmonic effects in materials.
+                \item Computes time-dependant observables.
+                \item Assumes fully classical nuclei.
+                \item Macroscropical observables from statistical ensembles 
+                \item System evolves in time (ehrenfest). Number of points to consider does NOT scale with system size.
+                \item Exact because time dependance is studied explicitly, not via harmonic approx.
+            \end{itemize}
+            \TODO{cleanup}
+        }}
+    \end{formula}
+
+    \begin{formula}{procedure}
+        \desc{MD simulation procedure}{}{}
+        \desc[german]{Ablauf von MD Simulationen}{}{}
+        \ttxt{\eng{
+            \begin{enumerate}
+                \item Initialize with optimized geometry, interaction potential, ensemble, integration scheme, temperature/pressure control
+                \item Equilibrate to desired temperature/pressure (eg with statistical starting velocities)
+                \item Production run, run MD long enough to calculate desired observables
+            \end{enumerate}
+        }}
+    \end{formula}
+
+    \Subsubsection[
+        \eng{Ab-initio molecular dynamics}
+        \ger{Ab-initio molecular dynamics}
+    ]{ab-initio}
+        \begin{formula}{bomd}
+            \abbrLabel{BOMD}
+            \desc{Born-Oppenheimer MD (BOMD)}{}{}
+            \desc[german]{Born-Oppenheimer MD (BOMD)}{}{}
+            \ttxt{\eng{
+                \begin{enumerate}
+                    \item Calculate electronic ground state of current nucleui configuration $\{\vecR(t)\}$ with \abbrRef{ksdft}
+                    \item \hyperref[f:comp:ad:opt:forces]{Calculate forces} from the \fqEqRef{comp:ad:bo:surface} 
+                    \item  Update positions and velocities
+                \end{enumerate}
+                \begin{itemize}
+                    \gooditem "ab-inito" - no empirical information required
+                    \baditem Many expensive \abbrRef{dft} calculations
+                \end{itemize}
+            }}
+        \end{formula}
+
+        \begin{formula}{cpmd}
+            \desc{Car-Parrinello MD (CPMD)}{}{$\mu$ electron orbital mass, $\varphi_i$ \abbrRef{ksdft} eigenststate, $\lambda_{ij}$ Lagrange multiplier}
+            \desc[german]{Car-Parrinello MD (CPMD)}{}{}
+            \ttxt{\eng{
+                Evolve electronic wave function $\varphi$ (adiabatically) along with the nuclei \Rightarrow only one full \abbrRef{ksdft} 
+            }}
+            \begin{gather}
+                M_I \odv[2]{\vecR_I}{t} = -\Grad_{\vecR_I} E[\{\varphi_i\},\{\vecR_I\}] \\
+                % not using pdv because of comma in parens
+                % E[\{\varphi_i\}\{\vecR_I\}] = \Braket{\psi_0|H_\text{el}^\text{KS}|\psi_0}
+                \mu \odv[2]{\varphi_i(\vecr,t)}{t} = - \frac{\partial}{\partial\varphi_i^*(\vecr,t)} E[\{\varphi_i\},\{\vecR_I\}] + \sum_j \lambda_{ij} \varphi_j(\vecr,t)
+            \end{gather}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Force-field MD}
+        \ger{Force-field MD}
+    ]{ff}
+
+        \begin{formula}{ffmd}
+            \desc{Force field MD (FFMD)}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{\eng{
+                \begin{itemize}
+                    \item Use empirical interaction potential instead of electronic structure
+                    \baditem Force fields need to be fitted for specific material \Rightarrow not transferable 
+                    \gooditem Faster than \abbrRef{bomd}
+                    \item Example: \absRef{lennard_jones}
+                \end{itemize}
+            }}
+        \end{formula}
+
+
+
+    \Subsubsection[
+        \eng{Integration schemes}
+        % \ger{}
+    ]{scheme}
+        \begin{ttext} 
+            \eng{Procedures for updating positions and velocities to obey the equations of motion.}
+        \end{ttext}
+        
+        \begin{formula}{euler}
+            \desc{Euler method}{First-order procedure for solving \abbrRef{ode}s with a given initial value.\\Taylor expansion of $\vecR/\vecv (t+\Delta t)$}{}
+            \desc[german]{Euler-Verfahren}{Prozedur um gewöhnliche DGLs mit Anfangsbedingungen in erster Ordnung zu lösen.\\Taylor Entwicklung von $\vecR/\vecv (t+\Delta t)$}{}
+            \eq{
+                \vecR(t+\Delta t) &= \vecR(t) + \vecv(t) \Delta t + \Order{\Delta t^2} \\
+                \vecv(t+\Delta t) &= \vecv(t) + \veca(t) \Delta t + \Order{\Delta t^2}
+            }
+            \ttxt{\eng{
+                Cumulative error scales linearly $\Order{\Delta t}$. Not time reversible.
+            }}
+        \end{formula}
+
+        \begin{formula}{verlet}
+            \desc{Verlet integration}{Preverses time reversibility, does not require velocity updates}{}
+            \desc[german]{Verlet-Algorithmus}{Zeitumkehr-symmetrisch}{}
+            \eq{
+                \vecR(t+\Delta t) = 2\vecR(t) -\vecR(t-\Delta t) + \veca(t) \Delta t^2 + \Order{\Delta t^4}
+            }
+        \end{formula}
+        
+        \begin{formula}{velocity-verlet}
+            \desc{Velocity-Verlet integration}{}{}
+            % \desc[german]{}{}{}
+            \eq{
+                \vecR(t+\Delta t) &= \vecR(t) + \vecv(t)\Delta t + \frac{1}{2} \veca(t) \Delta t^2 + \Order{\Delta t^4} \\
+                \vecv(t+\Delta t) &= \vecv(t) + \frac{\veca(t) + \veca(t+\Delta t)}{2} \Delta t + \Order{\Delta t^4} 
+            }
+        \end{formula}
+        
+        \TODO{leapfrog}
+
+    \Subsubsection[
+        \eng{Thermostats and barostats}
+        \ger{Thermostate und Barostate}
+    ]{stats}
+        \begin{formula}{velocity_rescaling}
+            \desc{Velocity rescaling}{Thermostat, keep temperature at $T_0$ by rescaling velocities. Does not allow temperature fluctuations and thus does not obey the \absRef{c_ensemble}}{$T$ target \qtyRef{temperature}, $M$ \qtyRef{mass} of nucleon $I$, $\vecv$ \qtyRef{velocity}, $f$ number of degrees of freedom, $\lambda$ velocity scaling parameter, \ConstRef{boltzmann}}
+            % \desc[german]{}{}{}
+            \eq{
+                \Delta T(t) &= T_0 - T(t) \\
+                            &= \sum_I^N \frac{M_I\,(\lambda \vecv_I(t))^2}{f\kB} - \sum_I^N \frac{M_I\,\vecv_I(t)^2}{f\kB} \\
+                            &= (\lambda^2 - 1) T(t)
+            }
+            \eq{\lambda = \sqrt{\frac{T_0}{T(t)}}}
+        \end{formula}
+
+        \begin{formula}{berendsen}
+            \desc{Berendsen thermostat}{Does not obey \absRef{c_ensemble} but efficiently brings system to target temperature}{}
+            % \desc[german]{}{}{}
+            \eq{\odv{T}{t} = \frac{T_0-T}{\tau}}
+        \end{formula}
+
+        \begin{formula}{nose-hoover}
+            \desc{Nosé-Hoover thermostat}{Control the temperature with by time stretching with an associated mass.\\Compliant with \absRef{c_ensemble}}{$s$ scaling factor, $Q$ associated "mass", $\mathcal{L}$ \absRef{lagrangian}, $g$ degrees of freedom}
+            \desc[german]{Nosé-Hoover Thermostat}{}{}
+            \begin{gather}
+                \d\tilde{t} = \tilde{s}\d t \\
+                \mathcal{L} = \sum_{I=1}^N \frac{1}{2} M_I \tilde{s}^2 v_i^2 - V(\tilde{\vecR}_1, \ldots, \tilde{\vecR}_I, \ldots, \tilde{\vecR}_N) + \frac{1}{2} Q \dot{\tilde{s}}^2 - g \kB T_0 \ln \tilde{s}
+            \end{gather}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Calculating observables}
+        \ger{Berechnung von Observablen}
+    ]{obs}
+        \begin{formula}{spectral_density}
+            \desc{Spectral density}{Wiener-Khinchin theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{$C$ \absRef{autocorrelation}}
+            \desc[german]{Spektraldichte}{Wiener-Khinchin Theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{}
+            \eq{S(\omega) = \int_{-\infty}^\infty \d\tau C(\tau) \e^{-\I\omega t} }
+        \end{formula}
+
+        \begin{formula}{vdos} \abbrLabel{VDOS}
+            \desc{Vibrational density of states (VDOS)}{}{$S_{v_i}$ velocity \secEqRef{spectral_density} of particle $I$}
+            \desc[german]{Vibrationszustandsdicht (VDOS)}{}{}
+            \eq{g(\omega) \sim \sum_{I=1}^N M_I S_{v_I}(\omega)}
+        \end{formula}

src/comp/comp.tex

@@ -0,0 +1,4 @@
+\Part[
+    \eng{Computational Physics}
+    \ger{Computergestützte Physik}
+]{comp}

src/comp/est.tex

@@ -0,0 +1,289 @@
+\Section[
+    \eng{Electronic structure theory}
+    % \ger{}
+]{est}
+
+\begin{formula}{kinetic_energy}
+    \desc{Kinetic energy}{of species $i$}{$i$ = nucleons/electrons, $N$ number of particles, $m$ \qtyRef{mass}}
+    \desc[german]{Kinetische Energie}{von Spezies $i$}{$i$ = Nukleonen/Elektronen, $N$ Teilchenzahl, $m$ \qtyRef{mass}}
+    \eq{\hat{T}_i &= -\sum_{n=1}^{N_i} \frac{\hbar^2}{2 m_i} \vec{\nabla}^2_n}
+\end{formula}
+\begin{formula}{potential_energy}
+    \desc{Electrostatic potential}{between species $i$ and $j$}{$i,j$ = nucleons/electrons, $r$ particle position, $Z_i$ charge of species $i$, \ConstRef{charge}}
+    \desc[german]{Elektrostatisches Potential}{zwischen Spezies $i$ und $j$}{}
+    \eq{\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j e^2}{\abs{\vecr_k - \vecr_l}}}
+\end{formula}
+\begin{formula}{hamiltonian}
+    \desc{Electronic structure Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:est:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
+    \eq{\hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe} + V_{\txn \leftrightarrow \txn}}
+\end{formula}
+\begin{formula}{mean_field}
+    \desc{Mean field approximation}{Replaces 2-particle operator by 1-particle operator}{Example for Coulomb interaction between many electrons}
+    \desc[german]{Molekularfeldnäherung}{Ersetzt 2-Teilchen Operator durch 1-Teilchen Operator}{Beispiel für Coulomb Wechselwirkung zwischen Elektronen}
+    \eq{
+        \frac{1}{2}\sum_{i\neq j} \frac{e^2}{\abs{\vec{r}_i - \vec{r}_j}} \approx \sum_{i} V_\text{eff}(\vec{r}_i)
+    }
+\end{formula}
+
+
+\Subsection[
+    \eng{Tight-binding}
+    \ger{Modell der stark gebundenen Elektronen / Tight-binding}
+]{tb}
+    \begin{formula}{assumptions}
+        \desc{Assumptions}{}{}
+        \desc[german]{Annahmen}{}{}
+        \ttxt{
+            \eng{
+                \begin{itemize}
+                    \item Atomic wave functions are localized \Rightarrow Small overlap, interaction cutoff
+                \end{itemize}
+            }
+        }
+    \end{formula}
+    \begin{formula}{hamiltonian}
+        \desc{Tight-binding Hamiltonian}{in second quantized form}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} create/destory an electron on site $i$, $\epsilon_i$ on-site energy, $t_{i,j}$ hopping amplitude, usually $\epsilon$ and $t$ are determined from experiments or other methods}
+        \desc[german]{Tight-binding Hamiltonian}{in zweiter Quantisierung}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} erzeugen/vernichten ein Elektron auf Platz $i$, $\epsilon_i$ on-site Energie, $t_{i,j}$ hopping Amplitude, meist werden $\epsilon$ und $t$ aus experimentellen Daten oder anderen Methoden bestimmt}
+        \eq{\hat{H} = \sum_i \epsilon_i \hat{a}_i^\dagger \hat{a}_i - \sum_{i,j} t_{i,j} \left(\hat{a}_i^\dagger \hat{a}_j + \hat{a}_j^\dagger \hat{a}_i\right)}
+    \end{formula}
+    
+
+
+\Subsection[
+    \eng{Density functional theory (DFT)}
+    \ger{Dichtefunktionaltheorie (DFT)}
+]{dft}
+    \abbrLink{dft}{DFT}
+    \Subsubsection[
+        \eng{Hartree-Fock}
+        \ger{Hartree-Fock}
+    ]{hf}
+        \begin{formula}{description}
+            \desc{Description}{}{}
+            \desc[german]{Beschreibung}{}{}
+            \begin{ttext}
+                \eng{
+                    \begin{itemize}
+                        \item Assumes wave functions are \fqEqRef{qm:other:slater_det} \Rightarrow Approximation
+                        \item \fqEqRef{comp:est:mean_field} theory obeying the Pauli principle
+                        \item Self-interaction free: Self interaction is cancelled out by the Fock-term
+                    \end{itemize}
+                }
+            \end{ttext}
+        \end{formula}
+        \begin{formula}{equation}
+            \desc{Hartree-Fock equation}{}{
+                $\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
+                $\hat{T}$ kinetic electron energy,
+                $\hat{V}_{\text{en}}$ electron-nucleus attraction,
+                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential},
+            }
+            \desc[german]{Hartree-Fock Gleichung}{}{
+                $\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
+                $\hat{T}$ kinetische Energie der Elektronen,
+                $\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
+                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}
+            }
+            \eq{
+                \left(\hat{T} + \hat{V}_{\text{en}} + \hat{V}_{\text{HF}}^\xi\right)\varphi_\xi(x) = \epsilon_\xi \varphi_\xi(x)
+            }
+        \end{formula}
+        \begin{formula}{potential}
+            \desc{Hartree-Fock potential}{}{}
+            \desc[german]{Hartree Fock Potential}{}{}
+            \eq{
+                V_{\text{HF}}^\xi(\vecr) = 
+                \sum_{\vartheta} \int \d x' 
+                \frac{e^2}{\abs{\vecr - \vecr'}}
+                \left(
+                    \underbrace{\abs{\varphi_\xi(x')}^2}_{\text{Hartree-Term}}
+                    - \underbrace{\frac{\varphi_{\vartheta}^*(x') \varphi_{\xi}(x') \varphi_{\vartheta}(x)}{\varphi_\xi(x)}}_{\text{Fock-Term}}
+                \right)
+            }
+        \end{formula}
+        \begin{formula}{scf}
+            \desc{Self-consistent field cycle}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{
+                \eng{
+                    \begin{enumerate}
+                        \item Initial guess for $\psi$
+                        \item Solve SG for each particle
+                        \item Make new guess for $\psi$
+                    \end{enumerate}
+                }
+            }
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Hohenberg-Kohn Theorems}
+        \ger{Hohenberg-Kohn Theoreme}
+    ]{hk}
+        \begin{formula}{hk1}
+            \desc{Hohenberg-Kohn theorem (HK1)}{}{}
+            \desc[german]{Hohenberg-Kohn Theorem (HK1)}{}{}
+            \ttxt{
+                \eng{For any system of interacting electrons, the ground state electron density $n(\vecr)$ determines $\hat{V}_\text{ext}$ uniquely up to a trivial constant. }
+                \ger{Die Elektronendichte des Grundzustandes $n(\vecr)$ bestimmt ein einzigartiges $\hat{V}_{\text{ext}}$ eines Systems aus interagierenden Elektronen bis auf eine Konstante.}
+            }
+        \end{formula}
+        \begin{formula}{hk2}
+            \desc{Hohenberg-Kohn theorem (HK2)}{}{}
+            \desc[german]{Hohenberg-Kohn Theorem (HK2)}{}{}
+            \ttxt{
+                \eng{Given the energy functional $E[n(\vecr)]$, the ground state density and energy can be obtained variationally. The density that minimizes the total energy is the ecxact ground state density. }
+                \ger{Für ein Energiefunktional $E[n(\vecr)]$ kann die Grundzustandsdichte und Energie durch systematische Variation bestimmt werden. Die Dichte, welche die Gesamtenergie minimiert ist die exakte Grundzustandsichte. }
+            }
+        \end{formula}
+
+        \begin{formula}{density}
+            \desc{Ground state electron density}{}{}
+            \desc[german]{Grundzustandselektronendichte}{}{}
+            \eq{n(\vecr) = \Braket{\psi_0|\sum_{i=1}^N \delta(\vecr-\vecr_i)|\psi_0}}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Kohn-Sham DFT}
+        \ger{Kohn-Sham DFT}
+    ]{ks}
+        \abbrLink{ksdft}{KS-DFT}
+        \begin{formula}{map}
+            \desc{Kohn-Sham map}{}{}
+            \desc[german]{Kohn-Sham Map}{}{}
+            \ttxt{
+                \eng{Maps fully interacting system of electrons to a system of non-interacting electrons with the same ground state density $n^\prime(\vecr) = n(\vecr)$}
+            }
+            \eq{n(\vecr) = \sum_{i=1}^N \abs{\phi_i(\vecr)}^2}
+        \end{formula}
+        \begin{formula}{functional}
+            \desc{Kohn-Sham functional}{}{$T_\text{KS}$ kinetic enery, $V_\text{ext}$ external potential, $E_\txH$ \hyperref[f:comp:est:dft:hf:potential]{Hartree term}, $E_\text{XC}$ \fqEqRef{comp:est:dft:xc:xc}}
+            \desc[german]{Kohn-Sham Funktional}{}{}
+            \eq{E_\text{KS}[n(\vecr)] = T_\text{KS}[n(\vecr)] + V_\text{ext}[n(\vecr)] + E_\text{H}[n(\vecr)] + E_\text{XC}[n(\vecr)] }
+        \end{formula}   
+
+        \begin{formula}{equation}
+            \desc{Kohn-Sham equation}{Exact single particle \abbrRef{schroedinger_equation} (though often exact $E_\text{XC}$ is not known)\\ Solving it uses up a large portion of supercomputer resources}{$\phi_i^\text{KS}$ KS orbitals, $\int\d^3r v_\text{ext}(\vecr)n(\vecr)=V_\text{ext}[n(\vecr)]$}
+            \desc[german]{Kohn-Sham Gleichung}{Exakte Einteilchen-\abbrRef{schroedinger_equation} (allerdings ist das exakte $E_\text{XC}$ oft nicht bekannt)\\ Die Lösung der Gleichung macht einen großen Teil der Supercomputer Ressourcen aus}{}
+            \begin{multline}
+                \biggr\{
+                    -\frac{\hbar^2\nabla^2}{2m} 
+                    + v_\text{ext}(\vecr)
+                    + e^2 \int\d^3 \vecr^\prime \frac{n(\vecr^\prime)}{\abs{\vecr-\vecr^\prime}} \\
+                    + \pdv{E_\txX[n(\vecr)]}{n(\vecr)} 
+                    + \pdv{E_\txC[n(\vecr)]}{n(\vecr)}
+                \biggr\} \phi_i^\text{KS}(\vecr) =\\
+                = \epsilon_i^\text{KS} \phi_i^\text{KS}(\vecr)
+            \end{multline}
+        \end{formula}
+        \begin{formula}{scf}
+            \desc{Self-consistent field cycle for Kohn-Sham}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{
+                \itemsep=\parsep
+                \eng{
+                    \begin{enumerate}
+                        \item Initial guess for $n(\vecr)$
+                        \item Calculate effective potential $V_\text{eff}$
+                        \item Solve \fqEqRef{comp:est:dft:ks:equation}
+                        \item Calculate density $n(\vecr)$
+                        \item Repeat 2-4 until self consistent
+                    \end{enumerate}
+                }
+            }
+        \end{formula}
+
+        \Subsubsection[
+            \eng{Exchange-Correlation functionals}
+            \ger{Exchange-Correlation Funktionale}
+        ]{xc}
+            \begin{formula}{xc}
+                \desc{Exchange-Correlation functional}{}{}
+                \desc[german]{Exchange-Correlation Funktional}{}{}
+                \eq{ E_\text{XC}[n(\vecr)] = \Braket{\hat{T}} - T_\text{KS}[n(\vecr)] + \Braket{\hat{V}_\text{int}} - E_\txH[n(\vecr)] }
+                \ttxt{\eng{
+                    Accounts for:
+                    \begin{itemize}
+                            \item Kinetic energy difference between interaction and non-interacting system
+                            \item Exchange energy due to Pauli principle
+                            \item Correlation energy due to many-body Coulomb interaction (not accounted for in mean field Hartree term $E_\txH$)
+                    \end{itemize}
+                }}
+            \end{formula}
+            \begin{formula}{lda}
+                \desc{Local density approximation (LDA)}{Simplest DFT functionals}{$\epsilon_\txX$ calculated exchange energy from \hyperref[f:comp:qmb:models:heg]{HEG model}, $\epsilon_\txC$ correlation energy calculated with \fqSecRef{comp:qmb:methods:qmonte-carlo}}
+                \desc[german]{}{}{}
+                \abbrLabel{LDA}
+                \eq{E_\text{XC}^\text{LDA}[n(\vecr)] = \int \d^3r\,n(r) \Big[\epsilon_\txX[n(\vecr)] + \epsilon_\txC[n(\vecr)]\Big]}
+            \end{formula}
+
+            \begin{formula}{gga}
+                \desc{Generalized gradient approximation (GGA)}{}{$\epsilon_\txX$ calculated exchange energy from \hyperref[f:comp:qmb:models:heg]{HEG model}, $F_\text{XC}$ function containing exchange-correlation energy dependency on $n$ and $\Grad n$}
+                \desc[german]{}{}{}
+                \abbrLabel{GGA}
+                \eq{E_\text{XC}^\text{GGA}[n(\vecr)] = \int \d^3r\,n(r) \epsilon_\txX[n(\vecr)]\,F_\text{XC}[n(\vecr), \Grad n(\vecr)]}
+            \end{formula}
+
+            \TODO{PBE}
+
+            \begin{formula}{hybrid}
+                \desc{Hybrid functionals}{}{}
+                \desc[german]{Hybride Funktionale}{}{$\alpha$ mixing paramter, $E_\txX$ exchange energy, $E_\txC$ correlation energy}
+                \eq{\alpha E_\txX^\text{HF} + (1-\alpha) E_\txX^\text{GGA} + E_\txC^\text{GGA}}
+                \ttxt{\eng{
+                    Include \hyperref[f:comp:dft:hf:potential]{Fock term} (exact exchange) in other functional, like \abbrRef{gga}. Computationally expensive
+                }}
+
+            \end{formula}
+
+
+            \begin{formula}{range-separated-hybrid}
+                \desc{Range separated hyrid functionals (RSH)}{Here HSE as example}{$\alpha$ mixing paramter, $E_\txX$ exchange energy, $E_\txC$ correlation energy}
+                % \desc[german]{}{}{}
+                \begin{gather}
+                    \frac{1}{r} = \frac{\erf(\omega r)}{r} + \frac{\erfc{\omega r}}{r} \\
+                    E_\text{XC}^\text{HSE} = \alpha E_\text{X,SR}^\text{HF}(\omega) + (1-\alpha)E_\text{X,SR}^\text{GGA}(\omega) + E_\text{X,LR}^\text{GGA}(\omega) + E_\txC^\text{GGA}
+                \end{gather}
+                \separateEntries
+                \ttxt{\eng{
+                        Use \abbrRef{gga} and \hyperref[comp:est:dft:hf:potential]{Fock} exchange for short ranges (SR) and only \abbrRef{GGA} for long ranges (LR).
+                        \abbrRef{GGA} correlation is always used. Useful when dielectric screening reduces long range interactions, saves computational cost.
+                }}
+            \end{formula}   
+
+            \begin{formula}{comparison}
+                \desc{Comparison of DFT functionals}{}{}
+                \desc[german]{Vergleich von DFT Funktionalen}{}{}
+                \begin{tabular}{l|c}
+                    \hyperref[f:comp:est:dft:hf:potential]{Hartree-Fock} & only exchange, no correlation \Rightarrow upper bound of GS energy \\
+                    \abbrRef{lda} & understimates e repulsion \Rightarrow Overbinding \\
+                    \abbrRef{gga} & underestimate band gap \\
+                    hybrid & underestimate band gap
+                \end{tabular}
+            \end{formula}
+    
+    \Subsubsection[
+        \eng{Basis sets}
+        \ger{Basis-Sets}
+    ]{basis}
+        \begin{formula}{plane_wave}
+            \desc{Plane wave basis}{Plane wave ansatz in \fqEqRef{comp:est:dft:ks:equation}\\Good for periodic structures, allows computation parallelization over a sample points in the \abbrRef{brillouin_zone}}{}
+            \desc[german]{Ebene Wellen als Basis}{}{}
+            \eq{\sum_{\vecG^\prime} \left[\frac{\hbar^2 \abs{\vecG+\veck}^2}{2m} \delta_{\vecG,\vecG^\prime} + V_\text{eff}(\vecG-\vecG^\prime)\right] c_{i,\veck,\vecG^\prime} = \epsilon_{i,\veck} c_{i,\veck,\vecG}}
+        \end{formula}
+        \begin{formula}{plane_wave_cutoff}
+            \desc{Plane wave cutoff}{Number of plane waves included in the calculation must be finite}{}
+            % \desc[german]{}{}{}
+            \eq{E_\text{cutoff} = \frac{\hbar^2 \abs{\veck+\vecG}^2}{2m}}
+        \end{formula}
+
+    \Subsubsection[
+        \eng{Pseudo-Potential method}
+        \ger{Pseudopotentialmethode}
+    ]{pseudo}
+        \begin{formula}{ansatz}
+            \desc{Ansatz}{}{}
+            \desc[german]{Ansatz}{}{}
+            \ttxt{\eng{
+                Core electrons are absorbed into the potential since they do not contribute much to interesting properties.
+            }}
+        \end{formula}

src/comp/ml.tex

@@ -0,0 +1,84 @@
+\Section[
+    \eng{Machine-Learning}
+    \ger{Maschinelles Lernen}
+]{ml}
+    \Subsection[
+        \eng{Performance metrics}
+        \ger{Metriken zur Leistungsmessung}
+    ]{performance}
+        \eng[cp]{correct predictions}
+        \ger[cp]{richtige Vorhersagen}
+        \eng[fp]{false predictions}
+        \ger[fp]{falsche Vorhersagen}
+
+        \eng[y]{ground truth}
+        \eng[yhat]{prediction}
+        \ger[y]{Wahrheit}
+        \ger[yhat]{Vorhersage}
+
+        \begin{formula}{accuracy}
+            \desc{Accuracy}{}{}
+            \desc[german]{Genauigkeit}{}{}
+            \eq{a = \frac{\tgt{cp}}{\tgt{fp} + \tgt{cp}}}
+        \end{formula}
+        \TODO{is $n$ the nuber of predictions or the number of output features?}
+        \begin{formula}{mean_abs_error}
+            \desc{Mean absolute error (MAE)}{}{$y$ \gt{y}, $\hat{y}$ \gt{yhat}, $n$ ?}
+            \desc[german]{Mittlerer absoluter Fehler (MAE)}{}{}
+            \eq{\text{MAE} = \frac{1}{n} \sum_{i=1}^n \abs{y_i - \hat{y}_i}}
+        \end{formula}
+        \begin{formula}{root_mean_square_error}
+            \desc{Root mean squared error (RMSE)}{}{$y$ \gt{y}, $\hat{y}$ \gt{yhat}, $n$ ?}
+            \desc[german]{Standardfehler der Regression}{Quadratwurzel des mittleren quadratischen Fehlers (RSME)}{}
+            \eq{\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \left(y_i - \hat{y}_i\right)^2}}
+        \end{formula}
+
+    \Subsection[
+        \eng{Regression}
+        \ger{Regression}
+    ]{reg}
+        \Subsubsection[
+            \eng{Linear Regression}
+            \ger{Lineare Regression}
+        ]{linear}
+            \begin{formula}{eq}
+                \desc{Linear regression}{Fits the data under the assumption of \hyperref[f:math:pt:distributions:cont:normal]{normally distributed errors}}{$\mat{x}\in\R^{N\times M}$ input data, $\mat{y}\in\R^{N\times L}$ output data, $\mat{b}$ bias, $\vec{W}$ weights, $N$ samples, $M$ features, $L$ output variables}
+                \desc[german]{Lineare Regression}{Fitted Daten unter der Annahme \hyperref[f:math:pt:distributions:cont:normal]{normalverteilter Fehler}}{}
+                \eq{\mat{y} = \mat{b} + \mat{x} \cdot \vec{W}}
+            \end{formula}
+            \begin{formula}{design_matrix}
+                \desc{Design matrix}{Stack column of ones to the feature vector\\Useful when $b$ is scalar}{$x_{ij}$ feature $j$ of sample $i$}
+                \desc[german]{Designmatrix Ansatz}{}{}
+                \eq{
+                    \mat{X} = \begin{pmatrix} 1 & x_{11} & \ldots & x_{1M} \\  \vdots & \vdots & \vdots & \vdots \\ 1 & x_{N1} & \ldots & x_{NM} \end{pmatrix} 
+                }
+            \end{formula}       
+            \begin{formula}{scalar_bias}
+                \desc{Linear regression with scalar bias}{Using the design matrix, the scalar is absorbed into the weight vector}{$\mat{y}$ output data, $\mat{X}$ \fqEqRef{comp:ml:reg:design_matrix}, $\vec{W}$ weights}
+                \desc[german]{Lineare Regression mit skalarem Bias}{Durch die Designmatrix wird der Bias in den Gewichtsvektor absorbiert}{}
+                \eq{\mat{y} = \mat{X} \cdot \vec{W}}
+            \end{formula}
+            \begin{formula}{normal_equation}
+                \desc{Normal equation}{Solves \fqEqRef{comp:ml:reg:linear:scalar_bias}}{$\mat{y}$ output data, $\mat{X}$ \fqEqRef{comp:ml:reg:linear:design_matrix}, $\vec{W}$ weights}
+                \desc[german]{Normalengleichung}{Löst \fqEqRef{comp:ml:reg:linear:scalar_bias}}{}
+                \eq{\vec{W} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}}
+            \end{formula}
+
+        \Subsubsection[
+            \eng{Ridge regression}
+            \ger{Ridge Regression}
+        ]{ridge}
+            \TODO{ridge reg, Kernel ridge reg, gaussian process reg}
+    % \Subsection[
+    %     \eng{Bayesian probability theory}
+    %     % \ger{}
+    % ]{bayesian}
+        
+
+
+    \Subsection[
+        \eng{Gradient descent}
+        \ger{Gradientenverfahren}
+    ]{gd}
+        \TODO{in lecture 30 CMP}
+

src/comp/qmb.tex

@@ -0,0 +1,39 @@
+\Section[
+    \eng{Quantum many-body physics}
+    \ger{Quanten-Vielteilchenphysik}
+]{qmb}
+    \Subsection[
+        \eng{Quantum many-body models}
+        \ger{Quanten-Vielteilchenmodelle}
+    ]{models}
+        \begin{formula}{heg}
+            \desc{Homogeneous electron gas (HEG)}{Also "Jellium"}{}
+            % \desc[german]{}{}{}
+            \ttxt{
+                \eng{Both positive (nucleus) and negative (electron) charges are distributed uniformly.}
+            }
+        \end{formula}
+        
+    \Subsection[
+        \eng{Methods}
+        \ger{Methoden}
+    ]{methods}
+        \Subsubsection[
+            \eng{Quantum Monte-Carlo}
+            \ger{Quantum Monte-Carlo}
+        ]{qmonte-carlo}
+        
+
+\TODO{TODO}
+    \Subsection[
+        \eng{Importance sampling}
+        \ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
+    ]{importance_sampling}
+    \TODO{Monte Carlo}
+
+    \Subsection[
+        \eng{Matrix product states}
+        \ger{Matrix Produktzustände}
+    ]{mps}
+
+

src/condensed_matter.tex

@@ -1,397 +0,0 @@
-\Part[
-    \eng{Condensed matter physics}
-    \ger{Festkörperphysik}
-    ]{cm}
-\Section[
-    \eng{Bravais lattice}
-    \ger{Bravais-Gitter}
-    ]{bravais}
-
-    % \begin{ttext}
-    %     \eng{
-
-    %     }
-    %     \ger{
-
-    %     }
-    % \end{ttext}
-
-    \eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
-    \ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}
-
-    \eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
-    \ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}
-
-    \Eng[lattice_system]{Lattice system}
-    \Ger[lattice_system]{Gittersystem}
-    \Eng[crystal_family]{Crystal system}
-    \Ger[crystal_family]{Kristall-system}
-    \Eng[point_group]{Point group}
-    \Ger[point_group]{Punktgruppe}
-    \eng[bravais_lattices]{Bravais lattices}
-    \ger[bravais_lattices]{Bravais Gitter}
-
-    \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
-    \renewcommand\tabularxcolumn[1]{m{#1}}
-    \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
-    \begin{table}[H]
-        \centering
-        \caption{\gt{bravais_table2}}
-        \label{tab:bravais2}
-    
-        \begin{adjustbox}{width=\textwidth}
-        \begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
-            \hline
-            \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
-                                                 & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
-            \GT{monoclinic} (m) & $\text{C}_\text{2}$   & \bvimg{mp} & \\ \hline
-            \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
-            \GT{tetragonal} (t) & $\text{D}_\text{4}$   & \bvimg{tp} & \\ \hline
-            \GT{hexagonal} (h) & $\text{D}_\text{6}$    & \bvimg{hp} & \\ \hline
-        \end{tabularx}
-        \end{adjustbox}
-    \end{table}
-    
-
-
-    \begin{table}[H]
-        \centering
-        \caption{\gt{bravais_table3}}
-        \label{tab:bravais3}
-    
-        % \newcolumntype{g}{>{\columncolor[]{0.8}}}
-        \begin{adjustbox}{width=\textwidth}
-            % \begin{tabularx}{\textwidth}{|c|}
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            % \end{tabularx}
-            % \begin{tabular}{|c|}
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            % \end{tabular}
-            % \\
-        \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
-            \hline
-            \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
-                                                 & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
-            \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP}  &  &  &  \\  \hline
-            \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS}  &  &  \\ \hline
-            \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
-            \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} &  & \bvimg{tI} & \\ \hline
-            \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} &  &  & \\ \cline{2-7}
-             & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} &  &  & \\ \hline
-            \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} &  & \bvimg{cI} & \bvimg{cF} \\ \hline
-        \end{tabularx}
-        \end{adjustbox}
-    \end{table}
-    
-
-\Section[
-    \eng{Reciprocal lattice}
-    \ger{Reziprokes Gitter}
-    ]{reci}
-    \begin{ttext}
-        \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
-        \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
-    \end{ttext}
-
-    \begin{formula}{vectors}
-        \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
-        \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
-        \eq{
-            \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
-            \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
-            \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
-        }
-    \end{formula}
-
-    \Subsection[
-        \eng{Scattering processes}
-        \ger{Streuprozesse}
-        ]{scatter}
-        \begin{formula}{matthiessen}
-            \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{$\mu$ mobility, $\tau$ scattering time}
-            \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{$\mu$ Moblitiät, $\tau$ Streuzeit}
-            \eq{
-                \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
-                \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
-            }
-        \end{formula}
-    
-
-\Section[
-    \eng{Free electron gas}
-    \ger{Freies Elektronengase}
-]{free_e_gas}
-    \begin{ttext}
-        \eng{Assumptions: electrons can move freely and independent of each other.}
-        \ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.}
-    \end{ttext}
-
-    \begin{formula}{drift_velocity}
-        \desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity}
-        \desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit}
-        \eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}}
-    \end{formula}
-
-    \begin{formula}{mean_free_time}
-        \desc{Mean free time}{}{}
-        \desc[german]{Streuzeit}{}{}
-        \eq{\tau}
-    \end{formula}
-
-    \begin{formula}{mean_free_path}
-        \desc{Mean free path}{}{}
-        \desc[german]{Mittlere freie Weglänge}{}{}
-        \eq{\ell = \braket{v} \tau}
-    \end{formula}
-
-    \begin{formula}{mobility}
-        \desc{Electrical mobility}{}{$q$ charge, $m$ mass}
-        \desc[german]{Beweglichkeit}{}{$q$ Ladung, $m$ Masse}
-        \eq{\mu = \frac{q \tau}{m}}
-    \end{formula}
-
-    \Subsection[
-        \eng{Drude model}
-        \ger{Drude-Modell}
-        ]{drude}
-        \begin{ttext}
-            \eng{Classical model describing the transport properties of electrons in materials (metals):
-                The material is assumed to be an ion lattice and with freely moving electrons (electron gas). The electrons are 
-                accelerated by an electric field and decelerated through collisions with the lattice ions.
-                The model disregards the Fermi-Dirac partition of the conducting electrons.
-            }
-            \ger{Ein klassisches Model zur Beschreibung der Transporteigenschaften von Elektronen in (v.a.) Metallen:
-                Der Festkörper wird als Ionenkristall mit frei beweglichen Elektronen (Elektronengas). 
-                Die Elektronen werden durch ein Elektrisches Feld $E$ beschleunigt und durch Stöße mit den Gitterionen gebremst.
-                Das Modell vernachlässigt die Fermi-Dirac Verteilung der Leitungselektronen.
-            }
-        \end{ttext}
-        \begin{formula}{motion}
-            \desc{Equation of motion}{}{$v$ electron speed, $\vec{v}_\text{D}$ drift velocity, $\tau$ mean free time between collisions}
-            \desc[german]{Bewegungsgleichung}{}{$v$ Elektronengeschwindigkeit, $\vec{v}_\text{D}$ Driftgeschwindigkeit, $\tau$ Stoßzeit}
-            \eq{\masse \odv{\vec{v}}{t} + \frac{\masse}{\tau} \vec{v}_\text{D} = -e \vec{E}}
-        \end{formula}
-        \begin{formula}{current_density}
-            \desc{Current density}{Ohm's law}{$n$ charge particle density}
-            \desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte}
-            \eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{E}}
-        \end{formula}
-        \begin{formula}{conductivity}
-            \desc{Drude-conductivity}{}{}
-            \desc[german]{Drude-Leitfähigkeit}{}{}
-            \eq{\sigma = \frac{\vec{j}}{\vec{E}} = \frac{e^2 \tau n}{\masse} = n e \mu}
-        \end{formula}
-
-    \Subsection[
-        \eng{Sommerfeld model}
-        \ger{Sommerfeld-Modell}
-        ]{sommerfeld}
-        \begin{ttext}
-            \eng{Assumes a gas of free fermions underlying the pauli-exclusion principle. Only electrons in an energy range of $\kB T$ around the Fermi energy $\EFermi$ participate in scattering processes.}
-            \ger{Annahme eines freien Fermionengases, welches dem Pauli-Prinzip unterliegt. Nur Elektronen in einem Energiebereich von $\kB T$ um die Fermi Energe $\EFermi$ nehmen an Streuprozessen teil.}
-        \end{ttext}
-        \begin{formula}{current_density}
-            \desc{Current density}{}{}
-            \desc[german]{Stromdichte}{}{}
-            \eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
-        \end{formula}
-        \TODO{The formula for the conductivity is the same as in the drude model?}
-
-    \Subsection[
-        \eng{2D electron gas}
-        \ger{2D Elektronengas}
-        ]{2deg}
-
-        \begin{ttext}
-            \eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
-            \ger{
-                Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird.
-            }
-        \end{ttext}
-        \begin{formula}{confinement_energy}
-            \desc{Confinement energy}{Raises ground state energy}{}
-            \desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{}
-            \eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}}
-        \end{formula}
-
-        \Eng[plain_wave]{plain wave}
-        \Ger[plain_wave]{ebene Welle}
-        \begin{formula}{energy}
-            \desc{Energy}{}{}
-            \desc[german]{Energie}{}{}
-            \eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}}
-        \end{formula}
-
-    \Subsection[
-        \eng{1D electron gas / quantum wire}
-        \ger{1D Eleltronengas / Quantendraht}
-        ]{1deg}
-
-        \begin{formula}{energy}
-            \desc{Energy}{}{}
-            \desc[german]{Energie}{}{}
-            \eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2}
-        \end{formula}
-        
-    \Subsection[
-        \eng{0D electron gas / quantum dot}
-        \ger{0D Elektronengase / Quantenpunkt}
-        ]{0deg}
-
-        \TODO{TODO}
-
-\Section[
-    \eng{Measurement techniques}
-    \ger{Messtechniken}
-]{meas}
-    \Subsection[
-        \eng{ARPES}
-        \ger{ARPES}
-        ]{arpes}
-        what?
-        in?
-        how?
-        plot
-
-    \Subsection[
-        \eng{Scanning probe microscopy SPM}
-        \ger{Rastersondenmikroskopie (SPM)}
-        ]{spm}
-        \begin{ttext}
-            \eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
-            \ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
-        \end{ttext}
-
-        \Eng[name]{Name}
-        \Ger[name]{Name}
-        \Eng[application]{Application}
-        \Ger[application]{Anwendung}
-
-
-        \begin{minipagetable}{amf}
-            \entry{name}{
-                \eng{Atomic force microscopy (AMF)}
-                \ger{Atomare Rasterkraftmikroskopie (AMF)}
-            }
-            \entry{application}{
-                \eng{Surface stuff}
-                \ger{Oberflächenzeug}
-            }
-            \entry{how}{
-                \eng{With needle}
-                \ger{Mit Nadel}
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
-                \caption{\cite{Bian2021}}
-            \end{figure}
-        \end{minipage}
-
-
-        \begin{minipagetable}{stm}
-            \entry{name}{
-                \eng{Scanning tunneling microscopy (STM)}
-                \ger{Rastertunnelmikroskop (STM)}
-            }
-            \entry{application}{
-                \eng{Surface stuff}
-                \ger{Oberflächenzeug}
-            }
-            \entry{how}{
-                \eng{With TUnnel}
-                \ger{Mit TUnnel}
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=0.8\textwidth]{img/cm_stm.pdf}
-                \caption{\cite{Bian2021}}
-            \end{figure}
-        \end{minipage}
-
-\Section[
-    \eng{Fabrication techniques}
-    \ger{Herstellungsmethoden}
-    ]{fab}
-    \begin{minipagetable}{cvd}
-        \entry{name}{
-            \eng{Chemical vapor deposition (CVD)}
-            \ger{Chemische Gasphasenabscheidung (CVD)}
-        }
-        \entry{how}{
-            \eng{
-                A substrate is exposed to volatile precursors, which react and/or decompose on the heated substrate surface to produce the desired deposit.
-                By-products are removed by gas flow through the chamber.
-            }
-            \ger{
-                An der erhitzten Oberfläche eines Substrates wird aufgrund einer chemischen Reaktion mit einem Gas eine Feststoffkomponente abgeschieden.
-                Nebenprodukte werden durch den Gasfluss durch die Kammer entfernt.
-            }
-        }
-        \entry{application}{
-            \eng{
-                \begin{itemize}
-                    \item Polysilicon \ce{Si}
-                    \item Silicon dioxide \ce{SiO_2}     
-                    \item Graphene
-                    \item Diamond
-                \end{itemize}
-            }
-            \ger{
-                \begin{itemize}
-                    \item Poly-silicon \ce{Si}
-                    \item Siliziumdioxid \ce{SiO_2}     
-                    \item Graphen
-                    \item Diamant
-                \end{itemize}
-            }
-        }
-    \end{minipagetable}
-    \begin{minipage}{0.5\textwidth}
-        \centering
-        \includegraphics[width=\textwidth]{img/cm_cvd_english.pdf}
-    \end{minipage}
-
-
-    \Subsection[
-        \eng{Epitaxy}
-        \ger{Epitaxie}
-        ]{epitaxy}
-        \begin{ttext}
-            \eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
-            \ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
-        \end{ttext}
-
-        \begin{minipagetable}{mbe}
-            \entry{name}{
-                \eng{Molecular Beam Epitaxy (MBE)}
-                \ger{Molekularstrahlepitaxie (MBE)}
-            } 
-            \entry{how}{
-                \eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
-                \ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
-            }
-            \entry{application}{
-                \eng{
-                    \begin{itemize}
-                        \item Gallium arsenide \ce{GaAs}
-                    \end{itemize}
-                    \TODO{Link to GaAs}
-                }
-                \ger{
-                    \begin{itemize}
-                        \item Galliumarsenid \ce{GaAs}
-                    \end{itemize}
-                }
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \centering
-            \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
-        \end{minipage}

src/constants.tex

@@ -0,0 +1,54 @@
+\Section[
+    \eng{Constants}
+    \ger{Konstanten}
+]{constants}
+    \begin{formula}{planck}
+        \desc{Planck Constant}{}{}
+        \desc[german]{Plancksches Wirkumsquantum}{}{}
+        \constant{h}{def}{
+            \val{6.62607015\cdot 10^{-34}}{\joule\s}
+            \val{4.135667969\dots\xE{-15}}{\eV\s}
+        }
+    \end{formula}
+
+    \begin{formula}{universal_gas}
+        \desc{Universal gas constant}{Proportionality factor for ideal gases}{\ConstRef{avogadro}, \ConstRef{boltzmann}}
+        \desc[german]{Universelle Gaskonstante}{Proportionalitätskonstante für ideale Gase}{}
+        \constant{R}{def}{
+            \val{8.31446261815324}{\joule\per\mol\kelvin}
+            \val{\NA \cdot \kB}{}
+        }
+    \end{formula}
+
+    \begin{formula}{avogadro}
+        \desc{Avogadro constant}{Number of molecules per mole}{}
+        \desc[german]{Avogadro-Konstante}{Anzahl der Moleküle pro mol}{}
+        \constant{\NA}{def}{
+            \val{6.02214076 \xE{23}}{1\per\mole}
+        }
+    \end{formula}
+
+    \begin{formula}{boltzmann}
+        \desc{Boltzmann constant}{Temperature-Energy conversion factor}{}
+        \desc[german]{Boltzmann-Konstante}{Temperatur-Energie Umrechnungsfaktor}{}
+        \constant{\kB}{def}{
+            \val{1.380649 \xE{-23}}{\joule\per\kelvin}
+        }
+    \end{formula}
+
+    \begin{formula}{faraday}
+        \desc{Faraday constant}{Electric charge of one mol of single-charged ions}{\ConstRef{avogadro}, \ConstRef{boltzmann}}
+        \desc[german]{Faraday-Konstante}{Elektrische Ladungs von einem Mol einfach geladener Ionen}{}
+        \constant{F}{def}{
+            \val{9.64853321233100184\xE{4}}{\coulomb\per\mol}
+            \val{\NA\,e}{}
+        }
+    \end{formula}
+
+    \begin{formula}{charge}
+        \desc{Unit charge}{}{}
+        \desc[german]{Elementarladung}{}{}
+        \constant{e}{def}{
+            \val{1.602176634\xE{-19}}{\coulomb}
+        }
+    \end{formula}

src/ed/ed.tex

@@ -0,0 +1,8 @@
+\Part[
+    \eng{Electrodynamics}
+    \ger{Elektrodynamik}
+]{ed}
+
+% pure electronic stuff in el
+% pure magnetic stuff in mag
+% electromagnetic stuff in em

src/ed/el.tex

@@ -0,0 +1,81 @@
+
+\Section[
+    \eng{Electric field}
+    \ger{Elektrisches Feld}
+]{el}
+\begin{formula}{electric_field}
+        \desc{Electric field}{Surrounds charged particles}{}
+        \desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{}
+        \quantity{\vec{\E}}{\volt\per\m=\kg\m\per\s^3\ampere}{v}
+    \end{formula}
+
+    \def\Epotential{\phi}
+    \begin{formula}{electric_scalar_potential}
+        \desc{Electric potential}{Work required to move a unit of charge between two points}{}
+        \desc[german]{Elektrisches Potential}{Benötigte Arbeit um eine Einheitsladung zwischen zwei Punkten zu bewegen}{}
+        \quantity{\Epotential}{\volt=\kg\m^2\per\s^3\ampere}{s}
+        \eq{\Epotential = -\int \vec{\E} \cdot\d\vecr}
+    \end{formula}
+
+    \begin{formula}{gauss_law}
+        \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface}
+        \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche}
+        \eq{\PhiE = \iint_S \vec{\E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}}
+    \end{formula}
+
+    \begin{formula}{permittivity}
+        \desc{Permittivity}{Dieletric function\\Electric polarizability of a dielectric material}{}
+        \desc[german]{Permitivität}{Dielektrische Konstante / Dielektrische Funktion\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{}
+        \quantity{\epsilon}{\ampere\s\per\volt\m=\farad\per\m=\coulomb\per\volt\m=C^2\per\newton\m^2=\ampere^2\s^4\per\kg\m^3}{}
+    \end{formula}
+    \begin{formula}{relative_permittivity}
+        \desc{Relative permittivity / Dielectric constant}{}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}}
+        \desc[german]{Relative Permittivität / Dielectric constant}{}{}
+        \eq{
+            \epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0}
+        }
+    \end{formula}
+
+    \begin{formula}{vacuum_permittivity}
+        \desc{Vacuum permittivity}{Electric constant}{}
+        \desc[german]{Vakuum Permittivität}{Elektrische Feldkonstante}{}
+        \constant{\epsilon_0}{exp}{
+            \val{8.8541878188(14)\xE{-1}}{\ampere\s\per\volt\m}
+        }
+    \end{formula}
+
+    \begin{formula}{electric_susceptibility}
+        \desc{Electric susceptibility}{Describes how polarized a dielectric material becomes when an electric field is applied}{$\epsilon_\txr$ \fqEqRef{ed:el:relative_permittivity}}
+        \desc[german]{Elektrische Suszeptibilität}{Beschreibt wie stark ein dielektrisches Material polarisiert wird, wenn ein elektrisches Feld angelegt wird}{}
+        \quantity{\chi_\txe}{}{s}
+        \eq{
+            \epsilon_\txr = 1 + \chi_\txe
+        }
+    \end{formula}
+    \begin{formula}{dielectric_polarization_density}
+        \desc{Dielectric polarization density}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_susceptibility}, \QtyRef{electric_field}}
+        \desc[german]{Dielektrische Polarisationsdichte}{}{}
+        \quantity{\vec{P}}{\coulomb\per\m^2}{v}
+        \eq{\vec{P} = \epsilon_0 \chi_\txe \vec{\E}}
+    \end{formula}
+
+    \begin{formula}{electric_displacement_field}
+        \desc{Electric displacement field}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_field}, \QtyRef{dielectric_polarization_density}}
+        \desc[german]{Elektrische Flussdichte / dielektrische Verschiebung}{}{}
+        \quantity{\vec{D}}{\coulomb\per\m^2=\ampere\s\per\m^2}{v}
+        \eq{\vec{D} = \epsilon_0 \vec{\E} + \vec{P}}
+    \end{formula}
+
+    \begin{formula}{electric_flux}
+        \desc{Electric flux}{through area $\vec{A}$}{\QtyRef{electric_displacement_field}}
+        \desc[german]{Elektrischer Fluss}{durch die Fläche $\vec{A}$}{}
+        \eq{\Phi_\txE = \int_A \vec{D}\cdot \d \vec{A}}
+    \end{formula}
+
+    \begin{formula}{power}
+        \desc{Electric power}{}{$U$ \qtyRef{electric_scalar_potential}, \QtyRef{current}}
+        \desc[german]{Elektrische Leistung}{}{}
+        \eq{P_\text{el} = U\,I}
+    \end{formula}
+
+

src/ed/em.tex

@@ -0,0 +1,111 @@
+\Section[
+    \eng{Electromagnetism}
+    \ger{Elektromagnetismus}
+]{em}
+    \begin{formula}{speed_of_light}
+        \desc{Speed of light}{in the vacuum}{}
+        \desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
+        \constant{c}{exp}{
+            \val{299792458}{\m\per\s}
+        }
+    \end{formula}
+    \begin{formula}{vacuum_relations}
+        \desc{Vacuum permittivity - permeability relation}{\TODO{Does this have a name?}}{\ConstRef{vacuum_permittivity}, \ConstRef{magnetic_vacuum_permeability}, \ConstRef{speed_of_light}}
+        \desc[german]{Vakuum Permittivität - Permeabilität Beziehung}{}{}
+        \eq{
+            \epsilon_0 \mu_0 = \frac{1}{c^2}
+        }
+    \end{formula}
+
+    \begin{formula}{poisson_equation}
+        \desc{Poisson equation for electrostatics}{}{\QtyRef{charge_density}, \QtyRef{permittivity}, $\Phi$ Potential}
+        \desc[german]{Poisson Gleichung in der Elektrostatik}{}{}
+        \eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}}
+        \TODO{double check $\Phi$}
+    \end{formula}
+
+    \begin{formula}{poynting}
+        \desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field [$\si{\W\per\m^2}$]}{}
+        \desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes  [$\si{\W\per\m^2}$]}{}
+        \eq{\vec{S} = \vec{E} \times \vec{H}}
+    \end{formula}
+
+    \begin{formula}{electric_field}
+        \desc{Electric field}{}{\QtyRef{electric_field}, \QtyRef{electric_scalar_potential}, \QtyRef{magnetic_vector_potential}}
+        \desc[german]{Elektrisches Feld}{}{}
+        \eq{\vec{\E} = -\Grad\Epotential - \pdv{\vec{A}}{t}}
+    \end{formula}
+
+    \begin{formula}{hamiltonian}
+        \desc{Hamiltonian of a particle in an electromagnetic field}{In the \fqEqRef{ed:em:gauge:coulomb}}{\QtyRef{mass}, $\hat{p}$ \fqEqRef{qm:se:momentum_operator}, \QtyRef{charge}, \QtyRef{magnetic_vector_potential}, \ConstRef{speed_of_light}}
+        \desc[german]{Hamiltonian eines Teilchens im elektromagnetischen Feld}{In der \fqEqRef{ed:em:gauge:coulomb}}{}
+        \eq{
+            \hat{H} = \frac{1}{2m} \left[\hat{p} \ \frac{e \vec{A}}{c}\right]^2
+        }
+    \end{formula}
+
+
+    \Subsection[
+        \eng{Maxwell-Equations}
+        \ger{Maxwell-Gleichungen}
+    ]{Maxwell}
+        \begin{formula}{vacuum}
+            \desc{Vacuum}{microscopic formulation}{}
+            \desc[german]{Vakuum}{Mikroskopische Formulierung}{}
+            \eq{
+                \Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\
+                \Div \vec{B} &= 0 \\
+                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
+                \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t}
+            }
+        \end{formula}
+
+        \begin{formula}{material}
+            \desc{Matter}{Macroscopic formulation}{}
+            \desc[german]{Materie}{Makroskopische Formulierung}{}
+            \eq{
+                \Div \vec{D} &= \rho_\text{el} \\
+                \Div \vec{B} &= 0 \\
+                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
+                \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
+            }
+        \end{formula}
+
+
+        \Subsubsection[
+            \eng{Gauges}
+            \ger{Eichungen}
+        ]{gauge}
+            \begin{formula}{coulomb}
+                \desc{Coulomb gauge}{}{\QtyRef{magnetic_vector_potential}}
+                \desc[german]{Coulomb-Eichung}{}{}
+                \eq{
+                    \Div \vec{A}  = 0
+                }
+            \end{formula}
+
+
+        \TODO{Polarization}
+
+    \Subsection[
+        \eng{Induction}
+        \ger{Induktion}
+    ]{induction}
+        \begin{formula}{farady_law}
+            \desc{Faraday's law of induction}{}{}
+            \desc[german]{Faradaysche Induktionsgesetz}{}{}
+            \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
+        \end{formula}
+
+        \begin{formula}{lenz}
+            \desc{Lenz's law}{}{}
+            \desc[german]{Lenzsche Regel}{}{}
+            \ttxt{
+                \eng{
+                    Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux.
+                }
+                \ger{
+                    Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt.
+                }
+            }
+        \end{formula}

src/ed/mag.tex

@@ -0,0 +1,122 @@
+\Section[
+    \eng{Magnetic field}
+    \ger{Magnetfeld}
+]{mag}
+
+    \begin{formula}{magnetic_flux}
+        \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
+        \desc[german]{Magnetischer Fluss}{}{}
+        \quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
+        \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
+    \end{formula}
+
+    \begin{formula}{magnetic_flux_density}
+        \desc{Magnetic flux density}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}}
+        \desc[german]{Magnetische Flussdichte}{Definiert über \fqEqRef{ed:mag:lorentz}}{}
+        \quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{}
+        \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
+    \end{formula}
+
+    \begin{formula}{magnetic_vector_potential}
+        \desc{Magnetic vector potential}{}{}
+        \desc[german]{Magnetisches Vektorpotential}{}{}
+        \quantity{\vec{A}}{\tesla\m=\volt\s\per\m=\kg\m\per\s^2\ampere}{ievs}
+        \eq{\Rot\vec{A}(\vecr) = \vec{B}(\vecr)}
+    \end{formula}
+
+    \begin{formula}{magnetic_field_intensity}
+        \desc{Magnetic field intensity}{}{}
+        \desc[german]{Magnetische Feldstärke}{}{}
+        \quantity{\vec{H}}{\ampere\per\m}{vector}
+        \eq{
+            \vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M}
+        }
+    \end{formula}
+
+    \begin{formula}{lorentz}
+        \desc{Lorentz force law}{Force on charged particle}{}
+        \desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{}
+        \eq{
+            \vec{F} = q \vec{\E} + q \vec{v}\times\vec{B}
+        }
+    \end{formula}
+
+    \begin{formula}{magnetic_permeability}
+        \desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
+        \desc[german]{Magnetisch Permeabilität}{}{}
+        \quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
+        \eq{\mu=\frac{B}{H}}
+    \end{formula}
+    \begin{formula}{magnetic_vacuum_permeability}
+        \desc{Magnetic vauum permeability}{}{}
+        \desc[german]{Magnetische Vakuumpermeabilität}{}{}
+        \constant{\mu_0}{exp}{
+            \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2}
+        }
+    \end{formula}
+    \begin{formula}{relative_permeability}
+        \desc{Relative permeability}{}{}
+        \desc[german]{Realtive Permeabilität}{}{}
+        \eq{
+            \mu_\txr = \frac{\mu}{\mu_0}
+        }
+    \end{formula}
+
+    \begin{formula}{gauss_law}
+        \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
+        \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
+        \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
+    \end{formula}
+
+    \begin{formula}{magnetization}
+        \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{}
+        \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{}
+        \quantity{\vec{M}}{\ampere\per\m}{vector}
+        \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}}
+    \end{formula}
+
+    \begin{formula}{magnetic_moment}
+        \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{}
+        \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{}
+        \quantity{\vec{m}}{\ampere\m^2}{vector}
+    \end{formula}
+
+    \begin{formula}{angular_torque}
+        \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}}
+        \desc[german]{Drehmoment}{}{}
+        \eq{\vec{\tau} = \vec{m} \times \vec{B}}
+    \end{formula}
+
+    \begin{formula}{magnetic_susceptibility}
+        \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}}
+        \desc[german]{Suszeptibilität}{}{}
+        \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
+    \end{formula}
+
+
+
+
+    \Subsection[
+        \eng{Magnetic materials}
+        \ger{Magnetische Materialien}
+    ]{materials}
+        \begin{formula}{paramagnetism}
+            \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
+            \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
+        \end{formula}
+
+        \begin{formula}{diamagnetism}
+            \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
+            \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
+        \end{formula}
+
+        \begin{formula}{ferromagnetism}
+            \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
+            \eq{
+                \mu_\txr \gg 1
+            }
+        \end{formula}
+

src/ed/misc.tex

@@ -0,0 +1,141 @@
+% TODO move
+\Section[
+    \eng{Hall-Effect}
+    \ger{Hall-Effekt}
+    ]{hall}
+
+    \begin{formula}{cyclotron}
+        \desc{Cyclontron frequency}{}{}
+        \desc[german]{Zyklotronfrequenz}{}{}
+        \eq{\omega_\text{c} = \frac{e B}{\masse}}
+    \end{formula}
+    \TODO{Move}
+
+
+    \Subsection[
+        \eng{Classical Hall-Effect}
+        \ger{Klassischer Hall-Effekt}
+        ]{classic}
+        \begin{ttext}
+            \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
+            \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
+        \end{ttext}
+        \begin{formula}{voltage}
+            \desc{Hall voltage}{}{$n$ charge carrier density}
+            \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
+            \eq{U_\text{H} = \frac{I B}{ne d}}
+        \end{formula}
+
+        \begin{formula}{coefficient}
+            \desc{Hall coefficient}{Sometimes $R_\txH$}{}
+            \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
+            \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
+        \end{formula}
+
+        \begin{formula}{resistivity}
+            \desc{Resistivity}{}{}
+            \desc[german]{Spezifischer Widerstand}{}{}
+            \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
+        \end{formula}
+
+
+    \Subsection[
+        \eng{Integer quantum hall effect}
+        \ger{Ganzahliger Quantenhalleffekt}
+    ]{quantum}  
+
+        \begin{formula}{conductivity}
+            \desc{Conductivity tensor}{}{}
+            \desc[german]{Leitfähigkeitstensor}{}{}
+            \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+        \end{formula}
+
+        \begin{formula}{resistivity_tensor}
+            \desc{Resistivity tensor}{}{}
+            \desc[german]{Spezifischer Widerstands-tensor}{}{}
+            \eq{
+                \rho = \sigma^{-1}
+                % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+            }
+        \end{formula}
+
+        \begin{formula}{resistivity}
+            \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
+            \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
+            \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
+        \end{formula}
+
+        % \begin{formula}{qhe}
+        %     \desc{Integer quantum hall effect}{}{}
+        %     \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
+        %     \fig{img/qhe-klitzing.jpeg}
+        % \end{formula}
+
+        \begin{formula}{fqhe}
+            \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
+            \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
+            \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
+        \end{formula}
+
+        \begin{ttext}
+            \eng{
+                \begin{itemize}
+                    \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
+                    \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
+                    \item \textbf{Spin} (QSHE): spin currents instead of charge currents
+                    \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
+                \end{itemize}
+            }
+            \ger{
+                \begin{itemize}
+                    \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
+                    \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
+                    \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
+                    \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
+                \end{itemize}
+            }
+        \end{ttext}
+    
+
+    \TODO{sort}
+
+
+\Section[
+    \eng{Dipole-stuff}
+    \ger{Dipol-zeug}
+]{dipole}
+
+    \begin{formula}{poynting}
+        \desc{Dipole radiation Poynting vector}{}{}
+        \desc[german]{Dipolsrahlung Poynting-Vektor}{}{}
+        \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}}
+    \end{formula}
+
+    \begin{formula}{power}
+        \desc{Time-average power}{}{}
+        \desc[german]{Zeitlich mittlere Leistung}{}{}
+        \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
+    \end{formula}
+
+\Section[
+    \eng{misc}
+    \ger{misc}
+]{misc}
+    \begin{formula}{impedance_r}
+        \desc{Impedance of an ohmic resistor}{}{\QtyRef{resistance}}
+        \desc[german]{Impedanz eines Ohmschen Widerstands}{}{}
+        \eq{Z_{R} = R}
+    \end{formula}
+    \begin{formula}{impedance_c}
+        \desc{Impedance of a capacitor}{}{\QtyRef{capacity}, \QtyRef{angular_velocity}}
+        \desc[german]{Impedanz eines Kondensators}{}{}
+        \eq{Z_{C} = \frac{1}{\I\omega C}}
+    \end{formula}
+
+    \begin{formula}{impedance_l}
+        \desc{Impedance of an inductor}{}{\QtyRef{inductance}, \QtyRef{angular_velocity}}
+        \desc[german]{Impedanz eines Induktors}{}{}
+        \eq{Z_{L} = \I\omega L}
+    \end{formula}
+
+    \TODO{impedance addition for parallel / linear}

src/ed/optics.tex

@@ -0,0 +1,103 @@
+\Section[
+    \eng{Optics}
+    \ger{Optik}
+]{optics}
+    \begin{ttext}
+        \eng{Properties of light and its interactions with matter}
+        \ger{Ausbreitung von Licht und die Interaktion mit Materie}
+    \end{ttext}
+    \separateEntries
+
+    \begin{formula}{refraction_index}
+        \eng[cm]{speed of light in the medium}
+        \ger[cm]{Lichtgeschwindigkeit im Medium}
+        \desc{Refraction index}{}{\QtyRef{relative_permittivity}, \QtyRef{relative_permeability}, \ConstRef{speed_of_light}, $c_\txM$ \gt{cm}}
+        \desc[german]{Brechungsindex}{}{}
+        \quantity{\complex{n}}{}{s}
+        \eq{
+            \complex{n} = \nreal + i\ncomplex
+        }
+        \eq{
+            n = \sqrt{\epsilon_\txr \mu_\txr}
+        }
+        \eq{
+            n = \frac{c_0}{c_\txM}
+        }
+    \end{formula}
+
+    \TODO{what does the complex part of the dielectric function represent?}
+
+    \begin{formula}{refraction_index_real}
+        \desc{Real part of the refraction index}{}{}
+        \desc[german]{Reller Teil des Brechungsindex}{}{}
+        \quantity{\nreal}{}{s}
+    \end{formula}
+    \begin{formula}{refraction_index_complex}
+        \desc{Extinction coefficient}{Complex part of the refraction index}{\GT{sometimes} $\kappa$}
+        \desc[german]{Auslöschungskoeffizient}{Komplexer Teil des Brechungsindex}{}
+        \quantity{\ncomplex}{}{s}
+    \end{formula}
+
+    \begin{formula}{reflectivity}
+        \desc{Reflectio}{}{\QtyRef{refraction_index}}
+        % \desc[german]{}{}{}
+        \eq{
+            R = \abs{\frac{\complex{n}-1}{\complex{n}+1}}
+        }
+    \end{formula}
+
+    \begin{formula}{snell}
+        \desc{Snell's law}{}{$\nreal_i$ \qtyRef{refraction_index_real}, $\theta_i$ incidence angle (normal to the surface)}
+        \desc[german]{Snelliussches Brechungsgesetz}{}{$n_i$ \qtyRef{refraction_index}, $\theta_i$ Einfallswinkel (normal zur Fläche)}
+        \eq{\nreal_1 \sin\theta_1 = \nreal_2\sin\theta_2}
+    \end{formula}
+
+    \begin{formula}{group_velocity}
+        \desc{Group velocity}{Velocity with which the envelope of a wave propagates through space}{\QtyRef{angular_frequency}, \QtyRef{angular_wavenumber}}
+        \desc[german]{Gruppengeschwindigkeit}{Geschwindigkeit, mit sich die Einhülende einer Welle ausbreitet}{}
+        \eq{
+            v_\txg \equiv \pdv{\omega}{k}
+        }
+    \end{formula}
+    \begin{formula}{phase_velocity}
+        \desc{Phase velocity}{Velocity with which a wave propagates through a medium}{\QtyRef{angular_frequency}, \QtyRef{angular_wavenumber}, \QtyRef{wavelength}, \QtyRef{time_period}}
+        \desc[german]{Phasengeschwindigkeit}{Geschwindigkeit, mit der sich eine Welle im Medium ausbreitet}{}
+        \eq{
+            v_\txp = \frac{\omega}{k} = \frac{\lambda}{T}
+        }
+    \end{formula}
+
+    \begin{formula}{absorption_coefficient}
+        \desc{Absorption coefficient}{Intensity reduction while traversing a medium, not necessarily by energy transfer to the medium}{\QtyRef{refraction_index_complex}, \ConstRef{speed_of_light}, \QtyRef{angular_frequency}}
+        \desc[german]{Absoprtionskoeffizient}{Intensitätsverringerung beim Druchgang eines Mediums, nicht zwingend durch Energieabgabe an Medium}{}
+        \quantity{\alpha}{\per\cm}{s}
+        \eq{
+            \alpha &= 2\ncomplex \frac{\omega}{c} \\
+            \alpha &= \frac{\omega}{nc} \epsilon^\prime \text{\TODO{For direct band gaps; from adv. sc: sheet 10 2b). Check which is correct}}
+        }
+    \end{formula}
+
+
+    \begin{formula}{intensity}
+        \desc{Electromagnetic radiation intensity}{Surface power density}{$S$ \fqEqRef{ed:poynting}}
+        \desc[german]{Elektromagnetische Strahlungsintensität}{Flächenleistungsdichte}{}
+        \quantity{I}{\watt\per\m^2=\k\per\s^3}{s}
+        \eq{I = \abs{\braket{S}_t}}
+    \end{formula}
+
+    % \begin{formula}{lambert_beer_law}
+    %     \desc{Beer-Lambert law}{Intensity in an absorbing medium}{$E_\lambda$ extinction, \QtyRef{absorption_coefficient}, \QtyRef{concentration}, $d$ Thickness of the medium}
+    %     \desc[german]{Lambert-beersches Gesetz}{Intensität in einem absorbierenden Medium}{$E_\lambda$ Extinktion, \QtyRef{refraction_index_complex}, \QtyRef{concentration}, $d$ Dicke des Mediums}
+    %     \eq{
+    %         E_\lambda = \log_{10} \frac{I_0}{I} = \kappa c d \\
+    %     }
+    % \end{formula}
+    \begin{formula}{lambert_beer_law}
+        \desc{Beer-Lambert law}{Intensity in an absorbing medium}{\QtyRef{intensity}, \QtyRef{absorption_coefficient}, $z$ penetration depth}
+        \desc[german]{Lambert-beersches Gesetz}{Intensität in einem absorbierenden Medium}{\QtyRef{intensity}, \QtyRef{absorption_coefficient}, $z$ Eindringtiefe}
+         \eq{
+            I(z) = I_0 \e^{-\kappa z}
+        }
+    \end{formula}
+
+

src/electrodynamics.tex

@@ -1,222 +0,0 @@
-\def\PhiB{\Phi_\text{B}}
-\def\PhiE{\Phi_\text{E}}
-
-\Part[
-    \eng{Electrodynamics}
-    \ger{Elektrodynamik}
-]{ed}
-
-
-\Section[
-    \eng{Maxwell-Equations}
-    \ger{Maxwell-Gleichungen}
-    ]{Maxwell}
-    \begin{formula}{vacuum}
-        \desc{Vacuum}{microscopic formulation}{}
-        \desc[german]{Vakuum}{Mikroskopische Formulierung}{}
-        \eq{
-            \Div \vec{E} &= \frac{\rho_\text{el}}{\epsilon_0} \\
-            \Div \vec{B} &= 0 \\
-            \Rot \vec{E} &= - \odv{\vec{B}}{t} \\
-            \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{E}}{t}
-        }
-    \end{formula}
-
-    \begin{formula}{material}
-        \desc{Matter}{Macroscopic formulation}{}
-        \desc[german]{Materie}{Makroskopische Formulierung}{}
-        \eq{
-            \Div \vec{D} &= \rho_\text{el} \\
-            \Div \vec{B} &= 0 \\
-            \Rot \vec{E} &= - \odv{\vec{B}}{t} \\
-            \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
-        }
-    \end{formula}
-
-\Section[
-    \eng{Fields}
-    \ger{Felder}
-    ]{fields}
-
-    \Subsection[
-        \eng{Electric field}
-        \ger{Elektrisches Feld}
-        ]{mag}
-        \begin{formula}{gauss_law}
-            \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface}
-            \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche}
-            \eq{\PhiE = \iint_S \vec{E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}}
-        \end{formula}
-
-    \Subsection[
-        \eng{Magnetic field}
-        \ger{Magnetfeld}
-        ]{mag}
-
-        \Eng[magnetic_flux]{Magnetix flux density}
-        \Ger[magnetic_flux]{Magnetische Flussdichte}
-
-        % \begin{quantity}{mag_flux}{\Phi}{\Wb}{\kg\m^2\per\s^2\A^1}{scalar}
-        %     \sign{}
-        %     \desc{Magnetic flux density}{}
-        %     \desc[german]{Magnetische Feldstärke}{}
-        % \end{quantity}
-
-        \begin{formula}{magnetic_flux}
-            \desc{Magnetic flux}{}{}
-            \desc[german]{Magnetischer Fluss}{}{}
-            \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
-        \end{formula}
-
-        \begin{formula}{gauss_law}
-            \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
-            \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
-            \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
-        \end{formula}
-
-        \begin{formula}{name}
-            \desc{}{}{}
-            \desc[german]{}{}{}
-            \eq{}
-        \end{formula}
-        \begin{formula}{magnetization}
-            \desc{Magnetization}{}{$m$ mag. moment, $V$ volume}
-            \desc[german]{Magnetisierung}{}{$m$ mag. Moment, $V$ Volumen}
-            \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\text{m} \cdot \vec{H}}
-        \end{formula}
-
-        \begin{formula}{angular_torque}
-            \desc{Torque}{}{$m$ mag. moment}
-            \desc[german]{Drehmoment}{}{$m$ mag. Moment}
-            \eq{\vec{\tau} = \vec{m} \times \vec{B}}
-        \end{formula}
-
-        \begin{formula}{suceptibility}
-            \desc{Susceptibility}{}{}
-            \desc[german]{Suszeptibilität}{}{}
-            \eq{\chi_\text{m} = \pdv{M}{B} = \frac{\mu}{\mu_0} - 1 }
-        \end{formula}
-
-
-        \begin{formula}{poynting}
-            \desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field [$\si{\W\per\m^2}$]}{}
-            \desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes  [$\si{\W\per\m^2}$]}{}
-            \eq{\vec{S} = \vec{E} \times \vec{H}}
-        \end{formula}
-
-
-
-        \Subsection[
-            \eng{Induction}
-            \ger{Unduktion}
-            ]{induction}
-            \begin{formula}{farady_law}
-                \desc{Faraday's law of induction}{}{}
-                \desc[german]{Faradaysche Induktionsgesetz}{}{}
-                \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
-            \end{formula}
-
-\Section[
-    \eng{Hall-Effect}
-    \ger{Hall-Effekt}
-    ]{hall}
-
-    \begin{formula}{cyclotron}
-        \desc{Cyclontron frequency}{}{}
-        \desc[german]{Zyklotronfrequenz}{}{}
-        \eq{\omega_\text{c} = \frac{e B}{\masse}}
-    \end{formula}
-    \TODO{Move}
-
-
-    \Subsection[
-        \eng{Classical Hall-Effect}
-        \ger{Klassischer Hall-Effekt}
-        ]{classic}
-        \begin{ttext}
-            \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
-            \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
-        \end{ttext}
-        \begin{formula}{voltage}
-            \desc{Hall voltage}{}{$n$ charge carrier density}
-            \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
-            \eq{U_\text{H} = \frac{I B}{ne d}}
-        \end{formula}
-
-        \begin{formula}{coefficient}
-            \desc{Hall coefficient}{}{}
-            \desc[german]{Hall-Koeffizient}{}{}
-            \eq{R_\text{H} = -\frac{Eg}{j_x Bg} = \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity}{}{}
-            \desc[german]{Spezifischer Widerstand}{}{}
-            \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
-        \end{formula}
-
-
-    \Subsection[
-        \eng{Integer quantum hall effect}
-        \ger{Ganzahliger Quantenhalleffekt}
-        ]{quantum}  
-
-        \begin{formula}{conductivity}
-            \desc{Conductivity tensor}{}{}
-            \desc[german]{Leitfähigkeitstensor}{}{}
-            \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity tensor}{}{}
-            \desc[german]{Spezifischer Widerstands-tensor}{}{}
-            \eq{
-                \rho = \sigma^{-1}
-                % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
-            }
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity}{}{$\nu \in \mathbb{Z}$}
-            \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$}
-            \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
-        \end{formula}
-
-        % \begin{formula}{qhe}
-        %     \desc{Integer quantum hall effect}{}{}
-        %     \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
-        %     \fig{img/qhe-klitzing.jpeg}
-        % \end{formula}
-    
-
-    \TODO{sort}
-    \begin{formula}{impedance_c}
-        \desc{Impedance of a capacitor}{}{}
-        \desc[german]{Impedanz eines Kondesnators}{}{}
-        \eq{Z_{C} = \frac{1}{i\omega C}}
-    \end{formula}
-
-    \begin{formula}{impedance_l}
-        \desc{Impedance of an inductor}{}{}
-        \desc[german]{Impedanz eines Induktors}{}{}
-        \eq{Z_{L} = i\omega L}
-    \end{formula}
-
-    \TODO{impedance addition for parallel / linear}
-
-\Section[
-    \eng{Dipole-stuff}
-    \ger{Dipol-zeug}
-    ]{dipole}
-
-    \begin{formula}{poynting}
-        \desc{Dipole radiation Poynting vector}{}{}
-        \desc[german]{Dipolsrahlung Poynting-Vektor}{}{}
-        \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}}
-    \end{formula}
-
-    \begin{formula}{power}
-        \desc{Time-average power}{}{}
-        \desc[german]{Zeitlich mittlere Leistung}{}{}
-        \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
-    \end{formula}

src/img/cm/sc_junction_metal_n_sc.tex

@@ -0,0 +1,54 @@
+\begin{tikzpicture}[scale=0.9]
+
+\pgfmathsetmacro{\tkW}{8}               % Total width
+\pgfmathsetmacro{\tkH}{5}               % Total height
+% left
+\pgfmathsetmacro{\tkLx}{0}              % Start
+\pgfmathsetmacro{\tkLW}{2}              % Right width
+\pgfmathsetmacro{\tkLyshift}{0.0}       % y-shift
+\pgfmathsetmacro{\tkLBendH}{0}        % Band bending height
+\pgfmathsetmacro{\tkLBendW}{0}    % Band bending width
+\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
+\pgfmathsetmacro{\tkLEf}{1.5+\tkLyshift}% Fermi level energy
+% right
+\pgfmathsetmacro{\tkRx}{\tkLW}          % Left start
+\pgfmathsetmacro{\tkRW}{\tkW-\tkRx}     % Left width
+\pgfmathsetmacro{\tkRyshift}{-0.5}      % y-shift
+\pgfmathsetmacro{\tkRBendH}{0.5}         % Band bending height
+\pgfmathsetmacro{\tkRBendW}{\tkRW/4}     % Band bending width
+\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
+\pgfmathsetmacro{\tkREc}{2.4+\tkRyshift}% Conduction band energy
+\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
+\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
+
+% materials
+\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
+\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
+\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
+\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
+\path[sc separate] (\tkLW,0) -- (\tkLW,\tkH);
+
+% axes
+\draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
+\draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east] {$E$};
+
+% right bands
+\path[sc occupied] (\tkRx, 0) -- \rightBandUp{}{\tkREv} -- (\tkW, 0) -- cycle;
+\draw[sc band con] \rightBandUp{$\Econd$}{\tkREc};
+\draw[sc band val] \rightBandUp{$\Evalence$}{\tkREv};
+\draw[sc band vac] (0,\tkLEV) -- \rightBandUp{$\Evac$}{\tkREV};
+\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
+% left bands
+\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
+\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
+
+% work functions
+\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
+\drawDArrow{\tkRx+\tkRW*3/4}{\tkREf}{\tkREV}{$e\Phi_\txS$}
+\drawDArrow{\tkRx+\tkRW*2/4}{\tkREc}{\tkREV}{$e\chi$}
+% barrier height
+\drawDArrow{\tkRx+\tkRBendW}{\tkREc}{\tkREc+\tkRBendH}{$eU_\text{Bias}$}
+\drawDArrow{\tkRx}{\tkREf}{\tkREc+\tkRBendH}{$e\Phi_\txB$}
+
+\end{tikzpicture}
+

src/img/cm/sc_junction_metal_n_sc_separate.tex

@@ -0,0 +1,49 @@
+\begin{tikzpicture}[scale=0.9]
+
+\pgfmathsetmacro{\tkW}{8}               % Total width
+\pgfmathsetmacro{\tkH}{5}               % Total height
+% left
+\pgfmathsetmacro{\tkLx}{0}              % Start
+\pgfmathsetmacro{\tkLW}{2}              % Right width
+\pgfmathsetmacro{\tkLyshift}{0.0}       % y-shift
+\pgfmathsetmacro{\tkLBendH}{0}        % Band bending height
+\pgfmathsetmacro{\tkLBendW}{0}    % Band bending width
+\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
+\pgfmathsetmacro{\tkLEf}{1.5+\tkLyshift}% Fermi level energy
+% right
+\pgfmathsetmacro{\tkRx}{4}              % Left start
+\pgfmathsetmacro{\tkRW}{\tkW-\tkRx}     % Left width
+\pgfmathsetmacro{\tkRyshift}{0}         % y-shift
+\pgfmathsetmacro{\tkRBendH}{0.5}         % Band bending height
+\pgfmathsetmacro{\tkRBendW}{\tkRW/4}     % Band bending width
+\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
+\pgfmathsetmacro{\tkREc}{2.4+\tkRyshift}% Conduction band energy
+\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
+\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
+
+% materials
+\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
+\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
+\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
+\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
+
+% axes
+\draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
+\draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east]  {$E$};
+
+% right bands
+\path[sc occupied] (\tkRx, 0) -- \rightBand{}{\tkREv} -- (\tkW, 0) -- cycle;
+\draw[sc band con] \rightBand{$\Econd$}{\tkREc};
+\draw[sc band val] \rightBand{$\Evalence$}{\tkREv};
+\draw[sc band vac] (0,\tkLEV) -- \rightBand{$\Evac$}{\tkREV};
+\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
+% left bands
+\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
+\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
+
+% work functions
+\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
+\drawDArrow{\tkRx+\tkRW*2/3}{\tkREf}{\tkREV}{$e\Phi_\txS$}
+\drawDArrow{\tkRx+\tkRW*1/3}{\tkREc}{\tkREV}{$e\chi$}
+
+\end{tikzpicture}

src/img/cm/sc_junction_ohmic.tex

@@ -0,0 +1,51 @@
+\begin{tikzpicture}[scale=1]
+
+\pgfmathsetmacro{\tkW}{8}               % Total width
+\pgfmathsetmacro{\tkH}{5}               % Total height
+% left
+\pgfmathsetmacro{\tkLx}{0}              % Start
+\pgfmathsetmacro{\tkLW}{2}              % Right width
+\pgfmathsetmacro{\tkLyshift}{-0.5}      % y-shift
+\pgfmathsetmacro{\tkLBendH}{0}        % Band bending height
+\pgfmathsetmacro{\tkLBendW}{0}    % Band bending width
+\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
+\pgfmathsetmacro{\tkLEf}{2.5+\tkLyshift}% Fermi level energy
+% right
+\pgfmathsetmacro{\tkRx}{\tkLW}          % Left start
+\pgfmathsetmacro{\tkRW}{\tkW-\tkRx}     % Left width
+\pgfmathsetmacro{\tkRyshift}{0}      % y-shift
+\pgfmathsetmacro{\tkRBendH}{-0.5}         % Band bending height
+\pgfmathsetmacro{\tkRBendW}{\tkRW/4}     % Band bending width
+\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
+\pgfmathsetmacro{\tkREc}{2.5+\tkRyshift}% Conduction band energy
+\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
+\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
+
+% materials
+\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
+\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
+\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
+\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
+\path[sc separate] (\tkRx,0) -- (\tkRx,\tkH);
+
+\drawAxes
+
+% right bands
+\path[sc occupied] (\tkRx, 0) -- \rightBandAuto{}{\tkREv} -- (\tkW, 0) -- cycle;
+\draw[sc band con] \rightBandAuto{$\Econd$}{\tkREc};
+\draw[sc band val] \rightBandAuto{$\Evalence$}{\tkREv};
+\draw[sc band vac] (0,\tkLEV) -- \rightBandAuto{$\Evac$}{\tkREV};
+\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
+% left bands
+\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
+\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
+
+% work functions
+\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
+\drawDArrow{\tkRx+\tkRW*3/4}{\tkREf}{\tkREV}{$e\Phi_\txS$}
+\drawDArrow{\tkRx+\tkRW*2/4}{\tkREc}{\tkREV}{$e\chi$}
+% barrier height
+\drawDArrow{\tkRx+\tkRBendW}{\tkREc}{\tkREc-\tkRBendH}{$eU_\text{Bias}$}
+
+\end{tikzpicture}
+

src/img/cm/sc_junction_ohmic_separate.tex

@@ -0,0 +1,48 @@
+\begin{tikzpicture}[scale=1]
+
+\pgfmathsetmacro{\tkW}{8}               % Total width
+\pgfmathsetmacro{\tkH}{5}               % Total height
+% left
+\pgfmathsetmacro{\tkLx}{0}              % Start
+\pgfmathsetmacro{\tkLW}{2}              % Right width
+\pgfmathsetmacro{\tkLyshift}{0.0}      % y-shift
+\pgfmathsetmacro{\tkLBendH}{0}        % Band bending height
+\pgfmathsetmacro{\tkLBendW}{0}    % Band bending width
+\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
+\pgfmathsetmacro{\tkLEf}{2.5+\tkLyshift}% Fermi level energy
+% right
+\pgfmathsetmacro{\tkRx}{4}          % Left start
+\pgfmathsetmacro{\tkRW}{\tkW-\tkRx}     % Left width
+\pgfmathsetmacro{\tkRyshift}{0}         % y-shift
+\pgfmathsetmacro{\tkRBendH}{0.5}         % Band bending height
+\pgfmathsetmacro{\tkRBendW}{\tkRW/4}     % Band bending width
+\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
+\pgfmathsetmacro{\tkREc}{2.5+\tkRyshift}% Conduction band energy
+\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
+\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
+
+% materials
+\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
+\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
+\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
+\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
+
+\drawAxes
+
+% right bands
+\path[sc occupied] (\tkRx, 0) -- \rightBand{}{\tkREv} -- (\tkW, 0) -- cycle;
+\draw[sc band con] \rightBand{$\Econd$}{\tkREc};
+\draw[sc band val] \rightBand{$\Evalence$}{\tkREv};
+\draw[sc band vac] (0,\tkLEV) -- \rightBand{$\Evac$}{\tkREV};
+\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
+% left bands
+\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
+\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
+
+% work functions
+\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
+\drawDArrow{\tkRx+\tkRW*2/3}{\tkREf}{\tkREV}{$e\Phi_\txS$}
+\drawDArrow{\tkRx+\tkRW*1/3}{\tkREc}{\tkREV}{$e\chi$}
+
+\end{tikzpicture}
+

src/img/cm/sc_junction_pn.tex

@@ -0,0 +1,65 @@
+\newcommand\tikzPnJunction[7]{
+\begin{tikzpicture}[scale=1.0]
+
+\pgfmathsetmacro{\tkW}{8}               % Total width
+\pgfmathsetmacro{\tkH}{5}               % Total height
+% left
+\pgfmathsetmacro{\tkLx}{0}              % Start
+\pgfmathsetmacro{\tkLW}{\tkW*#1}         % Width
+\pgfmathsetmacro{\tkLyshift}{#2}       % y-shift
+\pgfmathsetmacro{\tkLBendH}{#3}        % Band bending height
+\pgfmathsetmacro{\tkLBendW}{\tkLW/4}    % Band bending width
+\pgfmathsetmacro{\tkLEv}{0.7+\tkLyshift}% Valence band energy
+\pgfmathsetmacro{\tkLEc}{2.3+\tkLyshift}% Conduction band energy
+\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
+\pgfmathsetmacro{\tkLEf}{1.1+\tkLyshift}% Fermi level energy
+% right
+\pgfmathsetmacro{\tkRx}{\tkW*(1-#4)}       % Start
+\pgfmathsetmacro{\tkRW}{\tkW*#4}         % Width
+\pgfmathsetmacro{\tkRyshift}{#5}      % y-shift
+\pgfmathsetmacro{\tkRBendH}{#6}        % Band bending height
+\pgfmathsetmacro{\tkRBendW}{\tkRW/4}    % Band bending width
+\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
+\pgfmathsetmacro{\tkREc}{2.3+\tkRyshift}% Conduction band energy
+\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
+\pgfmathsetmacro{\tkREf}{1.9+\tkRyshift}% Fermi level energy
+
+% materials
+\draw[sc p type] (0,0) rectangle (\tkLW,\tkH);
+\node at (\tkLW/2,\tkH-0.2) {\GT{p-type}};
+\path[sc separate] (\tkRx,0) -- (\tkRx,\tkH);
+\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
+\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
+\path[sc separate] (\tkLW,0) -- (\tkLW,\tkH);
+
+\drawAxes
+
+% right bands
+\path[sc occupied] (\tkRx, 0) -- \rightBandAuto{}{\tkREv} -- (\tkW, 0) -- cycle;
+\draw[sc band con]    \rightBandAuto{$\Econd$}{\tkREc};
+\draw[sc band val]    \rightBandAuto{$\Evalence$}{\tkREv};
+\draw[sc band vac]    \rightBandAuto{$\Evac$}{\tkREV};
+\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
+% left bands
+\path[sc occupied] (\tkLx, 0) -- \leftBandAuto{}{\tkLEv} -- (\tkLW, 0) -- cycle;
+\draw[sc band con]    \leftBandAuto{$\Econd$}{\tkLEc};
+\draw[sc band val]    \leftBandAuto{$\Evalence$}{\tkLEv};
+\draw[sc band vac]    \leftBandAuto{$\Evac$}{\tkLEV};
+\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
+
+% work functions
+
+\drawDArrow{\tkRx+\tkRW*2/3}{\tkREf}{\tkREV}{$e\Phi_\txn$}
+\drawDArrow{\tkRx+\tkRW*1/3}{\tkREc}{\tkREV}{$e\chi_\txn$}
+\drawDArrow{\tkLx+\tkLW*2/3}{\tkLEf}{\tkLEV}{$e\Phi_\txp$}
+\drawDArrow{\tkLx+\tkLW*1/3}{\tkLEc}{\tkLEV}{$e\chi_\txp$}
+% barrier height
+% \drawDArrow{\tkRx+\tkRBendW}{\tkREc}{\tkREc+\tkRBendH}{$eU_\text{Bias}$}
+% \drawDArrow{\tkRx}{\tkREf}{\tkREc+\tkRBendH}{$e\Phi_\txB$}
+#7
+
+\end{tikzpicture}
+}
+% \tikzPnJunction{1/3}{0}{0}{1/3}{0}{0}{}
+% \tikzPnJunction{1/2}{0.4}{-0.4}{1/2}{-0.4}{0.4}{}
+

src/main.tex

@@ -1,142 +1,142 @@
+%! TeX program = lualatex
+% (for vimtex)
 \documentclass[11pt, a4paper]{article}
-% \usepackage[utf8]{inputenc}
+% SET LANGUAGE HERE
-\usepackage[english]{babel}
+\usepackage[german]{babel}
 \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
 % ENVIRONMENTS etc
 \usepackage{adjustbox}
-\usepackage{colortbl}  % color table
+\usepackage{colortbl}   % color table
-\usepackage{tabularx}  % bravais table
+\usepackage{tabularx}   % bravais table
-\usepackage{multirow}  % for superconducting qubit table
+\usepackage{multirow}   % for superconducting qubit table
-\usepackage{hhline}    % for superconducting qubit table
+\usepackage{hhline}     % for superconducting qubit table
 % TOOLING
 \usepackage{graphicx}
 \usepackage{etoolbox}
-\usepackage{luacode}
+% \usepackage{luacode}
-\usepackage{expl3} % switch case and other stuff
+\usepackage{expl3}      % switch case and other stuff
 \usepackage{substr}
 \usepackage{xcolor}
-\usepackage{float}
+% FORMATING
-\usepackage[hidelinks]{hyperref}
+\usepackage{float}                  % float barrier
-\usepackage{subcaption}
+\usepackage{subcaption}             % subfigures
-
+\usepackage[hidelinks]{hyperref}    % hyperrefs for \fqEqRef, \qtyRef, etc
-\usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
+\usepackage[shortlabels]{enumitem}  % easily change enum symbols to i), a. etc
-\hypersetup{colorlinks   = true,    % Colours links instead of ugly boxes
+\setlist{noitemsep}                 % no vertical space between items
-            urlcolor     = blue,    % Colour for external hyperlinks
+\setlist[1]{labelindent=\parindent} % < Usually a good idea
-            linkcolor    = cyan,    % Colour of internal links
+\setlist[itemize]{leftmargin=*}
-            citecolor    = red      % Colour of citations 
+% \setlist[enumerate]{labelsep=*, leftmargin=1.5pc}  % horizontal indent of items
-            }
-\usepackage{translations}
-\input{util/translation.tex}
-
-\usepackage{sectsty}
-\usepackage{titlesec}
-\input{util/colorscheme.tex}
 
+\usepackage{titlesec}   % colored titles
+\usepackage{array}      % more array options
+\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type
+% \usepackage{sectsty}
 % GRAPHICS
-\usepackage{tikz} % drawings
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.18}
+\usepackage{tikz}       % drawings
 \usetikzlibrary{decorations.pathmorphing}
+\usetikzlibrary{decorations.pathreplacing} % braces
 \usetikzlibrary{calc}
-\usepackage{circuitikz}
+\usetikzlibrary{patterns}
-
+\usetikzlibrary{patterns}
+\input{util/tikz_macros}
+% speed up compilation by externalizing figures
+% \usetikzlibrary{external}
+% \tikzexternalize[prefix=tikz_figures]
+% \tikzexternalize
+\usepackage{circuitikz} % electrical circuits with tikz
 % SCIENCE PACKAGES
 \usepackage{mathtools}
-\usepackage{MnSymbol}  % for >>> \ggg sign
+% set display math skips
+\AtBeginDocument{
+    \abovedisplayskip=0pt
+    \abovedisplayshortskip=0pt
+    \belowdisplayskip=0pt   
+    \belowdisplayshortskip=0pt
+}
+\usepackage{MnSymbol}   % for >>> \ggg sign
+\usepackage[version=4,arrows=pgf-filled]{mhchem}
+\usepackage{upgreek}    % upright greek letters for chemmacros
+\usepackage{chemmacros} % for orbitals images
 % \usepackage{esdiff} % derivatives
 % esdiff breaks when taking \dot{q} has argument
-\usepackage{derivative}
+\usepackage{derivative} % \odv, \pdv
-\usepackage[version=4,arrows=pgf-filled]{mhchem}
+\usepackage{bbold}      % \mathbb font
-\usepackage{bbold}  % \mathbb font
+\usepackage{braket}     % <bra|ket>
-\usepackage{braket}
+\usepackage{siunitx}    % \si \SI units
-\usepackage{siunitx}
 \sisetup{output-decimal-marker = {,}}
 \sisetup{separate-uncertainty}
 \sisetup{per-mode = power}
 \sisetup{exponent-product=\ensuremath{\cdot}}
 
+% DEBUG
+% \usepackage{lua-visual-debug}
+% DUMB STUFF
+% \usepackage{emoji}
+% \newcommand\temoji[1]{\text{\emoji{#1}}}
+% \def\sigma{\temoji{shark}}
+% \def\lambda{\temoji{sheep}}
+% \def\psi{\temoji{pickup-truck}}
+% \def\pi{\temoji{birthday-cake}}
+% \def\Pi{\temoji{hospital}}
+% \def\rho{\temoji{rhino}}
+% \def\nu{\temoji{unicorn}}
+% \def\mu{\temoji{mouse}}
 
-
+\newcommand{\TODO}[1]{{\color{fg-red}TODO:#1}}
-\newcommand{\TODO}[1]{{\color{bright_red}TODO:#1}}
 \newcommand{\ts}{\textsuperscript}
 
-% put an explanation above an equal sign
-% [1]: equality sign (or anything else)
-% 2: text (not in math mode!)
-\newcommand{\explUnderEq}[2][=]{%
-    \underset{\substack{\uparrow\\\mathrlap{\text{\hspace{-1em}#2}}}}{#1}}
-\newcommand{\explOverEq}[2][=]{%
-    \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}}
-    
-
-
-
-% "automate" sectioning
-% start <section>, get heading from translation, set label
-% fqname is the fully qualified name: the keys of all previous sections joined with a ':'
-% [1]: code to run after setting \fqname, but before the \part, \section etc
-% 2: key
-\newcommand{\Part}[2][desc]{
-    \newpage
-    \def\partname{#2}
-    \def\sectionname{}
-    \def\subsectionname{}
-    \def\subsubsectionname{}
-    \edef\fqname{\partname}
-    #1
-    \part{\GT{\fqname}} 
-    \label{sec:\fqname}
-}
-\newcommand{\Section}[2][]{
-    \def\sectionname{#2}
-    \def\subsectionname{}
-    \def\subsubsectionname{}
-    \edef\fqname{\partname:\sectionname}
-    #1
-    \section{\GT{\fqname}} 
-    \label{sec:\fqname}
-}
-% \newcommand{\Subsection}[1]{\Subsection{#1}{}}
-\newcommand{\Subsection}[2][]{
-    \def\subsectionname{#2}
-    \def\subsubsectionname{}
-    \edef\fqname{\partname:\sectionname:\subsectionname}
-    #1
-    \subsection{\GT{\fqname}}
-    \label{sec:\fqname}
-}
-\newcommand{\Subsubsection}[2][]{
-    \def\subsubsectionname{#2}
-    \edef\fqname{\partname:\sectionname:\subsectionname:\subsubsectionname}
-    #1
-    \subsubsection{\GT{\fqname}}
-    \label{sec:\fqname}
-}
-
-% Make the translation of #1 a reference to a equation
-% 1: key
-\newcommand{\fqEqRef}[1]{
-    \hyperref[eq:#1]{\GT{#1}}
-}
-% Make the translation of #1 a reference to a section
-% 1: key
-\newcommand{\fqSecRef}[1]{
-    \hyperref[sec:#1]{\GT{#1}}
-}
 
 % \usepackage{xstring}
 
 
-\input{circuit.tex}
+% Create a text file with relevant labels for vim-completion
+\newwrite\labelsFile
+\immediate\openout\labelsFile=\jobname.labels.txt
+\newcommand\storeLabel[1]{
+    \immediate\write\labelsFile{#1}%
+}
+\AtEndDocument{\immediate\closeout\labelsFile}
 
-% some translations
+\input{circuit.tex}
+\input{util/macros.tex}
+\input{util/environments.tex}   % requires util/translation.tex to be loaded first
+\usepackage{pkg/mqlua}
+\usepackage{pkg/mqfqname}
+% TRANSLATION
+% \usepackage{translations}
+\usepackage{pkg/mqtranslation}
+\input{util/colorscheme.tex}
+\input{util/colors.tex} % after colorscheme
+
+\usepackage{pkg/mqconstant}
+\usepackage{pkg/mqquantity}
+\usepackage{pkg/mqformula}
+\usepackage{pkg/mqperiodictable}
+
+% INPUT
+% 1: starting pattern of files to input using the Input command. All other files are ignored 
+\newcommand\InputOnly[1]{\edef\inputOnlyFile{#1}}
+\edef\inputOnlyFile{all}
+\newcommand\Input[1]{
+    % yes this could surely be done in tex
+    \directlua{
+        if '\luaescapestring{\inputOnlyFile}' == 'all' or string.startswith('\luaescapestring{#1}', '\luaescapestring{\inputOnlyFile}') then
+            tex.print("\\input{\luaescapestring{#1}}")
+        end
+    }
+}
 
 \title{Formelsammlung}
 \author{Matthias Quintern}
 \date{\today}
-
-\input{util/macros.tex}
-\input{util/environments.tex}
-
 \begin{document}
+\IfFileExists{\jobname.translations.aux}{%
+  \input{\jobname.translations.aux}
+}{}
+
+\makeatletter\let\percentchar\@percentchar\makeatother
 
 \maketitle
 \tableofcontents
@@ -145,32 +145,78 @@
 
 \input{util/translations.tex}
 
-\input{linalg.tex}
+% \InputOnly{ch}
 
-\input{geometry.tex}
+\Input{math/math}
+\Input{math/linalg}
+\Input{math/geometry}
+\Input{math/calculus}
+\Input{math/probability_theory}
 
-\input{analysis.tex}
+\Input{mechanics}
+\Input{statistical_mechanics}
 
-\input{probability_theory.tex}
+\Input{ed/ed}
+\Input{ed/el}
+\Input{ed/mag}
+\Input{ed/em}
+\Input{ed/optics}
+\Input{ed/misc}
 
-\input{mechanics.tex}
+\Input{qm/qm}
+\Input{qm/atom}
 
-\input{statistical_mechanics.tex}
+\Input{cm/cm}
+\Input{cm/crystal}
+\Input{cm/egas}
+\Input{cm/charge_transport}
+\Input{cm/low_temp}
+\Input{cm/semiconductors}
+\Input{cm/misc}
+\Input{cm/techniques}
+\Input{cm/topo}
+\Input{cm/mat}
 
-\input{electrodynamics.tex}
+\Input{particle}
-    
-\input{quantum_mechanics.tex}
-\input{atom.tex}
 
-\input{condensed_matter.tex}
+\Input{quantum_computing}
 
-% \input{topo.tex}
+\Input{comp/comp}
+\Input{comp/qmb}
+\Input{comp/est}
+\Input{comp/ad}
+\Input{comp/ml}
 
-% \input{quantum_computing.tex}
+\Input{ch/periodic_table}  % only definitions
+\Input{ch/ch}
+\Input{ch/el}
+\Input{ch/misc}
 
-% \input{many-body-simulations.tex}
+\newpage
+\Part[
+    \eng{Appendix}
+    \ger{Anhang}
+]{appendix}
+\begin{formula}{world}
+    \desc{World formula}{}{}
+    \desc[german]{Weltformel}{}{}
+    \eq{E = mc^2 +\text{AI}}
+\end{formula}
+\Input{quantities}
+\Input{constants}
+
+% \listofquantities
+\listoffigures
+\listoftables
+\Section[
+    \eng{List of elements}
+    \ger{Liste der Elemente}
+]{elements}
+    \printAllElements
+\newpage
+% \Input{test}
 
-%\newpage
 % \bibliographystyle{plain}
 % \bibliography{ref}
+
 \end{document}

src/many-body-simulations.tex

@@ -1,10 +0,0 @@
-\Part[
-    \eng{Many-body simulations}
-    \ger{Vielteilchen Simulationen}
-]{mbsim}
-
-    \Section[
-        \eng{Importance sampling}
-        \ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
-    ]{importance_sampling}
-

src/math/calculus.tex

@@ -0,0 +1,321 @@
+\Section[
+    \eng{Calculus}
+    \ger{Analysis}
+]{cal}
+
+    % \begin{formula}{shark}
+    %     \desc{Shark-midnight formula}{\emoji{shark}-s}{}
+    %     \desc[german]{Shark-Mitternachtformel}{}{}
+    %     \eq{
+    %         \temoji{seal}_{1,2} = \frac{-\temoji{shark}\pm \sqrt{\temoji{shark}^2-4\temoji{octopus}\temoji{tropical-fish}}}{2\temoji{octopus}}
+    %     }
+    % \end{formula}
+
+        
+    \Subsection[
+        \eng{Fourier analysis}
+        \ger{Fourieranalyse}
+    ]{fourier}
+        \Subsubsection[
+            \eng{Fourier series}
+            \ger{Fourierreihe}
+        ]{series}
+        \begin{formula}{series} \absLabel[fourier_series]
+                \desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
+                \desc[german]{Fourierreihe}{Komplexe Darstellung}{}
+                \eq{f(t) = \sum_{k=-\infty}^{\infty} c_k \Exp{\frac{2\pi \I kt}{T}}}
+            \end{formula}
+            \Eng[real]{real}
+            \Ger[real]{reellwertig}
+            \begin{formula}{coefficient-complex}
+                \desc{Fourier coefficients}{Complex representation}{}
+                \desc[german]{Fourierkoeffizienten}{Komplexe Darstellung}{}
+                \eq{
+                    c_k &= \frac{1}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Exp{-\frac{2\pi \I}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
+                    c_{-k} &= \overline{c_k} \quad \text{\GT{if} $f$ \GT{real}}
+                }
+            \end{formula}
+
+            \begin{formula}{series_sincos}
+                \desc{Fourier series}{Sine and cosine representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
+                \desc[german]{Fourierreihe}{Sinus und Kosinus Darstellung}{}
+                \eq{f(t) = \frac{a_0}{2} + \sum_{k=1}^{\infty} \left(a_k \Cos{\frac{2\pi}{T}kt} + b_k\Sin{\frac{2\pi}{T}kt}\right)}
+            \end{formula}
+            \begin{formula}{coefficient}
+                \desc{Fourier coefficients}{Sine and cosine representation\\If $f$ has point symmetry: $a_{k>0}=0$, if $f$ has axial symmetry: $b_k=0$}{}
+                \desc[german]{Fourierkoeffizienten}{Sinus und Kosinus Darstellung\\Wenn $f$ punktsymmetrisch: $a_{k>0}=0$, wenn $f$ achsensymmetrisch: $b_k=0$}{}
+                \eq{
+                    a_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Cos{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge0\\
+                    b_k &= \frac{2}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} f(t)\,\Sin{-\frac{2\pi}{T}kt}\d t \quad\text{\GT{for}}\,k\ge1\\
+                    a_k &= c_k + c_{-k}      \quad\text{\GT{for}}\,k\ge0\\
+                    b_k &= \I(c_k - c_{-k})  \quad\text{\GT{for}}\,k\ge1
+                }
+            \end{formula}
+        \TODO{cleanup}
+        
+
+        \Subsubsection[
+            \eng{Fourier transformation}
+            \ger{Fouriertransformation}
+        ]{trafo}
+            \begin{formula}{transform} \absLabel[fourier_transform]
+                \desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
+                \desc[german]{Fouriertransformierte}{}{}
+                \eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
+            \end{formula}
+
+            \Eng[linear_in]{linear in}
+            \Ger[linear_in]{linear in}
+            \GT{for} $f\in L^1(\R^n)$:
+            \begin{enumerate}[i)]
+                \item $f \mapsto \hat{f}$ \GT{linear_in} $f$
+                \item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
+                \item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
+                \item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
+            \end{enumerate}
+
+
+        \Subsubsection[
+            \eng{Convolution}
+            \ger{Faltung / Konvolution}
+        ]{conv}
+            \begin{ttext}
+                \eng{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}
+                \ger{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}
+            \end{ttext}
+            \begin{formula}{def}
+                \desc{Definition}{}{}
+                \desc[german]{Definition}{}{}
+                \eq{(f*g)(t) = f(t) * g(t) = \int_{-\infty}^\infty f(\tau) g(t-\tau) \d \tau}
+            \end{formula}
+            \begin{formula}{notation}
+                \desc{Notation}{}{}
+                \desc[german]{Notation}{}{}
+                \eq{
+                    f(t) * g(t-t_0) &= (f*g)(t-t_0) \\
+                    f(t-t_0) * g(t-t_0) &= (f*g)(t-2t_0)
+                }
+            \end{formula}
+            \begin{formula}{commutativity}
+                \desc{Commutativity}{}{}
+                \desc[german]{Kommutativität}{}{}
+                \eq{f * g = g * f}
+            \end{formula}
+
+            \begin{formula}{associativity}
+                \desc{Associativity}{}{}
+                \desc[german]{Assoziativität]}{}{}
+                \eq{(f*g)*h = f*(g*h)}
+            \end{formula}
+
+            \begin{formula}{distributivity}
+                \desc{Distributivity}{}{}
+                \desc[german]{Distributivität}{}{}
+                \eq{f * (g + h) = f*g + f*h}
+            \end{formula}
+
+            \begin{formula}{complex_conjugate}
+                \desc{Complex conjugate}{}{}
+                \desc[german]{Komplexe konjugation}{}{}
+                \eq{(f*g)^* = f^* * g^*}
+            \end{formula}
+
+
+    \Subsection[
+        \eng{Misc}
+        \ger{Verschiedenes}
+        ]{misc}
+        
+        \begin{formula}{stirling-approx}
+            \desc{Stirling approximation}{}{}
+            \desc[german]{Stirlingformel}{}{}
+            \eq{\ln (N!) \approx N \ln(N) - N + \Order(\ln(N))}
+        \end{formula}
+
+        \begin{formula}{error-function}
+            \desc{Error function}{$\erf: \C \to \C$ and complementary error function $\erfc$}{}
+            \desc[german]{Fehlerfunktion}{$\erf: \C \to \C$ und komplementäre Fehlerfunktion $\erfc$}{}
+            \eq{
+                \erf(x)  &= \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \d t \\
+                \erfc(x) &= 1 - \erf(x)\\
+                         &= \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} \d t
+            }
+        \end{formula}
+
+        \begin{formula}{delta_of_function}
+            \desc{Dirac-Delta of a function}{}{$g(x_0) = 0$}
+            \desc[german]{Dirac-Delta einer Funktion}{}{}
+            \eq{\delta(f(x)) = \frac{\delta(x-x_0)}{\abs{g^\prime(x_0)}}}
+        \end{formula}
+
+        \begin{formula}{geometric_series}
+            \desc{Geometric series}{}{$\abs{q}<1$}
+            \desc[german]{Geometrische Reihe}{}{}
+            \eq{\sum_{k=0}^{\infty}q^k = \frac{1}{1-q}}
+        \end{formula}
+
+
+    \Subsection[
+        \eng{Logarithm}
+        \ger{Logarithmus}
+    ]{log}
+        \begin{formula}{identities}
+            \desc{Logarithm identities}{}{}
+            \desc[german]{Logarithmus Identitäten}{Logarithmus Rechenregeln}{}
+            \eq{
+                \log(xy) &= \log(x) + \log(y) \\
+                \log \left(\frac{x}{y}\right) &= \log(x) - \log(y) \\
+                \log \left(x^d\right) &= d\log(x) \\
+                \log \left(\sqrt[y]{x}\right) &= \frac{\log(x)}{y} \\
+                x^{\log(y)} &= y^{\log(x)}
+            }
+        \end{formula}
+        \begin{formula}{intergral}
+            \desc{Integral of natural logarithm}{}{}
+            \desc[german]{Integral des natürluchen Logarithmus}{}{}
+            \eq{
+                \int \ln(x) \d x &= x \left(\ln(x) -1\right) \\
+                \int \ln(ax + b) \d x &= \frac{ax+b}{a} \left(\ln(ax + b) -1\right)
+            }
+        \end{formula}
+
+    \Subsection[
+        \eng{Vector calculus}
+        \ger{Vektor Analysis}
+    ]{vec}
+        \begin{formula}{laplace}
+            \desc{Laplace operator}{}{}
+            \desc[german]{Laplace-Operator}{}{}
+            \eq{\laplace = \Grad^2 = \pdv[2]{}{x} + \pdv[2]{}{y} + \pdv[2]{}{z}}
+        \end{formula}
+        \Subsubsection[
+            \eng{Spherical symmetry}
+            \ger{Kugelsymmetrie}
+        ]{sphere}
+            \begin{formula}{coordinates}
+                \desc{Spherical coordinates}{}{}
+                \desc[german]{Kugelkoordinaten}{}{}
+                \eq{
+                    x &= r \sin\phi,\cos\theta \\
+                    y &= r \cos\phi,\cos\theta \\
+                    z &= r \sin\theta
+                }
+            \end{formula}
+
+            \begin{formula}{laplace}
+                \desc{Laplace operator}{}{}
+                \desc[german]{Laplace-Operator}{}{}
+                \eq{\Grad^2 = \laplace = \frac{1}{r^2} \pdv{}{r} \left(r^2 \pdv{}{r}\right)}
+            \end{formula}
+
+
+    \Subsection[
+        \eng{Integrals}
+        \ger{Integralrechnung}
+    ]{integral}
+        \begin{formula}{partial}
+            \desc{Partial integration}{}{}
+            \desc[german]{Partielle integration}{}{}
+            \eq{
+                \int_a^b f^\prime(x)\cdot g(x) \d x= \left[f(x)\cdot g(x)\right]_a^b - \int_a^b f(x)\cdot g^\prime(x) \d x
+            }
+        \end{formula}
+
+        \begin{formula}{substitution}
+            \desc{Integration by substitution}{}{}
+            \desc[german]{Integration durch Substitution}{}{}
+            \eq{
+                \int_a^b f(g(x))\,g^\prime(x) \d x = \int_{g(a)}^{g(b)} f(z) \d z
+            }
+        \end{formula}
+
+        \begin{formula}{gauss}
+            \desc{Gauss's theorem / Divergence theorem}{Divergence in a volume equals the flux through the surface}{$A = \partial V$}
+            \desc[german]{Satz von Gauss}{Divergenz in einem Volumen ist gleich dem Fluss durch die Oberfläche}{}
+            \eq{
+                \iiint_V \Div{\vec{F}} \d V = \oiint_A \vec{F} \cdot \d\vec{A}
+            }
+        \end{formula}
+
+        \begin{formula}{stokes}
+            \desc{Stokes's theorem}{}{$S = \partial A$}
+            \desc[german]{Klassischer Satz von Stokes}{}{}
+            \eq{\int_A (\Rot{\vec{F}}) \cdot \d\vec{S} = \oint_{S} \vec{F} \cdot \d \vec{r}}
+        \end{formula}
+        \Subsubsection[
+            \eng{List of common integrals}
+            \ger{Liste nützlicher Integrale}
+        ]{list}
+            % Put links to other integrals here
+            \fqEqRef{cal:log:integral}
+
+            \begin{formula}{arcfunctions}
+                \desc{Arcsine, arccosine, arctangent}{}{}
+                \desc[german]{Arkussinus, Arkuskosinus, Arkustangens}{}{}
+                \eq{
+                    \int \frac{1}{\sqrt{1-x^2}} \d x  = \arcsin x \\
+                    \int -\frac{1}{\sqrt{1-x^2}} \d x = \arccos x \\
+                    \int \frac{1}{x^2+1} \d x         = \arctan x
+                }
+            \end{formula}
+            \begin{formula}{archyperbolicfunctions}
+                \desc{Arcsinh, arccosh, arctanh}{}{}
+                % \desc[german]{Arkussinus, Arkuskosinus, Arkustangens}{}{}
+                \eq{
+                    \int \frac{1}{\sqrt{x^2+1}} \d x &= \arsinh x \\
+                    \int \frac{1}{\sqrt{x^2-1}} \d x &= \arcosh x \quad\eqnote{\GT{for} $(x > 1)$}\\
+                    \int \frac{1}{1-x^2} \d x        &= \artanh x \quad\eqnote{\GT{for} $(\abs{x} < 1)$}\\
+                    \int \frac{1}{1-x^2} \d x        &= \arcoth x \quad\eqnote{\GT{for} $(\abs{x} > 1)$}
+                }
+            \end{formula}
+
+            \begin{formula}{spheical-coordinates-int}
+                \desc{Integration in spherical coordinates}{}{}
+                \desc[german]{Integration in Kugelkoordinaten}{}{}
+                \eq{\iiint\d x \d y \d z= \int_0^{\infty} \!\! \int_0^{2\pi} \!\! \int_0^\pi \d r \d\phi\d\theta \, r^2\sin\theta}
+            \end{formula}
+
+            \begin{formula}{riemann_zeta}
+                \desc{Riemann Zeta Function}{}{}
+                \desc[german]{Riemannsche Zeta-Funktion}{}{}
+                \eq{\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \frac{1}{(1-2^{(1-s)})\Gamma(s)} \int_0^\infty \d\eta \frac{\eta^{(s-1)}}{\e^\eta + 1}}
+            \end{formula}
+
+            \begin{formula}{gamma_function}
+                \desc{Gamma function}{}{}
+                \desc[german]{Gamma-Funktion}{}{}
+                \eq{
+                    \Gamma(n) &= (n-1)! \\
+                    \Gamma(z) &= \int_0^\infty t^{z-1} \e^{-t} \d t \\
+                    \Gamma(z+1) &= z\Gamma(z)
+                }
+            \end{formula}
+            \begin{formula}{upper_incomplete_gamma_function}
+                \desc{Upper incomplete gamma function}{}{}
+                \desc[german]{Unvollständige Gamma-Funktion der unteren Grenze}{}{}
+                \eq{\Gamma(s,x) = \int_x-^\infty t^{s-1}\e^{-t} \d t}
+            \end{formula}
+            \begin{formula}{lower_incomplete_gamma_function}
+                \desc{Lower incomplete gamma function}{}{}
+                \desc[german]{Unvollständige Gamma-Funktion der oberen Grenze}{}{}
+                \eq{\gamma(s,x) = \int_0^x t^{s-1}\e^{-t} \d t}
+            \end{formula}
+
+            \begin{formula}{beta_function}
+                \desc{Beta function}{Complete beta function}{}
+                \desc[german]{Beta-Funktion}{}{}
+                \eq{
+                    \txB(z_1,z_2) &= \int_0^1 t^{z_1-1} (1-t)^{z_2-1} \d t \\
+                    \txB(z_1, z_2) &= \frac{\Gamma(z_1) \Gamma(z_2)}{\Gamma(z_1+z_2)}
+                }
+            \end{formula}
+            \begin{formula}{incomplete_beta_function}
+                \desc{Incomplete beta function}{Complete beta function}{}
+                \desc[german]{Unvollständige Beta-Funktion}{}{}
+                \eq{\txB(x; z_1,z_2) = \int_0^x t^{z_1-1} (1-t)^{z_2-1} \d t}
+            \end{formula}
+
+
+            \TODO{differential equation solutions}
+
+

src/math/geometry.tex

@@ -1,53 +1,53 @@
-\Part[
+\Section[
     \eng{Geometry}
     \ger{Geometrie}
     ]{geo}
 
-\Section[
+\Subsection[
     \eng{Trigonometry}
     \ger{Trigonometrie}
-    ]{trig}
+]{trig}
 
-\begin{formula}{exponential_function}
+    \begin{formula}{exponential_function}
-    \desc{Exponential function}{}{}
+        \desc{Exponential function}{}{}
-    \desc[german]{Exponentialfunktion}{}{}
+        \desc[german]{Exponentialfunktion}{}{}
-    \eq{\exp(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}}
+        \eq{\exp(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}}
-\end{formula}
+    \end{formula}
 
-\begin{formula}{sine}
+    \begin{formula}{sine}
-    \desc{Sine}{}{}
+        \desc{Sine}{}{}
-    \desc[german]{Sinus}{}{}
+        \desc[german]{Sinus}{}{}
-    \eq{\sin(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{(2n+1)}}{(2n+1)!} \\
+        \eq{\sin(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{(2n+1)}}{(2n+1)!} \\
-                &= \frac{e^{ix}-e^{-ix}}{2i}}
+                    &= \frac{e^{ix}-e^{-ix}}{2i}}
-\end{formula}
+    \end{formula}
 
-\begin{formula}{cosine}
+    \begin{formula}{cosine}
-    \desc{Cosine}{}{}
+        \desc{Cosine}{}{}
-    \desc[german]{Kosinus}{}{}
+        \desc[german]{Kosinus}{}{}
-    \eq{\cos(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{(2n)}}{(2n)!} \\
+        \eq{\cos(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{(2n)}}{(2n)!} \\
-                &= \frac{e^{ix}+e^{-ix}}{2}}
+                    &= \frac{e^{ix}+e^{-ix}}{2}}
-\end{formula}
+    \end{formula}
 
 
-\begin{formula}{hyperbolic_sine}
+    \begin{formula}{hyperbolic_sine}
-    \desc{Hyperbolic sine}{}{}
+        \desc{Hyperbolic sine}{}{}
-    \desc[german]{Sinus hyperbolicus}{}{}
+        \desc[german]{Sinus hyperbolicus}{}{}
-    \eq{\sinh(x) &= -i\sin{ix} \\ &= \frac{e^{x}-e^{-x}}{2}}
+        \eq{\sinh(x) &= -i\sin{ix} \\ &= \frac{e^{x}-e^{-x}}{2}}
-\end{formula}
+    \end{formula}
 
-\begin{formula}{hyperbolic_cosine}
+    \begin{formula}{hyperbolic_cosine}
-    \desc{Hyperbolic cosine}{}{}
+        \desc{Hyperbolic cosine}{}{}
-    \desc[german]{Kosinus hyperbolicus}{}{}
+        \desc[german]{Kosinus hyperbolicus}{}{}
-    \eq{\cosh(x) &= \cos{ix} \\ &= \frac{e^{x}+e^{-x}}{2}}
+        \eq{\cosh(x) &= \cos{ix} \\ &= \frac{e^{x}+e^{-x}}{2}}
-\end{formula}
+    \end{formula}
 
-    \Subsection[
+\Subsection[
-        \eng{Various theorems}
+    \eng{Various theorems}
-        \ger{Verschiedene Theoreme}
+    \ger{Verschiedene Theoreme}
-    ]{theorems}
+]{theorems}
     \begin{formula}{sum}
-        \desc{}{}{}
+        \desc{Hypthenuse in the unit circle}{}{}
-        \desc[german]{}{}{}
+        \desc[german]{Hypothenuse im Einheitskreis}{}{}
         \eq{1 &= \sin^2 x + \cos^2 x}
     \end{formula}
 
@@ -71,17 +71,17 @@
         }
     \end{formula}
 
-    \begin{formula}{name}
+    \begin{formula}{other}
-        \desc{}{}{$\tan\theta = b$}
+        \desc{Other}{}{$\tan\theta = b$}
-        \desc[german]{}{}{$\tan\theta = b$}
+        \desc[german]{Sonstige}{}{$\tan\theta = b$}
         \eq{\cos x + b\sin x = \sqrt{1 + b^2}\cos(x-\theta)}
     \end{formula}
 
 
-    \Subsection[
+    \Subsubsection[
         \eng{Table of values}
         \ger{Wertetabelle}
-        ]{value_table}
+    ]{value_table}
         \begingroup
             \setlength{\tabcolsep}{0.9em}  % horizontal
             \renewcommand{\arraystretch}{2}  % vertical

src/math/linalg.tex

@@ -1,14 +1,66 @@
-\def\id{\mathbb{1}}
+\Section[
-
-\Part[
     \eng{Linear algebra}
     \ger{Lineare Algebra}
-    ]{linalg}
+]{linalg}
 
-    \Section[
+    \Subsection[
+        \eng{Matrix basics}
+        \ger{Matrizen Basics}
+    ]{matrix}
+
+        \begin{formula}{matrix_matrix_product}
+            \desc{Matrix-matrix product as sum}{}{}
+            \desc[german]{Matrix-Matrix Produkt als Summe}{}{}
+            \eq{C_{ij} = \sum_{k} A_{ik} B_{kj}}
+        \end{formula}
+        \begin{formula}{matrix_vector_product}
+            \desc{Matrix-vector product as sum}{}{}
+            \desc[german]{Matrix-Vektor Produkt als Summe}{}{}
+            \eq{\vec{c}_{i} = \sum_{j} A_{ij} \vec{b}_{j}}
+        \end{formula}
+
+        \begin{formula}{symmetric}
+            \desc{Symmetric matrix}{}{$A$ $n\times n$ \GT{matrix}}
+            \desc[german]{Symmetrische matrix}{}{}
+            \eq{A^\T = A}
+        \end{formula}
+
+        \begin{formula}{unitary}
+            \desc{Unitary matrix}{}{}
+            \desc[german]{Unitäre Matrix}{}{}
+            \eq{U ^\dagger U = \id}
+        \end{formula}
+
+        \Subsubsection[
+            \eng{Transposed matrix}
+            \ger{Transponierte Matrix}
+        ]{transposed}
+            \begin{formula}{sum}
+                \desc{Sum}{}{}
+                \desc[german]{Summe}{}{}
+                \eq{(A+B)^\T = A^\T + B^\T}
+            \end{formula}
+            \begin{formula}{product}
+                \desc{Product}{}{}
+                \desc[german]{Produkt}{}{}
+                \eq{(AB)^\T = B^\T A^\T}
+            \end{formula}
+            \begin{formula}{inverse}
+                \desc{Inverse}{}{}
+                \desc[german]{Inverse}{}{}
+                \eq{(A^{-1})^\T = (A^\T)^{-1}}
+            \end{formula}
+            \begin{formula}{exponential}
+                \desc{Exponential}{}{}
+                \desc[german]{Exponential}{}{}
+                \eq{\exp(A^\T) = (\exp A)^\T \\ \ln(A^\T)=(\ln A)^\T}
+            \end{formula}
+        
+
+    \Subsection[
         \eng{Determinant}
         \ger{Determinante}
-        ]{determinant}
+    ]{determinant}
         \begin{formula}{2x2}
             \desc{2x2 matrix}{}{}
             \desc[german]{2x2 Matrix}{}{}
@@ -43,9 +95,19 @@
         \end{formula}
 
 
-    \Section[
+    \Subsection[
+        \eng{Misc}
+        \ger{Misc}
+    ]{misc}
+
+        \begin{formula}{normal_equation}
+            \desc{Normal equation}{Solves a linear regression problem}{\mat{\theta} hypothesis / weight matrix, \mat{X} design matrix, \vec{y} output vector}
+            % \desc[german]{}{}{}
+            \eq{
+                \mat{\theta} = (\mat{X}^\T \mat{X})^{-1} \mat{X}^\T \vec{y}
+            }
+        \end{formula}   
         
-    ]{zeug}
 
         \begin{formula}{inverse_2x2}
             \desc{Inverse $2\times 2$ matrix}{}{}
@@ -56,12 +118,6 @@
             }
         \end{formula}
 
-        \begin{formula}{unitary}
-            \desc{Unitary matrix}{}{}
-            \desc[german]{Unitäre Matrix}{}{}
-            \eq{U ^\dagger U = \id}
-        \end{formula}
-
         \begin{formula}{svd}
             \desc{Singular value decomposition}{Factorization of complex matrices through rotating \rightarrow rescaling \rightarrow rotation.}{$A$: $m\times n$ matrix, $U$: $m\times m$ unitary matrix, $\Lambda$: $m\times n$ rectangular diagonal matrix with non-negative numbers on the diagonal, $V$: $n\times n$ unitary matrix}
             \desc[german]{Singulärwertzerlegung}{Faktorisierung einer reellen oder komplexen Matrix durch Rotation \rightarrow Skalierung \rightarrow Rotation.}{}
@@ -95,7 +151,7 @@
         \end{formula}
 
 
-    \Section[
+    \Subsection[
         \eng{Eigenvalues}
         \ger{Eigenwerte}
     ]{eigen}

src/math/math.tex

@@ -0,0 +1,5 @@
+\Part[
+    \eng{Mathematics}
+    \ger{Mathematik}
+]{math}
+

src/math/probability_theory.tex

@@ -0,0 +1,345 @@
+\Section[
+    \eng{Probability theory}
+    \ger{Wahrscheinlichkeitstheorie}
+]{pt}
+
+    \begin{formula}{mean}
+        \desc{Mean}{Expectation value}{}
+        \desc[german]{Mittelwert}{Erwartungswert}{}
+        \eq{\braket{x} = \int w(x)\, x\, \d x}
+    \end{formula}
+
+
+    \begin{formula}{variance}
+        \desc{Variance}{Square of the \fqEqRef{math:pt:std-deviation}}{}
+        \desc[german]{Varianz}{Quadrat der\fqEqRef{math:pt:std-deviation}}{}
+        \eq{\sigma^2 = (\Delta \hat{x})^2 = \Braket{\hat{x}^2} - \braket{\hat{x}}^2 = \braket{(x - \braket{x})^2}}
+    \end{formula}
+
+    \begin{formula}{covariance}
+        \desc{Covariance}{}{}
+        \desc[german]{Kovarianz}{}{}
+        \eq{\cov(x,y) = \sigma(x,y) = \sigma_{XY} = \Braket{(x-\braket{x})\,(y-\braket{y})}}
+    \end{formula}
+    
+    \begin{formula}{std-deviation}
+        \desc{Standard deviation}{}{}
+        \desc[german]{Standardabweichung}{}{}
+        \eq{\sigma = \sqrt{\sigma^2} = \sqrt{(\Delta x)^2}}
+    \end{formula}
+
+    \begin{formula}{median}
+        \desc{Median}{Value separating lower half from top half}{$x$ dataset with $n$ elements}
+        \desc[german]{Median}{Teilt die untere von der oberen Hälfte}{$x$ Reihe mit $n$ Elementen}
+        \eq{
+            \textrm{med}(x) = \left\{ \begin{array}{ll} x_{(n+1)/2} & \text{$n$ \GT{odd}} \\ \frac{x_{(n/2)}+x_{((n/2)+1)}}{2} & \text{$n$ \GT{even}} \end{array} \right.
+        }
+    \end{formula}
+
+    \begin{formula}{pdf}
+        \desc{Probability density function}{Random variable has density $f$. The integral gives the probability of $X$ taking a value $x\in[a,b]$.}{$f$ normalized: $\int_{-\infty}^\infty f(x) \d x= 1$}
+        \desc[german]{Wahrscheinlichkeitsdichtefunktion}{Zufallsvariable hat Dichte $f$. Das Integral gibt Wahrscheinlichkeit an, dass $X$ einen Wert $x\in[a,b]$ annimmt}{$f$ normalisiert $\int_{-\infty}^\infty f(x) \d x= 1$}
+        \eq{P([a,b]) := \int_a^b f(x) \d x}
+    \end{formula}
+
+    \begin{formula}{cdf}
+        \desc{Cumulative distribution function}{}{$f$ probability density function}
+        \desc[german]{Kumulative Verteilungsfunktion}{}{$f$ Wahrscheinlichkeitsdichtefunktion}
+        \eq{F(x) = \int_{-\infty}^x f(t) \d t}
+    \end{formula}
+
+    \begin{formula}{pmf}
+        \desc{Probability mass function}{Probability $p$ that \textbf{discrete} random variable $X$ has exact value $x$}{$P$ probability measure}
+        \desc[german]{Wahrscheinlichkeitsfunktion / Zählfunktion}{Wahrscheinlichkeit $p$ dass eine \textbf{diskrete} Zufallsvariable $X$ einen exakten Wert $x$ annimmt}{}
+        \eq{p_X(x) = P(X = x)}
+    \end{formula}
+
+    \begin{formula}{autocorrelation} \absLabel
+        \desc{Autocorrelation}{Correlation of $f$ to itself at an earlier point in time, $C$ is a covariance function}{$\tau$ lag-time}
+        \desc[german]{Autokorrelation}{Korrelation vonn $f$ zu sich selbst zu einem früheren Zeitpunkt. $C$ ist auch die Kovarianzfunktion}{$\tau$ Zeitverschiebung}
+        \eq{C_A(\tau) &= \lim_{T \to \infty} \frac{1}{2T}\int_{-T}^{T} f(t+\tau) f(t) \d t) \\ &= \braket{f(t+\tau)\cdot f(t)}}
+    \end{formula}
+
+    \begin{formula}{binomial_coefficient}
+        \desc{Binomial coefficient}{Number of possibilitites of choosing $k$ objects out of $n$ objects\\}{}
+        \desc[german]{Binomialkoeffizient}{Anzahl der Möglichkeiten, $k$ aus $n$ zu wählen\\ "$n$ über $k$"}{}
+        \eq{\binom{n}{k} = \frac{n!}{k!(n-k)!}}
+    \end{formula}
+
+    \Subsection[
+        \eng{Distributions}
+        \ger{Verteilungen}
+    ]{distributions}
+        \Subsubsection[
+            \eng{Continuous probability distributions}
+            \ger{Kontinuierliche Wahrscheinlichkeitsverteilungen}
+        ]{cont}
+            \begin{bigformula}{normal}
+                \desc{Gauß/Normal distribution}{}{}
+                \desc[german]{Gauß/Normal-Verteilung}{}{}
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_gauss.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
+                    \disteq{support}{x \in \R}
+                    \disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
+                    \disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
+                    \disteq{mean}{\mu}
+                    \disteq{median}{\mu}
+                    \disteq{variance}{\sigma^2}
+                \end{distribution}
+            \end{bigformula}
+
+            \begin{formula}{standard_normal_distribution}
+                \desc{Density function of the standard normal distribution}{$\mu = 0$, $\sigma = 1$}{}
+                \desc[german]{Dichtefunktion der Standard-Normalverteilung}{$\mu = 0$, $\sigma = 1$}{}
+                \eq{\varphi(x) = \frac{1}{\sqrt{2\pi}} \e^{-\frac{1}{2}x^2}}
+            \end{formula}
+
+            \begin{bigformula}{cauchy}
+                \desc{Cauchys / Lorentz distribution}{Also known as Cauchy-Lorentz distribution, Lorentz(ian) function, Breit-Wigner distribution.}{}
+                \desc[german]{Cauchy / Lorentz-Verteilung}{Auch bekannt als Cauchy-Lorentz Verteilung, Lorentz Funktion, Breit-Wigner Verteilung.}{}
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_cauchy.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
+                    \disteq{support}{x \in \R}
+                    \disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
+                    \disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
+                    \disteq{mean}{\text{\GT{undefined}}}
+                    \disteq{median}{x_0}
+                    \disteq{variance}{\text{\GT{undefined}}}
+                \end{distribution}
+            \end{bigformula}
+
+            \begin{bigformula}{maxwell-boltzmann}
+                \desc{Maxwell-Boltzmann distribution}{}{}
+                \desc[german]{Maxwell-Boltzmann Verteilung}{}{}
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{a > 0}
+                    \disteq{support}{x \in (0, \infty)}
+                    \disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
+                    \disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
+                    \disteq{mean}{2a \frac{2}{\pi}}
+                    \disteq{median}{}
+                    \disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
+                \end{distribution}
+            \end{bigformula}
+
+
+            \begin{bigformula}{gamma}
+                \desc{Gamma Distribution}{with $\lambda$ parameter}{$\Gamma$ \fqEqRef{math:cal:integral:list:gamma}, $\gamma$ \fqEqRef{math:cal:integral:list:lower_incomplete_gamma_function}}
+                \desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{}
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_gamma.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{\alpha > 0, \lambda > 0}
+                    \disteq{support}{x\in(0,1)}
+                    \disteq{pdf}{\frac{\lambda^\alpha}{\Gamma(\alpha) x^{\alpha-1} \e^{-\lambda x}}}
+                    \disteq{cdf}{\frac{1}{\Gamma(\alpha) \gamma(\alpha, \lambda x)}}
+                    \disteq{mean}{\frac{\alpha}{\lambda}}
+                    \disteq{variance}{\frac{\alpha}{\lambda^2}}
+                \end{distribution}
+            \end{bigformula}
+
+            \begin{bigformula}{beta}
+                \desc{Beta Distribution}{}{$\txB$ \fqEqRef{math:cal:integral:list:beta_function} / \fqEqRef{math:cal:integral:list:incomplete_beta_function}}
+                \desc[german]{Beta Verteilung}{}{}
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_beta.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{\alpha \in \R, \beta \in \R}
+                    \disteq{support}{x\in[0,1]}
+                    \disteq{pdf}{\frac{x^{\alpha-1} (1-x)^{\beta-1}}{\txB(\alpha,\beta)}}
+                    \disteq{cdf}{\frac{\txB(x;\alpha,\beta)}{\txB(\alpha,\beta)}}
+                    \disteq{mean}{\frac{\alpha}{\alpha+\beta}}
+                    % \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
+                    \disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
+                \end{distribution}
+            \end{bigformula}
+
+
+        \Subsubsection[
+            \eng{Discrete probability distributions}
+            \ger{Diskrete Wahrscheinlichkeitsverteilungen}
+        ]{discrete}
+            \begin{bigformula}{binomial}
+                \desc{Binomial distribution}{}{}
+                \desc[german]{Binomialverteilung}{}{}
+                \begin{ttext}
+                    \eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the   \hyperref[sec:pb:distributions:poisson]{poisson distribution}}
+                    \ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions:poisson]{Poissonverteilung}}
+                \end{ttext}\\
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_binomial.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
+                    \disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
+                    \disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
+                    % \disteq{cdf}{\text{regularized incomplete beta function}}
+                    \disteq{mean}{np}
+                    \disteq{median}{\floor{np} \text{ or } \ceil{np}}
+                    \disteq{variance}{npq = np(1-p)}
+                \end{distribution}
+            \end{bigformula}
+
+            \begin{bigformula}{poisson}
+                \desc{Poisson distribution}{}{}
+                \desc[german]{Poissonverteilung}{}{}
+                \begin{minipage}{\distleftwidth}
+                    \begin{figure}[H]
+                        \centering
+                        \includegraphics[width=\textwidth]{img/distribution_poisson.pdf}
+                    \end{figure}
+                \end{minipage}
+                \begin{distribution}
+                    \disteq{parameters}{\lambda \in (0,\infty)}
+                    \disteq{support}{k \in \N}
+                    \disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
+                    \disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
+                    \disteq{mean}{\lambda}
+                    \disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
+                    \disteq{variance}{\lambda}
+                \end{distribution}
+            \end{bigformula}
+
+
+
+        % TEMPLATE
+        % \begin{distribution}{maxwell-boltzmann}
+        %     \distdesc{Maxwell-Boltzmann distribution}{}
+        %     \distdesc[german]{Maxwell-Boltzmann Verteilung}{}
+        %     \disteq{parameters}{}
+        %     \disteq{pdf}{}
+        %     \disteq{cdf}{}
+        %     \disteq{mean}{}
+        %     \disteq{median}{}
+        %     \disteq{variance}{}
+        % \end{distribution}
+
+
+    \Subsection[
+        \eng{Central limit theorem}
+        \ger{Zentraler Grenzwertsatz}
+        ]{cls}  
+        \begin{ttext}
+            \eng{
+                Suppose $X_1, X_2, \dots$ is a sequence of independent and identically distributed random variables with $\braket{X_i} = \mu$ and $(\Delta X_i)^2 = \sigma^2 < \infty$.
+                As $N$ approaches infinity, the random variables $\sqrt{N}(\bar{X}_N - \mu)$ converge to a normal distribution $\mathcal{N}(0, \sigma^2)$.
+                \\ That means that the variance scales with $\frac{1}{\sqrt{N}}$ and statements become accurate for large $N$.
+            }
+            \ger{
+                Sei $X_1, X_2, \dots$ eine Reihe unabhängiger und gleichverteilter Zufallsvariablen mit $\braket{X_i} = \mu$ und $(\Delta X_i)^2 = \sigma^2 < \infty$.
+                Für $N$ gegen unendlich konvergieren die Zufallsvariablen $\sqrt{N}(\bar{X}_N - \mu)$ zu einer Normalverteilung $\mathcal{N}(0, \sigma^2)$.
+                \\ Das bedeutet, dass die Schwankung mit $\frac{1}{\sqrt{N}}$ wächst und Aussagen für große $N$ scharf werden.
+            }
+        \end{ttext}
+
+    \Subsection[
+        \eng{Propagation of uncertainty / error}
+        \ger{Fehlerfortpflanzung}
+    ]{error}
+        \begin{formula}{generalised}
+            \desc{Generalized error propagation}{}{$V$ \fqEqRef{math:pt:covariance} matrix, $J$ \fqEqRef{math:cal:jacobi-matrix}}
+            \desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fqEqRef{math:pt:covariance} Matrix, $J$ \fqEqRef{cal:jacobi-matrix}}{}
+            \eq{V_y = J(x) \cdot V_x \cdot J^{\T} (x)}
+        \end{formula}
+
+        \begin{formula}{uncorrelated}
+            \desc{Propagation of uncorrelated errors}{Linear approximation}{}
+            \desc[german]{Fortpflanzung unabhängiger fehlerbehaftete Größen}{Lineare Näherung}{}
+            \eq{u_y = \sqrt{ \sum_{i} \left(\pdv{y}{x_i}\cdot u_i\right)^2}}
+        \end{formula}
+
+        \begin{formula}{weight}
+            \desc{Weight}{Variance is a possible choice for a weight}{$\sigma$ \fqEqRef{math:pt:variance}}
+            \desc[german]{Gewicht}{Varianz ist eine mögliche Wahl für ein Gewicht}{}
+            \eq{w_i = \frac{1}{\sigma_i^2}}
+        \end{formula}
+
+        \begin{formula}{weighted-mean}
+            \desc{Weighted mean}{}{$w_i$ \fqEqRef{math:pt:error:weight}}
+            \desc[german]{Gewichteter Mittelwert}{}{}
+            \eq{\overline{x} = \frac{\sum_{i} (x_i  w_i)}{\sum_i w_i}}
+        \end{formula}
+
+        \begin{formula}{weighted-mean-error}
+            \desc{Variance of weighted mean}{}{$w_i$ \fqEqRef{math:pt:error:weight}}
+            \desc[german]{Varianz des gewichteten Mittelwertes}{}{}
+            \eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
+        \end{formula}
+
+    \Subsection[
+        \eng{Maximum likelihood estimation}
+        \ger{Maximum likelihood Methode}
+    ]{mle}
+        \begin{formula}{likelihood}
+            \desc{Likelihood function}{Likelihood of observing $x$ when parameter is $\theta$\\in general not normalized!}{$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ depending on parameter $\theta$, $\Theta$ parameter space}
+            \desc[german]{Likelihood Funktion}{"Plausibilität" $x$ zu messen, wenn der Parameter $\theta$ ist\\nicht normalisiert!}{$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ hängt ab von Parameter $\theta$, $\Theta$ Parameterraum}
+            \eq{L:\Theta \rightarrow [0,1], \quad \theta \mapsto \rho(x|\theta)}
+        \end{formula}
+        \begin{formula}{likelihood_independant}
+            \desc{Likelihood function}{for independent and identically distributed random variables}{$x_i$ $n$ random variables, $\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ depending on parameter $\theta$}
+            \desc[german]{Likelihood function}{für unabhängig und identisch verteilte Zufallsvariablen}{$x_i$ $n$ Zufallsvariablen$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ hängt ab von Parameter $\theta$}
+            \eq{L(\theta) = \prod_{i=1}^n f(x_i;\theta)}
+        \end{formula}
+        \begin{formula}{maximum_likelihood_estimate}
+            \desc{Maximum likelihood estimate (MLE)}{Paramater for which outcome is most likely}{$L$ \fqEqRef{pt:mle:likelihood}, $\theta$ parameter of a \fqEqRef{math:pt:pdf}}
+            \desc[german]{Maximum likelihood-Schätzung (MLE)}{Paramater, für den das Ergebnis am Wahrscheinlichsten ist}{$L$ \fqEqRef{math:pt:mle:likelihood}, $\theta$ Parameter einer \fqEqRef{math:pt:pdf}}
+            \eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)}
+        \end{formula}
+
+    \Subsection[
+        \eng{Bayesian probability theory}
+        \ger{Bayessche Wahrscheinlichkeitstheorie}
+    ]{bayesian}
+        \begin{formula}{prior}
+            \desc{Prior distribution}{Expected distribution before conducting the experiment}{$\theta$ parameter}
+            \desc[german]{Prior Verteilung}{}{}
+            \eq{p(\theta)}
+        \end{formula}
+
+        \begin{formula}{evidence}
+            \desc{Evidence}{}{$p(\mathcal{D}|\theta)$ \fqEqRef{math:pt:mle:likelihood}, $p(\theta)$ \fqEqRef{math:pt:bayesian:prior}, $\mathcal{D}$ data set}
+            % \desc[german]{}{}{}
+            \eq{p(\mathcal{D}) = \int\d\theta \,p(\mathcal{D}|\theta)\,p(\theta)}
+        \end{formula}
+
+        \begin{formula}{theorem}
+            \desc{Bayes' theorem}{}{$p(\theta|\mathcal{D})$ posterior distribution, $p(\mathcal{D}|\theta)$ \fqEqRef{math:pt:mle:likelihood}, $p(\theta)$ \fqEqRef{math:pt:bayesian:prior}, $p(\mathcal{D})$ \fqEqRef{math:pt:bayesian:evidence}, $\mathcal{D}$ data set}
+            \desc[german]{Satz von Bayes}{}{}
+            \eq{p(\theta|\mathcal{D}) = \frac{p(\mathcal{D}|\theta)\,p(\theta)}{p(\mathcal{D})}}
+        \end{formula}
+
+        \begin{formula}{map}
+            \desc{Maximum a posterior estimation (MAP)}{}{}
+            % \desc[german]{}{}{}
+            \eq{\theta_\text{MAP} = \argmax_\theta p(\theta|\mathcal{D}) = \argmax_\theta p(\mathcal{D}|\theta)\,p(\theta)}
+        \end{formula}
+

src/mechanics.tex

@@ -3,6 +3,46 @@
     \ger{Mechanik}
 ]{mech}
 
+\Section[
+    \eng{Newton}
+    \ger{Newton}
+]{newton}
+    \begin{formula}{newton_laws}
+        \desc{Newton's laws}{}{}
+        \desc[german]{Newtonsche Gesetze}{}{}
+        \ttxt{
+            \eng{
+                \begin{enumerate}
+                    \item A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force
+                    \item $$\vec{F} = m \cdot \vec{a}$$
+                    \item If two bodies exert forces on each other, these force have the same magnitude but opposite directions
+                        $$\vec{F}_{\txA\rightarrow\txB} = -\vec{F}_{\txB\rightarrow\txA}$$
+                \end{enumerate}
+
+            }
+            \ger{
+                \begin{enumerate}
+                    \item Ein kräftefreier Körper bleibt in Ruhe oder bewegt sich geradlinig mit konstanter Geschwindigkeit
+                    \item $$\vec{F} = m \cdot \vec{a}$$
+                    \item Eine Kraft von Körper A auf Körper B geht immer mit einer gleich große, aber entgegen gerichteten Kraft von Körper B auf Körper A einher:
+                        $$\vec{F}_{\txA\rightarrow\txB} = -\vec{F}_{\txB\rightarrow\txA}$$
+                \end{enumerate}
+            }
+        }
+    \end{formula}
+
+\Section[
+    \eng{Misc}
+    \ger{Verschiedenes}
+]{misc}
+    \begin{formula}{hook}
+        \desc{Hooke's law}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ spring length}
+        \desc[german]{Hookesches Gesetz}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ Federlänge}
+        \eq{
+            F = D\Delta l
+        }
+    \end{formula}
+
 \def\lagrange{\mathcal{L}}
 \Section[
     \eng{Lagrange formalism}
@@ -26,7 +66,7 @@
             Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
         }
     \end{ttext}
-    \begin{formula}{lagrangian}
+    \begin{formula}{lagrangian} \absLabel
         \desc{Lagrange function}{}{$T$ kinetic energy, $V$ potential energy }
         \desc[german]{Lagrange-Funktion}{}{$T$ kinetische Energie, $V$ potentielle Energie}
         \eq{\lagrange = T - V}

src/particle.tex

@@ -0,0 +1,114 @@
+\Part[
+    \eng{Particle physics}
+    \ger{Teilchenphysik}
+]{particle}
+
+    \begin{formula}{electron_mass}
+        \desc{Electron mass}{}{}
+        \desc[german]{Elektronenmasse}{}{}
+        \constant{m_\txe}{exp}{
+            \val{9.1093837139(28) \xE{-31}}{\kg}
+        }
+    \end{formula}
+
+    \begin{formula}{spin}
+        \desc{Spin}{}{}
+        \desc[german]{Spin}{}{}
+        \quantity{\sigma}{}{v}
+    \end{formula}
+
+    \begin{bigformula}{standard_model}
+        \desc{Standard model}{}{}
+        \desc[german]{Standartmodell}{}{}
+        \centering
+
+\tikzset{%
+          label/.style = { black, midway, align=center },
+       toplabel/.style = { label, above=.5em, anchor=south },
+      leftlabel/.style = { midway, left=.5em, anchor=east },   
+    bottomlabel/.style = { label, below=.5em, anchor=north },
+          force/.style = { rotate=-90,scale=0.4 },
+          round/.style = { rounded corners=2mm },
+         legend/.style = { anchor=east },
+          nosep/.style = { inner sep=0pt },
+     generation/.style = { anchor=base },
+          brace/.style = { decoration={brace,mirror},decorate }
+}
+
+% [1]: color
+% 2: symbol
+% 3: name
+% 4: mass
+% 5: spin
+% 6: charge
+% 7: colors 
+\newcommand\drawParticle[7][white]{%
+    \begin{tikzpicture}[x=2.2cm, y=2.2cm]
+        % \path[fill=#1,blur shadow={shadow blur steps=5}] (0,0) -- (1,0) -- (1,1) -- (0,1) -- cycle;
+        % \path[fill=#1,stroke=black,blur shadow={shadow blur steps=5},rounded corners] (0,0) rectangle (1,1);
+        \path[fill=#1!20!bg0,draw=#1,thick] (0.02,0.02) rectangle (0.98,0.98);
+        \node at(0.92, 0.50) [nosep,anchor=east]{\Large #2};
+        % \node at(0.95, 0.15) [nosep,anchor=south east]{\footnotesize #3};
+        \node at(0.05, 0.15) [nosep,anchor=south west]{\footnotesize #3};
+        % \ifstrempty{#2}{}{\node at(0)  [nosep,anchor=west,scale=1.5] {#2};}
+        % \ifstrempty{#3}{}{\node at(0.1,-0.85) [nosep,anchor=west,scale=0.3] {#3};}
+        \ifstrempty{#4}{}{\node at(0.05,0.85)  [nosep,anchor=west] {\footnotesize #4};}
+        \ifstrempty{#5}{}{\node at(0.05,0.70)  [nosep,anchor=west] {\footnotesize #5};}
+        \ifstrempty{#6}{}{\node at(0.05,0.55)  [nosep,anchor=west] {\footnotesize #6};}
+        % \ifstrempty{#7}{}{\node at(0.05,0.40)  [nosep,anchor=west] {\footnotesize #7};}
+    \end{tikzpicture}
+}
+\def\colorLepton{bg-aqua}
+\def\colorQuarks{bg-purple}
+\def\colorGauBos{bg-red}
+\def\colorScaBos{bg-yellow}
+\eng[quarks]{Quarks}
+\ger[quarks]{Quarks}
+\eng[leptons]{Leptons}
+\ger[leptons]{Leptonen}
+\eng[fermions]{Fermions}
+\ger[fermions]{Fermionen}
+\eng[bosons]{Bosons}
+\ger[bosons]{Bosonen}
+
+\begin{tikzpicture}[x=2.2cm, y=2.2cm]
+    \node at(0, 0)   {\drawParticle[\colorQuarks]{$u$}        {up}            {$2.3$ MeV}{1/2}{$2/3$}{R/G/B}};
+    \node at(0,-1)   {\drawParticle[\colorQuarks]{$d$}        {down}          {$4.8$ MeV}{1/2}{$-1/3$}{R/G/B}};
+    \node at(0,-2)   {\drawParticle[\colorLepton]{$e$}        {electron}      {$511$ keV}{1/2}{$-1$}{}};
+    \node at(0,-3)   {\drawParticle[\colorLepton]{$\nu_e$}    {$e$ neutrino}  {$<2.2$ eV}{1/2}{0}{}};
+    \node at(1, 0)   {\drawParticle[\colorQuarks]{$c$}        {charm}         {$1.275$ GeV}{1/2}{$2/3$}{R/G/B}};
+    \node at(1,-1)   {\drawParticle[\colorQuarks]{$s$}        {strange}       {$95$ MeV}{1/2}{$-1/3$}{R/G/B}};
+    \node at(1,-2)   {\drawParticle[\colorLepton]{$\mu$}      {muon}          {$105.7$ MeV}{1/2}{$-1$}{}};
+    \node at(1,-3)   {\drawParticle[\colorLepton]{$\nu_\mu$}  {$\mu$ neutrino}{$<170$ keV}{1/2}{0}{}};
+    \node at(2, 0)   {\drawParticle[\colorQuarks]{$t$}        {top}           {$173.2$ GeV}{1/2}{$2/3$}{R/G/B}};
+    \node at(2,-1)   {\drawParticle[\colorQuarks]{$b$}        {bottom}        {$4.18$ GeV}{1/2}{$-1/3$}{R/G/B}};
+    \node at(2,-2)   {\drawParticle[\colorLepton]{$\tau$}     {tau}           {$1.777$ GeV}{1/2}{$-1$}{}};
+    \node at(2,-3)   {\drawParticle[\colorLepton]{$\nu_\tau$} {$\tau$ neutrino} {$<15.5$ MeV}{1/2}{0}{}};
+    \node at(3, 0)   {\drawParticle[\colorGauBos]{$g$}        {gluon}         {0}{1}{0}{color}};
+    \node at(3,-1)   {\drawParticle[\colorGauBos]{$\gamma$}   {photon}        {0}{1}{0}{}};
+    \node at(3,-2)   {\drawParticle[\colorGauBos]{$Z$}        {}              {$91.2$ GeV}{1}{0}{}};
+    \node at(3,-3)   {\drawParticle[\colorGauBos]{$W_\pm$}    {}              {$80.4$ GeV}{1}{$\pm1$}{}}; 
+    \node at(4,0)    {\drawParticle[\colorScaBos]{$H$}        {Higgs}         {$125.1$ GeV}{0}{0}{}};
+    
+    \draw [->] (-0.7, 0.35) node [legend] {\qtyRef{mass}}  -- (-0.5, 0.35);
+    \draw [->] (-0.7, 0.20) node [legend] {\qtyRef{spin}}  -- (-0.5, 0.20);
+    \draw [->] (-0.7, 0.05) node [legend] {\qtyRef{charge}} -- (-0.5, 0.05);
+    \draw [->] (-0.7,-0.10) node [legend] {\GT{colors}} -- (-0.5,-0.10);
+    
+    \draw [brace,draw=\colorQuarks] (-0.55, 0.5) -- (-0.55,-1.5) node[leftlabel,color=\colorQuarks] {\gt{quarks}};
+    \draw [brace,draw=\colorLepton] (-0.55,-1.5) -- (-0.55,-3.5) node[leftlabel,color=\colorLepton] {\gt{leptons}};
+    \draw [brace] (-0.5,-3.55) -- ( 2.5,-3.55) node[bottomlabel] {\gt{fermions}};
+    \draw [brace] ( 2.5,-3.55) -- ( 4.5,-3.55) node[bottomlabel] {\gt{bosons}};
+    
+    
+    \draw [brace] (0.5,0.55) -- (-0.5,0.55) node[toplabel] {\small standard matter};
+    \draw [brace] (2.5,0.55) -- ( 0.5,0.55) node[toplabel] {\small unstable matter};
+    \draw [brace] (4.5,0.55) -- ( 2.5,0.55) node[toplabel] {\small force carriers};
+    
+    \node at (0,0.85) [generation] {\small   I};
+    \node at (1,0.85) [generation] {\small  II};
+    \node at (2,0.85) [generation] {\small III};
+    \node at (1,1.05) [generation] {\small generation};
+\end{tikzpicture}
+
+    \end{bigformula}

src/pkg/mqconstant.sty

@@ -0,0 +1,62 @@
+\ProvidesPackage{mqconstant}
+\RequirePackage{mqlua}
+\RequirePackage{etoolbox}
+
+\directLuaAux{
+    if constants == nil then
+        constants = {}
+    end
+}
+
+% [1]: label to point to
+% 2: key
+% 3: symbol
+% 4: either exp or def; experimentally or defined constant
+\newcommand{\constant@new}[4][\relax]{
+    \directLuaAux{
+        constants["#2"] = {}
+        constants["#2"]["symbol"]  = [[\detokenize{#3}]]
+        constants["#2"]["exp_or_def"]   = [[\detokenize{#4}]]
+        constants["#2"]["values"] = {} %-- array of {value, unit}
+    }
+    \ifstrempty{#1}{}{
+        \directLuaAuxExpand{
+            constants["#2"]["linkto"] = [[#1]] %-- fqname required for getting the translation key
+        }
+    }
+}
+
+% 1: key
+% 2: value
+% 3: units
+\newcommand{\constant@addValue}[3]{
+    \directlua{
+        table.insert(constants["#1"]["values"], { value = [[\detokenize{#2}]], unit = [[\detokenize{#3}]] })
+    }
+}
+
+% 1: key
+\newcommand\constant@print[1]{
+    \begingroup % for label
+        Symbol: $\luavar{constants["#1"]["symbol"]}$
+        % \\Unit: $\directlua{split_and_print_units(constants["#1"]["units"])}$
+        \directlua{
+            tex.print("\\\\\\GT{const:"..constants["#1"]["exp_or_def"].."}")
+        }
+        \directlua{
+            %--tex.sprint("Hier steht Luatext" .. ":", #constVals)
+            for i, pair in ipairs(constants["#1"]["values"]) do
+            tex.sprint("\\\\\\hspace*{1cm}${", pair["value"], "}\\,\\si{", pair["unit"], "}$")
+                %--tex.sprint("VALUE ", i, v)
+            end
+        }
+        % label it only once
+        \directlua{ 
+            if constants["#1"]["labeled"] == nil then
+                constants["#1"]["labeled"] = true
+                tex.print("\\label{const:#1}")
+            end
+        }
+    \endgroup
+}
+\newcounter{constant}

src/pkg/mqformula.sty

@@ -0,0 +1,250 @@
+\ProvidesPackage{mqformula}
+
+\RequirePackage{mqfqname}
+\RequirePackage{mqconstant}
+\RequirePackage{mqquantity}
+
+%
+% FORMULA ENVIRONMENT
+% The following commands are meant to be used with the formula environment
+%
+
+% Name in black and below description in gray
+% [1]: minipage width
+% 2: fqname of name
+% 3: fqname of a translation that holds the explanation
+\newcommand{\NameWithDescription}[3][\descwidth]{
+    \begin{minipage}{#1}
+        \IfTranslationExists{#2}{
+            \raggedright
+            \GT{#2}
+        }{\detokenize{#2}}
+        \IfTranslationExists{#3}{
+            \\ {\color{fg1} \GT{#3}}
+        }{}
+    \end{minipage}
+}
+
+
+% TODO: rename
+\newsavebox{\contentBoxBox}
+% [1]: minipage width
+% 2: fqname of a translation that holds the explanation
+\newenvironment{ContentBoxWithExplanation}[2][\eqwidth]{
+    \def\ContentFqName{#2}
+    \begin{lrbox}{\contentBoxBox}
+    \begin{minipage}{#1}
+}{
+        \IfTranslationExists{\ContentFqName}{%
+            \smartnewline
+            \noindent
+            \begingroup
+                \color{fg1} 
+                \GT{\ContentFqName}
+                % \edef\temp{\GT{#1_defs}}
+                % \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
+            \endgroup
+        }{}
+    \end{minipage}
+    \end{lrbox}
+    \fbox{\usebox{\contentBoxBox}}
+}
+
+
+% Class defining commands shared by all formula environments
+% 1: key
+\newenvironment{formulainternal}[1]{
+    % [1]: language
+    % 2: name
+    % 3: description
+    % 4: definitions/links
+    \newcommand{\desc}[4][english]{
+        % language, name, description, definitions
+        \ifblank{##2}{}{\dt[#1]{##1}{##2}}
+        \ifblank{##3}{}{\dt[#1_desc]{##1}{##3}}
+        \ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
+    }
+    \directlua{n_formulaEntries = 0}
+
+    % makes this formula referencable with \abbrRef{<name>}
+    % [1]: label to use
+    % 2: Abbreviation to use for references
+    \newcommand{\abbrLabel}[2][#1]{
+        \abbrLink[f:\fqname]{##1}{##2}
+    }
+    % makes this formula referencable with \absRef{<name>}
+    % [1]: label to use
+    \newcommand{\absLabel}[1][#1]{
+        \absLink[f:\fqname]{##1}
+    }
+
+    \newcommand{\newFormulaEntry}{
+        \directlua{
+            if n_formulaEntries > 0 then
+            tex.print("\\vspace{0.3\\baselineskip}\\hrule\\vspace{0.3\\baselineskip}")
+            end
+            n_formulaEntries = n_formulaEntries + 1
+        }
+        % \par\noindent\ignorespaces
+    }
+    % 1: equation for align environment
+    \newcommand{\eq}[1]{
+        \newFormulaEntry
+        \begin{align}
+            % \label{eq:\fqname:#1}
+            ##1
+        \end{align}
+    }
+    % 1: equation for alignat environment
+    \newcommand{\eqAlignedAt}[2]{
+        \newFormulaEntry
+        \begin{flalign}%
+            \TODO{\text{remove macro}}
+            % dont place label when one is provided
+            % \IfSubStringInString{label}\unexpanded{#3}{}{
+            %     \label{eq:#1}
+            % }
+            ##1%
+        \end{flalign}
+    }
+    % 1: equation for flalign environment
+    \newcommand{\eqFLAlign}[2]{
+        \newFormulaEntry
+        \begin{alignat}{##1}%
+            % dont place label when one is provided
+            % \IfSubStringInString{label}\unexpanded{#3}{}{
+            %     \label{eq:#1}
+            % }
+            ##2%
+        \end{alignat}
+    }
+    \newcommand{\fig}[2][1.0]{
+        \newFormulaEntry
+        \centering
+        \includegraphics[width=##1\textwidth]{##2}
+    }
+    % 1: content for the ttext environment
+    \newcommand{\ttxt}[2][#1:desc]{
+        \newFormulaEntry
+        \begin{ttext}[##1]
+            ##2
+        \end{ttext}
+    }
+    % 1: symbol
+    % 2: units
+    % 3: comment key to translation
+    \newcommand{\quantity}[3]{%
+        \quantity@new[\fqname]{#1}{##1}{##2}{##3}
+        \newFormulaEntry
+        \quantity@print{#1}
+    }
+
+    % must be used only in third argument of "constant" command
+    % 1: value
+    % 2: unit
+    \newcommand{\val}[2]{
+        \constant@addValue{#1}{##1}{##2}
+    }
+    % 1: symbol
+    % 2: either exp or def; experimentally or defined constant
+    % 3: one or more \val{value}{unit} commands
+    \newcommand{\constant}[3]{
+        \constant@new[\fqname]{#1}{##1}{##2}
+        \begingroup
+            ##3
+        \endgroup
+        \newFormulaEntry
+        \constant@print{#1}
+    }
+}{}
+
+\newenvironment{formula}[1]{
+    \begin{formulainternal}{#1}
+
+    \begingroup
+        \label{f:\fqname:#1}
+        \storeLabel{\fqname:#1}
+        \par\noindent\ignorespaces
+        % \textcolor{gray}{\hrule}
+        % \vspace{0.5\baselineskip}
+        \NameWithDescription[\descwidth]{\fqname:#1}{\fqname:#1_desc}
+        \hfill
+        \begin{ContentBoxWithExplanation}{\fqname:#1_defs}
+}{
+        \end{ContentBoxWithExplanation}
+    \endgroup
+    \separateEntries
+    % \textcolor{fg3}{\hrule}
+    % \vspace{0.5\baselineskip}
+    \ignorespacesafterend
+    \end{formulainternal}
+}
+
+
+% BIG FORMULA
+\newenvironment{bigformula}[1]{
+    \begin{formulainternal}{#1}
+
+    \edef\tmpFormulaName{#1}
+    \par\noindent
+    \begin{minipage}{\textwidth}  % using a minipage to now allow line breaks within the bigformula
+        \label{f:\fqname:#1}
+        \par\noindent\ignorespaces
+        % \textcolor{gray}{\hrule}
+        % \vspace{0.5\baselineskip}
+        \textbf{
+            \IfTranslationExists{\fqname:#1}{%
+                    \raggedright
+                    \GT{\fqname:#1}
+            }{\detokenize{#1}}
+        }
+        \IfTranslationExists{\fqname:#1_desc}{
+               : {\color{fg1} \GT{\fqname:#1_desc}}
+        }{}
+        \hfill
+        \par
+}{
+        \edef\tmpContentDefs{\fqname:\tmpFormulaName_defs}
+        \IfTranslationExists{\tmpContentDefs}{%
+            \smartnewline
+            \noindent
+            \begingroup
+                \color{fg1} 
+                \GT{\tmpContentDefs}
+                % \edef\temp{\GT{#1_defs}}
+                % \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
+            \endgroup
+        }{}
+    \end{minipage}
+    \separateEntries
+    % \textcolor{fg3}{\hrule}
+    % \vspace{0.5\baselineskip}
+    \ignorespacesafterend
+    \end{formulainternal}
+}
+
+\newenvironment{hiddenformula}[1]{
+    \begin{formulainternal}{#1}
+    \renewcommand{\eq}[1]{}
+    \renewcommand{\eqAlignedAt}[2]{}
+    \renewcommand{\eqFLAlign}[2]{}
+    \renewcommand{\fig}[2][1.0]{}
+    \renewcommand{\ttxt}[2][#1:desc]{}
+    % 1: symbol
+    % 2: units
+    % 3: comment key to translation
+    \renewcommand{\quantity}[3]{%
+        \quantity@new[\fqname]{#1}{##1}{##2}{##3}
+    }
+    % 1: symbol
+    % 2: either exp or def; experimentally or defined constant
+    % 3: one or more \val{value}{unit} commands
+    \renewcommand{\constant}[3]{
+        \constant@new[\fqname]{#1}{##1}{##2}
+        \begingroup
+            ##3
+        \endgroup
+    }
+}{
+    \end{formulainternal}
+}

src/pkg/mqfqname.sty

@@ -0,0 +1,209 @@
+\ProvidesPackage{mqfqname}
+\RequirePackage{mqlua}
+\RequirePackage{etoolbox}
+
+
+\directlua{
+    sections = sections or {}
+
+    function fqnameEnter(name)
+      table.insert(sections, name)
+      % table.sort(sections)
+    end
+
+    function fqnameLeave()
+      if table.getn(sections) > 0 then
+        table.remove(sections)
+      end
+    end
+
+    function fqnameGet()
+      return table.concat(sections, ":")
+    end
+
+    function fqnameLeaveOnlyFirstN(n)
+      if n >= 0 then
+        while table.getn(sections) > n do
+          table.remove(sections)
+        end
+      end
+    end
+}
+\newcommand{\mqfqname@update}{%
+  \edef\fqname{\luavar{fqnameGet()}}
+}
+\newcommand{\mqfqname@enter}[1]{%
+  \directlua{fqnameEnter("\luaescapestring{#1}")}%
+  \mqfqname@update
+}
+\newcommand{\mqfqname@leave}{%
+  \directlua{fqnameLeave()}%
+  \mqfqname@update
+}
+
+\newcommand{\mqfqname@leaveOnlyFirstN}[1]{%
+  \directlua{fqnameLeaveOnlyFirstN(#1)}%
+}
+
+% SECTIONING
+% start <section>, get heading from translation, set label
+% secFqname is the fully qualified name of sections: the keys of all previous sections joined with a ':'
+% fqname is secFqname:<key> where <key> is the key/id of some environment, like formula
+% [1]: code to run after setting \fqname, but before the \part, \section etc
+% 2: key
+\newcommand{\Part}[2][desc]{
+    \newpage
+    \mqfqname@leaveOnlyFirstN{0}
+    \mqfqname@enter{#2}
+    \edef\secFqname{\fqname}
+    #1
+    % this is necessary so that \part/\section... takes the fully expanded string. Otherwise the pdf toc will have just the fqname
+    \edef\fqnameText{\GT{\fqname}}
+    \part{\fqnameText} 
+    \label{sec:\fqname}
+}
+\newcommand{\Section}[2][]{
+    \mqfqname@leaveOnlyFirstN{1}
+    \mqfqname@enter{#2}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\GT{\fqname}}
+    \section{\fqnameText}
+    \label{sec:\fqname}
+}
+\newcommand{\Subsection}[2][]{
+    \mqfqname@leaveOnlyFirstN{2}
+    \mqfqname@enter{#2}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\GT{\fqname}}
+    \subsection{\fqnameText}
+    \label{sec:\fqname}
+}
+\newcommand{\Subsubsection}[2][]{
+    \mqfqname@leaveOnlyFirstN{3}
+    \mqfqname@enter{#2}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\GT{\fqname}}
+    \subsubsection{\fqnameText}
+    \label{sec:\fqname}
+}
+\edef\fqname{NULL}
+
+\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
+
+
+\newcommand\luaDoubleFieldValue[3]{%
+    \directlua{
+        if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
+            tex.sprint(#1[#2][#3])
+            return
+        end
+        luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
+        tex.sprint("???")
+    }%
+}
+% REFERENCES
+% All xyzRef commands link to the key using the translated name
+% Uppercase (XyzRef) commands have different link texts, but the same link target
+% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
+
+% Equations/Formulas
+% \newrobustcmd{\fqEqRef}[1]{%
+\newrobustcmd{\fqEqRef}[1]{%
+    % \edef\fqeqrefname{\GT{#1}}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[f:#1]{\GT{#1}}%
+}
+% Formula in the current section
+\newrobustcmd{\secEqRef}[1]{%
+    % \edef\fqeqrefname{\GT{#1}}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[f:\secFqname:#1]{\GT{\secFqname:#1}}%
+}
+
+% Section
+% <name>
+\newrobustcmd{\fqSecRef}[1]{%
+    \hyperref[sec:#1]{\GT{#1}}%
+}
+% Quantities
+% <symbol>
+\newrobustcmd{\qtyRef}[1]{%
+    \edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"linkto"}}%
+    \hyperref[qty:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\QtyRef}[1]{%
+    $\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
+}
+% Constants
+% <name>
+\newrobustcmd{\constRef}[1]{%
+    \edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"linkto"}}%
+    \hyperref[const:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\ConstRef}[1]{%
+    $\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
+}
+% Element from periodic table
+% <symbol>
+\newrobustcmd{\elRef}[1]{%
+    \hyperref[el:#1]{{\color{fg0}#1}}%
+}
+% <name>
+\newrobustcmd{\ElRef}[1]{%
+    \hyperref[el:#1]{\GT{el:#1}}%
+}
+
+
+
+% "LABELS"
+% These currently do not place a label,
+% instead they provide an alternative way to reference an existing label
+\directLuaAux{
+    absLabels = absLabels or {}
+    abbrLabels = abbrLabel or {}
+}
+% [1]: target (fqname to point to)
+% 2: key
+\newcommand{\absLink}[2][sec:\fqname]{
+    \directLuaAuxExpand{
+        absLabels["#2"] = [[#1]] 
+    } 
+}
+% [1]: target (fqname to point to)
+% 2: key
+% 3: label (abbreviation)
+\newcommand{\abbrLink}[3][sec:\fqname]{
+    \directLuaAuxExpand{
+        abbrLabels["#2"] = {}
+        abbrLabels["#2"]["abbr"] = [[#3]] 
+        abbrLabels["#2"]["fqname"] = [[#1]] 
+    } 
+}
+% [1]: 
+\newrobustcmd{\absRef}[2][\relax]{%
+    \directlua{
+        if absLabels["#2"] == nil then
+            tex.sprint("\\detokenize{#2}???")
+        else
+            if "#1" == "" then  %-- if [#1]  is not given, use translation of key as text, else us given text
+                tex.sprint("\\hyperref[" .. absLabels["#2"] .. "]{\\GT{" .. absLabels["#2"] .. "}}")
+            else
+                tex.sprint("\\hyperref[" .. absLabels["#2"] .. "]{\luaescapestring{#1}}")
+            end
+        end
+    }
+}
+\newrobustcmd{\abbrRef}[1]{%
+    \directlua{
+        if abbrLabels["#1"] == nil then
+            tex.sprint("\\detokenize{#1}???")
+        else
+            tex.sprint("\\hyperref[" .. abbrLabels["#1"]["fqname"] .. "]{" .. abbrLabels["#1"]["abbr"] .. "}")
+        end
+    }
+}

src/pkg/mqlua.sty

@@ -0,0 +1,88 @@
+\ProvidesPackage{mqlua}
+
+\RequirePackage{luacode}
+\LuaCodeDebugOn
+
+\newcommand\luavar[1]{\directlua{tex.sprint(#1)}}
+
+\begin{luacode*}
+function warning(message)
+  -- Get the current file name and line number
+  -- local info = debug.getinfo(2, "Sl")
+  -- local file_name = info.source
+  -- local line_number = info.currentline
+  -- tex.error(string.format("Warning  %s at %s:%d", message, file_name, line_number))
+  texio.write("\nWARNING: " .. message .. "\n")
+end
+
+OUTDIR = os.getenv("TEXMF_OUTPUT_DIRECTORY") or "."
+
+function fileExists(file)
+    local f = io.open(file, "rb")
+    if f then f:close() end
+    return f ~= nil
+end
+  
+
+warning("TEST")
+\end{luacode*}
+
+% units: siunitx units arguments, possibly chained by '='
+% returns: 1\si{unit1} = 1\si{unit2} = ...
+\directlua{
+function split_and_print_units(units)
+    if units == nil then
+        tex.print("1")
+        return
+    end
+        
+    local parts = {}
+    for part in string.gmatch(units, "[^=]+") do
+        table.insert(parts, part)
+    end
+    local result = ""
+    for i, unit in ipairs(parts) do
+        if i > 1 then result = result .. " = " end
+        result = result .. "\\SI{1}{" .. unit .. "}"
+    end
+    tex.print(result)
+end
+}
+
+% STRING UTILITY
+\luadirect{
+  function string.startswith(s, start)
+      return string.sub(s,1,string.len(start)) == start
+  end
+
+  function string.sanitize(s) 
+      % -- Use gsub to replace the specified characters with an empty string
+      local result = s:gsub("[_^&]", "")
+      return result
+  end
+}
+% Write directlua command to aux and run it as well
+% This one expands the argument in the aux file:
+\newcommand\directLuaAuxExpand[1]{
+    \immediate\write\luaAuxFile{\noexpand\directlua{#1}}
+    \directlua{#1}
+}
+% This one does not:
+\newcommand\directLuaAux[1]{
+    \immediate\write\luaAuxFile{\noexpand\directlua{\detokenize{#1}}}
+    \directlua{#1}
+}
+
+% read
+\IfFileExists{\jobname.lua.aux}{%
+  \input{\jobname.lua.aux}%
+}{%
+    % \@latex@warning@no@line{"Lua aux not loaded!"}
+}
+\def\luaAuxLoaded{False}
+
+% write
+\newwrite\luaAuxFile
+\immediate\openout\luaAuxFile=\jobname.lua.aux
+\immediate\write\luaAuxFile{\noexpand\def\noexpand\luaAuxLoaded{True}}%
+\AtEndDocument{\immediate\closeout\luaAuxFile}

src/pkg/mqperiodictable.sty

@@ -0,0 +1,170 @@
+\ProvidesPackage{mqperiodictable}
+\RequirePackage{mqtranslation}
+\RequirePackage{mqlua}
+% Store info about elements in a lua table
+% Print as list or as periodic table
+% The data is taken from https://pse-info.de/de/data as json and parsed by the scripts/periodic_table.py
+
+% INFO
+\directLuaAux{
+    if elements == nil then
+        elements = {}       %-- Symbol: {symbol, atomic_number, properties, ... }
+        elementsOrder = {}  %-- Number: Symbol
+    end
+}
+
+% 1: symbol
+% 2: nr
+% 3: period
+% 4: column
+\newenvironment{element}[4]{
+    % [1]: language
+    % 2: name
+    % 3: description
+    % 4: definitions/links
+    \newcommand{\desc}[4][english]{
+        % language, name, description, definitions
+        \ifblank{##2}{}{\DT[el:#1]{##1}{##2}}
+        \ifblank{##3}{}{\DT[el:#1_desc]{##1}{##3}}
+        \ifblank{##4}{}{\DT[el:#1_defs]{##1}{##4}}
+    }
+    \directLuaAux{
+        elementsOrder[#2] = "#1";
+        elements["#1"] = {};
+        elements["#1"]["symbol"]  = [[\detokenize{#1}]];
+        elements["#1"]["atomic_number"]  = [[\detokenize{#2}]];
+        elements["#1"]["period"]  = [[\detokenize{#3}]];
+        elements["#1"]["column"]  = [[\detokenize{#4}]];
+        elements["#1"]["properties"]  = {};
+    }
+    % 1: key
+    % 2: value
+    \newcommand{\property}[2]{
+        \directlua{  %-- writing to aux is only needed for references for now
+            elements["#1"]["properties"]["##1"] = "\luaescapestring{\detokenize{##2}}" %-- cant use [[ ]] because electron_config ends with ]
+        }
+    }
+    \edef\lastElementName{#1}
+}{
+    % \expandafter\printElement{\lastElementName}
+    \ignorespacesafterend
+}
+
+% LIST
+\newcommand\printElement[1]{
+    \edef\elementName{el:#1}
+    \par\noindent\ignorespaces
+    \vspace{0.5\baselineskip}
+    \begingroup
+        % label it only once
+        % \detokenize{\label{el:#1}}
+        \directlua{ 
+            if elements["#1"]["labeled"] == nil then
+                elements["#1"]["labeled"] = true
+                tex.print("\\phantomsection\\label{el:#1}")
+            end
+        }
+        \NameWithDescription[\descwidth]{\elementName}{\elementName_desc}
+        \hfill
+        \begin{ContentBoxWithExplanation}{\elementName_defs}
+            \directlua{
+                tex.sprint("Symbol: \\ce{"..elements["#1"]["symbol"].."}")
+                tex.sprint("\\\\Number: "..elements["#1"]["atomic_number"])
+            }
+            \directlua{
+                %--tex.sprint("Hier steht Luatext" .. ":", #elementVals)
+                for key, value in pairs(elements["#1"]["properties"]) do
+                    tex.sprint("\\\\\\hspace*{1cm}{\\GT{", key, "}: ", value, "}")
+                    %--tex.sprint("VALUE ", i, v)
+                end
+            }
+        \end{ContentBoxWithExplanation}
+    \endgroup
+    \textcolor{fg3}{\hrule}
+    \vspace{0.5\baselineskip}
+    \ignorespacesafterend
+}
+\newcommand{\printAllElements}{
+    \directlua{
+            %-- tex.sprint("\\printElement{"..val.."}")
+        for key, val in ipairs(elementsOrder) do
+            %-- tex.sprint(key, val);
+            tex.print("\\printElement{"..val.."}")
+        end
+    }
+}
+
+% PERIODIC TABLE
+\directlua{
+    category2color = {
+        metal               = "bg-blue!50!bg0",
+        metalloid           = "fg-orange!50!bg0",
+        transitionmetal     = "fg-blue!50!bg0",
+        lanthanoide         = "bg-orange!50!bg0",
+        alkalimetal         = "fg-red!50!bg0",
+        alkalineearthmetal  = "fg-purple!50!bg0",
+        nonmetal            = "fg-aqua!50!bg0",
+        halogen             = "fg-yellow!50!bg0",
+        noblegas            = "bg-purple!50!bg0"
+    }
+}
+\directlua{
+    function getColor(cat) 
+        local color = category2color[cat]
+        if color == nil then
+            return "bg3"
+        else
+            return color
+        end
+    end
+}
+\newcommand{\drawPeriodicTable}{
+    \def\ptableUnit{0.90cm}
+    \begin{tikzpicture}[
+        element/.style={anchor=north west, draw, minimum width=\ptableUnit, minimum height=\ptableUnit, align=center},
+        element_annotation/.style={anchor=north west, font=\tiny, inner sep=1pt},
+        x=\ptableUnit,
+        y=\ptableUnit
+    ]
+    \directlua{
+        for k, v in pairs(elements) do
+            local column = tonumber(v.column)
+            local period = tonumber(v.period)
+            if 5 < period and 4 <= column and column <= 17 then
+                period = period + 3
+            elseif column > 17 then
+                column = column - 14
+            end
+            tex.print("\\node[element,fill=".. getColor(v.properties.set) .."] at (".. column ..", -".. period ..") {\\elRef{".. v.symbol .."}};")
+            tex.print("\\node[element_annotation] at (".. column ..", -".. period ..") {".. v.atomic_number .."};")
+            if v.properties.atomic_mass \string~= nil then
+                tex.print("\\node[element_annotation,anchor=south west] at (".. column ..", -".. period+1 ..") {".. string.format("\percentchar .3f", v.properties.atomic_mass) .."};")
+            end
+        end
+    }
+    \draw[ultra thick,fg-purple] (4,-6) -- (4,-11);
+    % color legend for categories
+    \directlua{
+        local x0 = 4
+        local y0 = -1
+        local x = 0
+        local y = 0
+        local ystep = 0.4
+        for set, color in pairs(category2color) do
+        %-- tex.print("\\draw[fill=".. color .."] ("..x0+x..","..y0+y..") rectangle ("..x0+x..","..y0+y..")()")
+            tex.print("\\node[anchor=west, align=left] at ("..x0+x..","..y0-y..") {{\\color{".. color .."}\\blacksquare} \\GT{".. set .."}};")
+            y = y + 1*ystep
+            if y > 4*ystep then
+                y = 0
+                x = x+4
+            end
+        end
+    }
+    % period numbers
+    \directlua{
+        for i = 1, 7 do
+            tex.print("\\node[anchor=east,align=right] at (1,".. -i-0.5 ..") {".. i .."};")
+        end
+    }
+    \end{tikzpicture}
+}

src/pkg/mqquantity.sty

@@ -0,0 +1,43 @@
+\ProvidesPackage{mqquantity}
+\RequirePackage{mqlua}
+\RequirePackage{etoolbox}
+
+\directLuaAux{
+    if quantities == nil then
+        quantities = {}
+    end
+}
+
+% [1]: label to point to
+% 2: key - must expand to a valid lua string!
+% 3: symbol
+% 4: units
+% 5: comment key to translation
+\newcommand{\quantity@new}[5][\relax]{%
+    \directLuaAux{
+        quantities["#2"] = {} 
+        quantities["#2"]["symbol"]  = [[\detokenize{#3}]]
+        quantities["#2"]["units"]   = [[\detokenize{#4}]]
+        quantities["#2"]["comment"] = [[\detokenize{#5}]]
+    }
+    \ifstrempty{#1}{}{
+        \directLuaAuxExpand{
+            quantities["#2"]["linkto"]  = [[#1]] %-- fqname required for getting the translation key
+        }
+    }
+}
+
+% 1: key
+\newcommand\quantity@print[1]{
+    \begingroup % for label
+        Symbol: $\luavar{quantities["#1"]["symbol"]}$
+        \\Unit: $\directlua{split_and_print_units(quantities["#1"]["units"])}$
+        % label it only once
+        \directlua{ 
+            if quantities["#1"]["labeled"] == nil then
+                quantities["#1"]["labeled"] = true
+                tex.print("\\label{qty:#1}")
+            end
+        }
+    \endgroup
+}

src/pkg/mqtranslation.sty

@@ -0,0 +1,177 @@
+\ProvidesPackage{mqtranslation}
+\RequirePackage{mqfqname}
+\RequirePackage{etoolbox}
+\RequirePackage{amsmath}
+\RequirePackage{mqlua}
+
+% TODO resolve circular dependency with fqname
+
+\begin{luacode}
+    translations = translations or {} 
+    -- string to append to missing translations
+    -- unknownTranslation = "???"
+    unknownTranslation = ""
+    language = "\languagename"
+    fallbackLanguage = "english"
+    -- using additional .aux extension because vimtex wouldnt stop compiling otherwise
+    translationsFilepath = OUTDIR .. "/translations.lua.aux" or "/tmp/translations.lua"
+
+    function tlAdd(language, key, value)
+        if value == "" then 
+            return
+        end
+        if translations[language] == nil then
+            translations[language] = {}
+        end
+        translations[language][key] = value
+    end
+
+
+    function tlExists(language, key)
+        return not (translations[language] == nil or translations[language][key] == nil)
+    end
+
+    function tlExistsFallback(language, key)
+        if tlExists(language, key) then
+            return true
+        end
+        return tlExists(fallbackLanguage, key)
+    end
+
+
+    function tlGet(language, key)
+        if tlExists(language, key) then
+            return translations[language][key]
+        end
+        return string.sanitize(key .. unknownTranslation)
+    end
+
+    function tlGetFallback(language, key)
+        if tlExists(language, key) then
+            return translations[language][key]
+        end
+        if language ~= fallbackLanguage then
+            if tlExists(fallbackLanguage, key) then
+                return translations[fallbackLanguage][key]
+            end
+        end
+        return string.sanitize(key .. unknownTranslation)
+    end
+
+    function tlGetCurrent(key)
+        return tlGet(language, key)
+    end
+
+    function tlGetFallbackCurrent(key)
+        return tlGetFallback(language, key)
+    end
+
+\end{luacode}
+
+% Write the translations table as lua code to an auxiliary file
+% If the file exists, read it when loading the package.
+% This way, translations may be used before they are defined, since it will exist in the second compilation.
+\begin{luacode*}
+    function serialize(tbl)
+        local result = {}
+        for k, v in pairs(tbl) do
+        local key = type(k) == "string" and ("[\"%s\"]"):format(k) or "[" .. tostring(k) .. "]"
+            -- using level 2 multiline string to avoid problems when a string ends with ]
+            local value = type(v) == "table" and serialize(v) or "[==[" .. tostring(v) .. "]==]"
+            table.insert(result, key .. " = " .. value)
+        end
+        return "{" .. table.concat(result, ",\n" ) .. "}\n"
+    end
+
+
+    function dumpTranslations()
+        local file = io.open(translationsFilepath, "w")
+        file:write("return " .. serialize(translations) .. "\n")
+        file:close()
+    end
+
+    if fileExists(translationsFilepath) then
+        translations = dofile(translationsFilepath) or {}
+    end
+\end{luacode*}
+        
+
+\AtEndDocument{\directlua{dumpTranslations()}}
+
+%
+% TRANSLATION COMMANDS
+%
+% The lower case commands use \fqname based keys, the upper case absolute keys.
+% Example:
+%   \dt[example]{german}{Beispiel}  % defines the key \fqname:example
+%   \ger[example]{Beispiel}         % defines the key \fqname:example
+%   \DT[example]{german}{Beispiel}  % defines the key example
+%   \Ger[example]{Beispiel}         % defines the key example
+%
+% For ease of use in the ttext environment and the optional argument of the \Part, \Section, ... commands,
+% all "define translation" commands use \fqname as default key
+
+% Get a translation
+% expandafter required because the translation commands dont expand anything
+% shortcuts for translations
+% 1: key
+\newcommand{\gt}[1]{\luavar{tlGetFallbackCurrent(\luastring{\fqname:#1})}}
+\newrobustcmd{\robustGT}[1]{\luavar{tlGetFallbackCurrent(\luastring{#1})}}
+\newcommand{\GT}[1]{\luavar{tlGetFallbackCurrent(\luastring{#1})}}
+
+% text variants for use in math mode
+\newcommand{\tgt}[1]{\text{\gt{#1}}}
+\newcommand{\tGT}[1]{\text{\GT{#1}}}
+
+% Define a new translation
+% [1]: key, 2: lang, 3: translation
+\newcommand{\dt}[3][\fqname]{%
+    \directlua{
+        if \luastring{#1} == \luastring{\fqname} then
+            tlAdd(\luastring{#2}, \luastring{\fqname}, \luastringN{#3})
+        else
+            tlAdd(\luastring{#2}, \luastring{\fqname:#1}, \luastringN{#3})
+        end
+    }
+}
+
+% Define a new translation
+% [1]: key, 2: lang, 3: translation
+\newcommand{\DT}[3][\fqname]{%
+    \directlua{
+        if \luastring{#1} == \luastring{\fqname} then
+            tlAdd(\luastring{#2}, \luastring{\fqname}, \luastringN{#3})
+        else
+            tlAdd(\luastring{#2}, \luastring{#1}, \luastringN{#3})
+        end
+    }
+}
+% [1]: key, 2: translation
+\newcommand{\ger}[2][\fqname]{\dt[#1]{german}{#2}}
+\newcommand{\eng}[2][\fqname]{\dt[#1]{english}{#2}}
+
+\newcommand{\Ger}[2][\fqname]{\DT[#1]{german}{#2}}
+\newcommand{\Eng}[2][\fqname]{\DT[#1]{english}{#2}}
+
+\newcommand{\IfTranslationExists}[3]{%
+    \directlua{
+        if tlExistsFallback(language, \luastring{#1}) then
+            tex.sprint(\luastringN{#2})
+        else
+            tex.sprint(\luastringN{#3})
+        end
+    }
+}
+
+
+% use this to define text in different languages for the key <env arg>
+% the translation for <env arg> is printed when the environment ends.
+% (temporarily change fqname to the \fqname:<env arg> to allow
+% the use of \eng and \ger without the key parameter)
+% [1]: key
+\newenvironment{ttext}[1][desc]{%
+    \mqfqname@enter{#1}%
+}{%
+    \GT{\fqname}%
+    \mqfqname@leave%
+}

src/probability_theory.tex

@@ -1,194 +0,0 @@
-\Part[
-    \eng{Probability theory}
-    \ger{Wahrscheinlichkeitstheorie}
-    ]{pt}
-
-    \begin{formula}{mean}
-        \desc{Mean}{}{}
-        \desc[german]{Mittelwert}{}{}
-        \eq{\braket{x} = \int w(x)\, x\, \d x}
-    \end{formula}
-
-    \begin{formula}{variance}
-        \desc{Variance}{}{}
-        \desc[german]{Varianz}{}{}
-        \eq{\sigma^2 = (\Delta \hat{x})^2 = \braket{\hat{x}^2} - \braket{\hat{x}}^2 = \braket{(x - \braket{x})^2}}
-    \end{formula}
-    
-    \begin{formula}{std_deviation}
-        \desc{Standard deviation}{}{}
-        \desc[german]{Standardabweichung}{}{}
-        \eq{\sigma = \sqrt{(\Delta x)^2}}
-    \end{formula}
-
-    \begin{formula}{median}
-        \desc{Median}{Value separating lower half from top half}{$x$ dataset with $n$ elements}
-        \desc[german]{Median}{Teilt die untere von der oberen Hälfte}{$x$ Reihe mit $n$ Elementen}
-        \eq{
-            \textrm{med}(x) = \left\{ \begin{array}{ll} x_{(n+1)/2} & \text{$n$ \GT{odd}} \\ \frac{x_{(n/2)}+x_{((n/2)+1)}}{2} & \text{$n$ \GT{even}} \end{array} \right.
-        }
-    \end{formula}
-
-    \begin{formula}{pdf}
-        \desc{Probability density function}{Random variable has density $f$. The integral gives the probability of $X$ taking a value $x\in[a,b]$.}{$f$ normalized: $\int_{-\infty}^\infty f(x) \d x= 1$}
-        \desc[german]{Wahrscheinlichkeitsdichtefunktion}{Zufallsvariable hat Dichte $f$. Das Integral gibt Wahrscheinlichkeit an, dass $X$ einen Wert $x\in[a,b]$ annimmt}{$f$ normalisiert $\int_{-\infty}^\infty f(x) \d x= 1$}
-        \eq{P([a,b]) := \int_a^b f(x) \d x}
-    \end{formula}
-
-    \begin{formula}{cdf}
-        \desc{Cumulative distribution function}{}{$f$ probability density function}
-        \desc[german]{Kumulative Verteilungsfunktion}{}{$f$ Wahrscheinlichkeitsdichtefunktion}
-        \eq{F(x) = \int_{-\infty}^x f(t) \d t}
-    \end{formula}
-
-\Section[
-    \eng{Distributions}
-    \ger{Verteilungen}
-    ]{distributions}
-    \Subsubsection[
-        \eng{Gauß/Normal distribution}
-        \ger{Gauß/Normal-Verteilung}
-        ]{normal}
-        \begin{minipage}{\distleftwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=\textwidth]{img/distribution_gauss.pdf}
-            \end{figure}
-        \end{minipage}
-        \begin{distribution}
-            \disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
-            \disteq{support}{x \in \R}
-            \disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
-            \disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
-            \disteq{mean}{\mu}
-            \disteq{median}{\mu}
-            \disteq{variance}{\sigma^2}
-        \end{distribution}
-
-        \begin{formula}{standard_normal_distribution}
-            \desc{Density function of the standard normal distribution}{$\mu = 0$, $\sigma = 1$}{}
-            \desc[german]{Dichtefunktion der Standard-Normalverteilung}{$\mu = 0$, $\sigma = 1$}{}
-            \eq{\varphi(x) = \frac{1}{\sqrt{2\pi}} \e^{-\frac{1}{2}x^2}}
-        \end{formula}
-
-    \Subsubsection[
-        \eng{Cauchys / Lorentz distribution}
-        \ger{Cauchy / Lorentz-Verteilung}
-        ]{cauchy}
-        \begin{minipage}{\distleftwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=\textwidth]{img/distribution_cauchy.pdf}
-            \end{figure}
-        \end{minipage}
-        \begin{distribution}
-            \disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
-            \disteq{support}{x \in \R}
-            \disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
-            \disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
-            \disteq{mean}{\text{\GT{undefined}}}
-            \disteq{median}{x_0}
-            \disteq{variance}{\text{\GT{undefined}}}
-        \end{distribution}
-
-        \begin{ttext}
-            \eng{Also known as \textbf{Cauchy-Lorentz distribution}, \textbf{Lorentz(ian) function}, \textbf{Breit-Wigner distribution}.}
-            \ger{Auch bekannt als \textbf{Cauchy-Lorentz Verteilung}, \textbf{Lorentz Funktion}, \textbf{Breit-Wigner Verteilung}.}
-        \end{ttext}
-
-
-    \Subsubsection[
-        \eng{Binomial distribution}
-        \ger{Binomialverteilung}
-        ]{binomial}
-        \begin{ttext}
-            \eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the   \hyperref[sec:pb:distributions::poisson]{poisson distribution}}
-            \ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions::poisson]{Poissonverteilung}}
-        \end{ttext}
-        \begin{minipage}{\distleftwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=\textwidth]{img/distribution_binomial.pdf}
-            \end{figure}
-        \end{minipage}
-        \begin{distribution}
-            \disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
-            \disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
-            \disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
-            % \disteq{cdf}{\text{regularized incomplete beta function}}
-            \disteq{mean}{np}
-            \disteq{median}{\floor{np} \text{ or } \ceil{np}}
-            \disteq{variance}{npq = np(1-p)}
-        \end{distribution}
-    \Subsubsection[
-        \eng{Poisson distribution}
-        \ger{Poissonverteilung}
-        ]{poisson}
-        \begin{minipage}{\distleftwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=\textwidth]{img/distribution_poisson.pdf}
-            \end{figure}
-        \end{minipage}
-        \begin{distribution}
-            \disteq{parameters}{\lambda \in (0,\infty)}
-            \disteq{support}{k \in \N}
-            \disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
-            \disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
-            \disteq{mean}{\lambda}
-            \disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
-            \disteq{variance}{\lambda}
-        \end{distribution}
-                    
-
-    \Subsubsection[
-        \eng{Maxwell-Boltzmann distribution}
-        \ger{Maxwell-Boltzmann Verteilung}
-        ]{maxwell-boltzmann}
-        \begin{minipage}{\distleftwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf}
-            \end{figure}
-        \end{minipage}
-        \begin{distribution}
-            \disteq{parameters}{a > 0}
-            \disteq{support}{x \in (0, \infty)}
-            \disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
-            \disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
-            \disteq{mean}{2a \frac{2}{\pi}}
-            \disteq{median}{}
-            \disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
-        \end{distribution}
-
-
-
-    % \begin{distribution}{maxwell-boltzmann}
-    %     \distdesc{Maxwell-Boltzmann distribution}{}
-    %     \distdesc[german]{Maxwell-Boltzmann Verteilung}{}
-    %     \disteq{parameters}{}
-    %     \disteq{pdf}{}
-    %     \disteq{cdf}{}
-    %     \disteq{mean}{}
-    %     \disteq{median}{}
-    %     \disteq{variance}{}
-    % \end{distribution}
-
-
-    \Subsection[
-        \eng{Central limit theorem}
-        \ger{Zentraler Grenzwertsatz}
-        ]{cls}  
-        \begin{ttext}
-            \eng{
-                Suppose $X_1, X_2, \dots$ is a sequence of independent and identically distributed random variables with $\braket{X_i} = \mu$ and $(\Delta X_i)^2 = \sigma^2 < \infty$.
-                As $N$ approaches infinity, the random variables $\sqrt{N}(\bar{X}_N - \mu)$ converge to a normal distribution $\mathcal{N}(0, \sigma^2)$.
-                \\ That means that the variance scales with $\frac{1}{\sqrt{N}}$ and statements become accurate for large $N$.
-            }
-            \ger{
-                Sei $X_1, X_2, \dots$ eine Reihe unabhängiger und gleichverteilter Zufallsvariablen mit $\braket{X_i} = \mu$ und $(\Delta X_i)^2 = \sigma^2 < \infty$.
-                Für $N$ gegen unendlich konvergieren die Zufallsvariablen $\sqrt{N}(\bar{X}_N - \mu)$ zu einer Normalverteilung $\mathcal{N}(0, \sigma^2)$.
-                \\ Das bedeutet, dass die Schwankung mit $\frac{1}{\sqrt{N}}$ wächst und Aussagen für große $N$ scharf werden.
-            }
-        \end{ttext}
-

src/qm/atom.tex

@@ -28,7 +28,7 @@
     \end{formula}
 
     \begin{formula}{wave_function}
-        \desc{Wave function}{}{}
+        \desc{Wave function}{}{$R_{nl}(r)$ \fqEqRef{qm:h:radial}, $Y_{lm}$ \fqEqRef{qm:spherical_harmonics}}
         \desc[german]{Wellenfunktion}{}{}
         \eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
     \end{formula}
@@ -49,10 +49,36 @@
         \eq{E_n &= \frac{Z^2\mu e^4}{n^2(4\pi\epsilon_0)^2 2\hbar^2} = -E_\textrm{H}\frac{Z^2}{n^2}}
     \end{formula}
 
+    \begin{formula}{rydberg_constant_heavy}
+        \desc{Rydberg constant}{for heavy atoms}{\ConstRef{electron_mass}, \ConstRef{elementary_charge}, \QtyRef{vacuum_permittivity}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
+        \desc[german]{Rydberg-Konstante}{für schwere Atome}{}
+        \constant{R_\infty}{exp}{
+            \val{10973731.568157(12)}{\per\m}
+        }
+        \eq{
+            R_\infty = \frac{m_e e^4}{8\epsilon_0^2 h^3 c}
+        }
+    \end{formula}
+
+    \begin{formula}{rydberg_constant_corrected}
+        \desc{Rydberg constant}{corrected for nucleus mass $M$}{\QtyRef{rydberg_constant_heavy}, $\mu = \left(\frac{1}{m_\txe} + \frac{1}{M}\right)^{-1}$ \GT{reduced_mass}, \ConstRef{electron_mass}}
+        \desc[german]{Rydberg Konstante}{korrigiert für Kernmasse $M$}{}
+        \eq{R_\txM = \frac{\mu}{m_\txe} R_\infty}
+    \end{formula}
+
     \begin{formula}{rydberg_energy}
-        \desc{Rydberg energy}{}{}
+        \desc{Rydberg energy}{Energy unit}{\ConstRef{rydberg_constant_heavy}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
-        \desc[german]{Rydberg-Energy}{}{}
+        \desc[german]{Rydberg-Energy}{Energie Einheit}{}
-        \eq{E_\textrm{H} = h\,c\,R_\textrm{H} = \frac{\mu e^4}{(4\pi\epsilon_0)^2 2\hbar^2}}
+        \eq{1\,\text{Ry} = hc\,R_\infty}
+    \end{formula}
+
+    \begin{formula}{bohr_radius}
+        \desc{Bohr radius}{}{\ConstRef{vacuum_permittivity}, \ConstRef{electron_mass}}
+        \desc[german]{Bohrscher Radius}{}{}
+        \constant{a_0}{exp}{
+            \val{5.29177210544(82) \xE{-11}}{\m}
+        }
+        \eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
     \end{formula}
 
 
@@ -178,5 +204,18 @@
     \ger{Effekte im Magnetfeld}
 ]{mag_effects}
     \TODO{all} 
-
     \\\TODO{Hunds rules}
+
+\Subsection[
+    \eng{misc}
+    \ger{Sonstiges}
+]{other}
+    \begin{formula}{auger_effect}
+        \desc{Auger-Meitner-Effekt}{Auger-Effect}{}
+        \desc[german]{Auger-Meitner-Effekt}{Auger-Effekt}{}
+        \ttxt{
+            \eng{An excited electron relaxes into a lower, unoccupied energy level. The released energy causes the emission of another electron in a higher energy level (Auger-Electron)}
+            \ger{Ein angeregtes Elektron fällt in ein unbesetztes, niedrigeres Energieniveau zurück. Durch die frei werdende Energie verlässt ein Elektron aus einer höheren Schale das Atom (Auger-Elektron).}
+        }
+    \end{formula}
+

src/qm/qm.tex

@@ -53,6 +53,44 @@
                 \eq{\hat{A} = \hat{A}^\dagger}
             \end{formula}
 
+            \Subsubsection[
+                \eng{Measurement}
+                \ger{Messung}
+            ]{measurement}  
+                \begin{ttext}
+                    \eng{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}
+                    \ger{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}
+                \end{ttext}
+                \begin{formula}{name}
+                    \desc{Measurement probability}{Probability to measure $\psi$ in state $\lambda$}{}
+                    \desc[german]{Messwahrscheinlichkeit}{Wahrscheinlichkeit, $\psi$ im Zustand $\lambda$ zu messen}{}
+                    \eq{p(\lambda) = \braket{\psi|\hat{P}_\lambda|\psi}}
+                \end{formula}
+                \begin{formula}{state_after}
+                    \desc{State after measurement}{}{}
+                    \desc[german]{Zustand nach der Messung}{}{}
+                    \eq{\ket{\psi}_\text{post} = \frac{1}{\sqrt{p(\lambda)}}\hat{P}_\lambda \ket{\psi}}
+                \end{formula}
+                
+            
+            \Subsubsection[
+                \eng{Pauli matrices}
+                \ger{Pauli-Matrizen}
+            ]{pauli_matrices}
+                \begin{formula}{pauli_matrices}
+                    \desc{Pauli matrices}{}{}
+                    \desc[german]{Pauli Matrizen}{}{}
+                    \newFormulaEntry
+                    \begin{alignat}{2}
+                        \sigma_x &= \sigmaxmatrix &&= \sigmaxbraket \label{eq:pauli_x} \\
+                        \sigma_y &= \sigmaymatrix &&= \sigmaybraket \label{eq:pauli_y} \\
+                        \sigma_z &= \sigmazmatrix &&= \sigmazbraket \label{eq:pauli_z}
+                    \end{alignat}
+                \end{formula}
+            % $\sigma_x$ NOT
+            % $\sigma_y$ PHASE
+            % $\sigma_z$ Sign
+
         \Subsection[
             \ger{Wahrscheinlichkeitstheorie}
             \eng{Probability theory}
@@ -84,23 +122,6 @@
                     \sigma_A \sigma_B &\ge \frac{1}{2} \abs{\braket{[\hat{A},\hat{B}]}}
                 }
             \end{formula}
-            
-            \Subsubsection[
-                \eng{Pauli matrices}
-                \ger{Pauli-Matrizen}
-            ]{pauli_matrices}
-                \begin{formula}{pauli_matrices}
-                    \desc{Pauli matrices}{}{}
-                    \desc[german]{Pauli Matrizen}{}{}
-                    \eqAlignedAt{2}{
-                        \sigma_x &= \sigmaxmatrix &&= \sigmaxbraket \label{eq:pauli_x} \\
-                        \sigma_y &= \sigmaymatrix &&= \sigmaybraket \label{eq:pauli_y} \\
-                        \sigma_z &= \sigmazmatrix &&= \sigmazbraket \label{eq:pauli_z}
-                    }
-                \end{formula}
-            % $\sigma_x$ NOT
-            % $\sigma_y$ PHASE
-            % $\sigma_z$ Sign
 
 
         \Subsection[
@@ -157,7 +178,7 @@
     \Section[
         \eng{Schrödinger equation}
         \ger{Schrödingergleichung}
-    ]{schroedinger_equation}
+    ]{se}
         \begin{formula}{energy_operator}
             \desc{Energy operator}{}{}
             \desc[german]{Energieoperator}{}{}
@@ -185,9 +206,18 @@
         \begin{formula}{schroedinger_equation}
             \desc{Schrödinger equation}{}{}
             \desc[german]{Schrödingergleichung}{}{}
+            \abbrLabel{SE}
             \eq{i\hbar\frac{\partial}{\partial t}\psi(x, t) = (- \frac{\hbar^2}{2m} \vec{\nabla}^2 + \vec{V}(x)) \psi(x)}
         \end{formula}
 
+        \begin{formula}{hellmann_feynmann} \absLabel
+            \desc{Hellmann-Feynman-Theorem}{Derivative of the energy to a parameter}{}
+            \desc[german]{Hellmann-Feynman-Theorem}{Abletiung der Energie nach einem Parameter}{}
+            \eq{
+                \odv{E_\lambda}{\lambda} = \int \d^3r \psi^*_\lambda \odv{\hat{H}_\lambda}{\lambda} \psi_\lambda = \Braket{\psi(\lambda)|\odv{\hat{H}_{\lambda}}{\lambda}|\psi(\lambda)}
+            }
+        \end{formula}
+
         \Subsection[
             \eng{Time evolution}
             \ger{Zeitentwicklug}
@@ -212,6 +242,7 @@
             \end{formula}
 
 
+
             \TODO{unitary transformation of time dependent H}
 
             \Subsubsection[
@@ -250,27 +281,28 @@
                 ]{ehrenfest_theorem}
                 \GT{see_also} \ref{sec:qm:basics:schroedinger_equation:correspondence_principle}
                 \begin{formula}{ehrenfest_theorem}
-                    \desc{Ehrenfesttheorem}{applies to both pictures}{}
+                    \desc{Ehrenfest theorem}{applies to both pictures}{}
                     \desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{}
                     \eq{
                         \odv{}{t} \braket{\hat{A}} = \frac{1}{i\hbar}\braket{[\hat{A},\hat{H}]} + \Braket{\pdv{\hat{A}}{t}}
                     }
                 \end{formula}
                 \begin{formula}{ehrenfest_theorem_x}
-                    \desc{}{Example for $x$}{}
+                    \desc{Ehrenfest theorem example}{Example for $x$}{}
-                    \desc[german]{}{Beispiel für $x$}{}
+                    \desc[german]{Ehrenfest-Theorem Beispiel}{Beispiel für $x$}{}
                     \eq{m\odv[2]{}{t}\braket{x} = -\braket{\nabla V(x)} = \braket{F(x)}}
                 \end{formula}
                 % \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time}
 
-            \Subsection[
+            % TODO: wo gehört das hin?
-                \ger{Korrespondenzprinzip}
+            \begin{formula}{correspondence_principle}
-                \eng{Correspondence principle}
+                \desc{Correspondence principle}{}{}
-                ]{correspondence_principle}
+                \desc[german]{Korrespondenzprinzip}{}{}
-                \begin{ttext}[desc]
+                \ttxt{
                     \ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
                     \eng{The classical mechanics can be derived from quantum mechanics in the limit of large quantum numbers.}
-                \end{ttext}
+                }
+            \end{formula}
                 
 
 
@@ -279,8 +311,8 @@
         \ger{Störungstheorie}
         ]{qm_pertubation}
         \begin{ttext}
-            \eng[desc]{The following holds true if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}
+            \eng{The following holds true if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}
-            \ger[desc]{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}
+            \ger{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}
         \end{ttext}
         \begin{formula}{pertubation_hamiltonian}
             \desc{Hamiltonian}{}{}
@@ -310,7 +342,7 @@
             \desc{2. order energy shift}{}{}
             \desc[german]{Energieverschiebung 2. Ordnung}{}{}
             % \eq{E_n^{(1)} = \Braket{\psi_n^{(0)}|\hat{H_1}|\psi_n^{(0)}}}
-            \eq{E_n^{(2)} = \sum_{k\neq n}\frac{\abs*{\Braket{\psi_k^{(0)}|\hat{H_1}|\psi_n^{(0)}}}^2}{E_n^{(0)} - E_k^{(0)}}}
+            \eq{E_n^{(2)} = \sum_{k\neq n}\frac{\abs{\Braket{\psi_k^{(0)}|\hat{H_1}|\psi_n^{(0)}}}^2}{E_n^{(0)} - E_k^{(0)}}}
         \end{formula}
         % \begin{formula}{qm:pertubation:}
         %     \desc{1. order states}{}{}
@@ -319,16 +351,16 @@
         % \end{formula}
 
         \begin{formula}{golden_rule}
-            \desc{Fermi\'s golden rule}{Transition rate from initial state $\ket{i}$ under a pertubation $H^1$ to final state $\ket{f}$}{}
+            \desc{Fermi's golden rule}{Transition rate from initial state $\ket{i}$ under a pertubation $H^1$ to final state $\ket{f}$}{}
             \desc[german]{Fermis goldene Regel}{Übergangsrate des initial Zustandes $\ket{i}$ unter einer Störung $H^1$ zum Endzustand $\ket{f}$}{}
-            \eq{\Gamma_{i\to f} = \frac{2\pi}{\hbar} \abs*{\braket{f | H^1 | i}}^2\,\rho(E_f)}
+            \eq{\Gamma_{i\to f} = \frac{2\pi}{\hbar} \abs{\braket{f | H^1 | i}}^2\,\rho(E_f)}
         \end{formula}
 
 
     \Section[
         \eng{Harmonic oscillator}
         \ger{Harmonischer Oszillator}
-    ]{qm_hosc}
+    ]{hosc}
         \begin{formula}{hamiltonian}
             \desc{Hamiltonian}{}{}
             \desc[german]{Hamiltonian}{}{}
@@ -379,6 +411,31 @@
                 }
             \end{formula}
 
+            \begin{formula}{c_a_matrices}
+                \desc{Matrix forms}{}{}
+                \desc[german]{Matrix-Form}{}{}
+                \eq{
+                    \hat{n} &= \begin{pmatrix}
+                        0 & 0 & 0 & 0 \\
+                        0 & 1 & 0 & 0 \\
+                        0 & 0 & \ddots & 0 \\
+                        0 & 0 & 0 & N
+                    \end{pmatrix} \\
+                    \hat{a} &= \begin{pmatrix}
+                        0 & \sqrt{1} & 0      & 0 \\
+                        0 & 0        & \ddots & 0 \\
+                        0 & 0        & 0      & \sqrt{N} \\
+                        0 & 0        & 0      & 0 
+                    \end{pmatrix} \\
+                    \hat{a}^\dagger &= \begin{pmatrix}
+                        0        & 0      & 0        & 0 \\
+                        \sqrt{1} & 0      & 0        & 0 \\
+                        0        & \ddots & 0        & 0 \\
+                        0        & 0      & \sqrt{N} & 0
+                    \end{pmatrix}
+                }
+            \end{formula}
+
             \Subsubsection[
                 \eng{Harmonischer Oszillator}
                 \ger{Harmonic Oscillator}
@@ -413,6 +470,21 @@
         \eng{Angular momentum}
         \ger{Drehmoment}
         ]{angular_momentum}
+
+        \Subsection[
+            \eng{Aharanov-Bohm effect}
+            \ger{Aharanov-Bohm Effekt}
+            ]{aharanov_bohm}
+            \begin{formula}{phase}
+                \desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{}
+                \desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{}
+                \eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
+            \end{formula}
+            \TODO{replace with loop intergral symbol and add more info}
+    \Section[
+        \eng{Periodic potentials}
+        \ger{Periodische Potentiale}
+    ]{periodic}
         \begin{formula}{bloch_waves}
             \desc{Bloch waves}{
                 Solve the stat. SG in periodic potential with period 
@@ -429,16 +501,14 @@
             \eq{\psi_k(\vec{r}) = e^{i \vec{k}\cdot \vec{r}} \cdot u_{\vec{k}}(\vec{r})}
         \end{formula}
 
-        \Subsection[
+        \begin{formula}{periodicity}
-            \eng{Aharanov-Bohm effect}
+            \desc{Periodicity}{}{\QtyRef{lattice_vector}, \QtyRef{reciprocal_lattice_vector}}
-            \ger{Aharanov-Bohm Effekt}
+            \desc[german]{Periodizität}{}{}
-            ]{aharanov_bohm}
+            \eq{
-            \begin{formula}{phase}
+                u_\vec{k}(\vec{r} + \vec{R}) = u_\vec{k}(\vec{r}) \\
-                \desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{}
+                \psi_{\vec{k}+\vec{G}}(\vec{r}) = \psi_\vec{k}(\vec{r})
-                \desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{}
+            }
-                \eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
+        \end{formula}
-            \end{formula}
-            \TODO{replace with loop intergral symbol and add more info}
 
 
     \Section[
@@ -482,7 +552,7 @@
             \eq{H &= \underbrace{\hbar\omega_c \hat{a}^\dagger \hat{a}}_\text{\GT{field}} 
                     + \underbrace{\hbar\omega_\text{a} \frac{\hat{\sigma}_z}{2}}_\text{\GT{atom}} 
                     + \underbrace{\frac{\hbar\Omega}{2} \hat{E} \hat{S}}_\text{int} \\
-                \shortintertext{\GT{after} \hyperref[eq:qm:other:RWS]{RWA}:} \\
+                \shortintertext{\GT{after} \hyperref[eq:qm:other:RWA]{RWA}:} \\
                   &= \hbar\omega_c \hat{a}^\dagger \hat{a} 
                     + \hbar\omega_\text{a} \hat{\sigma}^\dagger \hat{\sigma}
                     + \frac{\hbar\Omega}{2} (\hat{a}\hat{\sigma^\dagger} + \hat{a}^\dagger \hat{\sigma})
@@ -493,10 +563,33 @@
         \eng{Other}
         \ger{Sonstiges}
         ]{other}
-        \begin{formula}{RWS}
+        \begin{formula}{RWA}
             \desc{Rotating Wave Approximation (RWS)}{Rapidly oscilating terms are neglected}{$\omega_\text{L}$ light frequency, $\omega_0$ transition frequency}
             \desc[german]{Rotating Wave Approximation / Drehwellennäherung (RWS)}{Schnell oscillierende Terme werden vernachlässigt}{$\omega_\text{L}$ Frequenz des Lichtes, $\omega_0$ Übergangsfrequenz}
             \eq{\Delta\omega \coloneq \abs{\omega_0 - \omega_\text{L}} \ll \abs{\omega_0 + \omega_\text{L}} \approx 2\omega_0}
         \end{formula}
 
+        \begin{formula}{adiabatic_theorem} \absLabel
+            \desc{Adiabatic theorem}{}{}
+            \desc[german]{Adiabatentheorem}{}{}
+            \ttxt{
+                \eng{A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.}
+                \ger{Ein quantenmechanisches System bleibt in im derzeitigen Eigenzustand falls eine Störung langsam genug wirkt und der Eigenwert durch eine Lücke vom Rest des Spektrums getrennt ist.}
+            }
+        \end{formula}
+
+        \begin{formula}{slater_det}
+            \desc{Slater determinant}{Construction of a fermionic (antisymmetric) many-particle wave function from single-particle wave functions}{}
+            \desc[german]{Slater Determinante}{Konstruktion einer fermionischen (antisymmetrischen) Vielteilchen Wellenfunktion aus ein-Teilchen Wellenfunktionen}{}
+            \eq{
+                \Psi(q_1, \dots, q_N) = \frac{1}{\sqrt{N!}}
+                \begin{vmatrix}
+                \phi_a(q_1) & \phi_a(q_2) & \cdots & \phi_a(q_N) \\
+                \phi_b(q_1) & \phi_b(q_2) & \cdots & \phi_b(q_N) \\
+                \vdots & \vdots & \ddots & \vdots \\
+                \phi_z(q_1) & \phi_z(q_2) & \cdots & \phi_z(q_N)
+                \end{vmatrix}
+            }
+        \end{formula}
+
 

src/quantities.tex

@@ -0,0 +1,161 @@
+% if this causes a compilation error, check that none of the units have been redefined
+
+% Put quantites here that are referenced often, even if they are not exciting themselves.
+% This could later allow making a list of all links to this quantity, creating a list of releveant formulas
+
+\Section[
+    \eng{Physical quantities}
+    \ger{Physikalische Größen}
+]{quantities}
+
+\Subsection[
+    \eng{SI quantities}
+    \ger{SI-Basisgrößen}
+]{si}
+    \begin{formula}{time}
+        \desc{Time}{}{}
+        \desc[german]{Zeit}{}{}
+        \quantity{t}{\second}{}
+    \end{formula}
+
+    \begin{formula}{length}
+        \desc{Length}{}{}
+        \desc[german]{Länge}{}{}
+        \quantity{l}{\m}{e}
+    \end{formula}
+
+    \begin{formula}{mass}
+        \desc{Mass}{}{}
+        \desc[german]{Masse}{}{}
+        \quantity{m}{\kg}{es}
+    \end{formula}
+
+    \begin{formula}{temperature}
+        \desc{Temperature}{}{}
+        \desc[german]{Temperatur}{}{}
+        \quantity{T}{\kelvin}{is}
+    \end{formula}
+
+    \begin{formula}{current}
+        \desc{Electric current}{}{}
+        \desc[german]{Elektrischer Strom}{}{}
+        \quantity{I}{\ampere}{es}
+    \end{formula}
+
+    \begin{formula}{amount}
+        \desc{Amount of substance}{}{}
+        \desc[german]{Stoffmenge}{}{}
+        \quantity{n}{\mol}{es}
+    \end{formula}
+
+    \begin{formula}{luminous_intensity}
+        \desc{Luminous intensity}{}{}
+        \desc[german]{Lichtstärke}{}{}
+        \quantity{I_\text{V}}{\candela}{s}
+    \end{formula}
+
+\Subsection[
+    \eng{Mechanics}
+    \ger{Mechanik}
+]{mech}
+    \begin{formula}{force}
+        \desc{Force}{}{}
+        \desc[german]{Kraft}{}{}
+        \quantity{\vec{F}}{\newton=\kg\m\per\second^2}{ev}
+    \end{formula}
+
+    \begin{formula}{spring_constant}
+        \desc{Spring constant}{}{}
+        \desc[german]{Federkonstante}{}{}
+        \quantity{k}{\newton\per\m=\kg\per\second^2}{s}
+    \end{formula}
+
+    \begin{formula}{velocity}
+        \desc{Velocity}{}{}
+        \desc[german]{Geschwindigkeit}{}{}
+        \quantity{\vec{v}}{\m\per\s}{v}
+    \end{formula}
+
+    \begin{formula}{torque}
+        \desc{Torque}{}{}
+        \desc[german]{Drehmoment}{}{}
+        \quantity{\tau}{\newton\m=\kg\m^2\per\s^2}{v}
+    \end{formula}
+
+    \begin{formula}{pressure}
+        \desc{Pressure}{}{}
+        \desc[german]{Druck}{}{}
+        \quantity{p}{\newtone\per\m^2}{}
+    \end{formula}
+    
+
+\Subsection[
+    \eng{Thermodynamics}
+    \ger{Thermodynamik}
+]{td}
+    \begin{formula}{volume}
+        \desc{Volume}{$d$ dimensional Volume}{}
+        \desc[german]{Volumen}{$d$ dimensionales Volumen}{}
+        \quantity{V}{\m^d}{}
+    \end{formula}
+    \begin{formula}{heat_capacity}
+        \desc{Heat capacity}{}{}
+        \desc[german]{Wärmekapazität}{}{}
+        \quantity{C}{\joule\per\kelvin}{}
+    \end{formula}
+
+\Subsection[
+    \eng{Electrodynamics}
+    \ger{Elektrodynamik}
+]{el}
+    \begin{formula}{charge}
+        \desc{Charge}{}{}
+        \desc[german]{Ladung}{}{}
+        \quantity{q}{\coulomb=\ampere\s}{}
+    \end{formula}
+
+    \begin{formula}{charge_number}
+        \desc{Charge number}{}{}
+        \desc[german]{Ladungszahl}{Anzahl der Elementarladungen}{}
+        \quantity{Z}{}{}
+    \end{formula}
+    \begin{formula}{charge_density}
+        \desc{Charge density}{}{}
+        \desc[german]{Ladungsdichte}{}{}
+        \quantity{\rho}{\coulomb\per\m^3}{s}
+    \end{formula}
+
+    \begin{formula}{frequency}
+        \desc{Frequency}{}{}
+        \desc[german]{Frequenz}{}{}
+        \quantity{f}{\hertz=\per\s}{s}
+    \end{formula}
+    \begin{formula}{angular_frequency}
+        \desc{Angular frequency}{}{\QtyRef{time_period}, \QtyRef{frequency}}
+        \desc[german]{Kreisfrequenz}{}{}
+        \quantity{\omega}{\radian\per\s}{s}
+        \eq{\omega = \frac{2\pi/T}{2\pi f}}
+    \end{formula}
+
+    \begin{formula}{time_period}
+        \desc{Time period}{}{\QtyRef{frequency}}
+        \desc[german]{Periodendauer}{}{}
+        \quantity{T}{\s}{s}
+        \eq{T = \frac{1}{f}}
+    \end{formula}
+
+    \begin{formula}{conductivity}
+        \desc{Conductivity}{}{}
+        \desc[german]{Leitfähigkeit}{}{}
+        \quantity{\sigma}{\per\ohm\m}{}
+    \end{formula}
+
+\Subsection[
+    \eng{Others}
+    \ger{Sonstige}
+]{other}
+    \begin{formula}{area}
+        \desc{Area}{}{}
+        \desc[german]{Fläche}{}{}
+        \quantity{A}{m^2}{v}
+    \end{formula}

src/quantum_computing.tex

@@ -22,14 +22,18 @@
     \ger{Gates}
 ]{gates}
     \begin{formula}{gates}
-        \desc{}{}{}
+        \desc{Gates}{}{}
-        \desc[german]{}{}{}
+        \desc[german]{Gates}{}{}
-        \eqAlignedAt{2}{
+        \eng[bitflip]{Bitflip}
+        \eng[bitphaseflip]{Bit-Phase flip}
+        \eng[phaseflip]{Phaseflip}
+        \eng[hadamard]{Hadamard}
+        \begin{alignat}{2}
             & \text{\gt{bitflip}:}      & \hat{X} &= \sigma_x = \sigmaxmatrix \\
             & \text{\gt{bitphaseflip}:} & \hat{Y} &= \sigma_y = \sigmaymatrix \\
             & \text{\gt{phaseflip}:}    & \hat{Z} &= \sigma_z = \sigmazmatrix \\
             & \text{\gt{hadamard}:}     & \hat{H} &= \frac{1}{\sqrt{2}}(\hat{X}-\hat{Z}) = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}
-        }
+        \end{alignat}
     \end{formula}
     % \begin{itemize}
     %     \item \gt{bitflip}: $\hat{X} = \sigma_x = \sigmaxmatrix$
@@ -92,12 +96,10 @@
             \begin{formula}{circuit}
                 \desc{SQUID}{Superconducting quantum interference device, consists of parallel \hyperref{sec:qc:scq:josephson_junction}{josephson junctions}, can be used to measure extremely weak magnetic fields}{}
                 \desc[german]{SQUID}{Superconducting quantum interference device, besteht aus parralelen \hyperref{sec:qc:scq:josephson_junction}{Josephson Junctions} und kann zur Messung extrem schwacher Magnetfelder genutzt werden}{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{circuitikz}
+                    \draw (0, 0) \squidloop{loop}{};
-                        \draw (0, 0) \squidloop{loop}{};
+                \end{tikzpicture}
-                    \end{circuitikz}
-                }
             \end{formula}
             \begin{formula}{hamiltonian}
                 \desc{Hamiltonian}{}{$\hat{\phi}$ phase difference across the junction}
@@ -109,7 +111,7 @@
             \eng{Josephson Qubit??}
             \ger{TODO}
             ]{josephson_qubit}
-            \begin{circuitikz}
+            \begin{tikzpicture}
               \draw (0,0) to[capacitor] (0,2);
               \draw (0,0) to (2,0);
               \draw (0,2) to (2,2);
@@ -117,10 +119,10 @@
 
               \draw[->] (3,1) -- (4,1);
               \draw (5,0) to[josephsoncap=$C_\text{J}$] (5,2);
-            \end{circuitikz}
+            \end{tikzpicture}
             \TODO{Include schaltplan}
 
-            \begin{circuitikz}
+            \begin{tikzpicture}
               \draw (0,0) to[sV=$V_\text{g}$] (0,2);
               \draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
               \draw (2,2) to (4,2);
@@ -128,7 +130,7 @@
               \draw (4,0) to[capacitor=$C_C$] (4,2);
               \draw (0,0) to (2,0);
               \draw (2,0) to (4,0);
-            \end{circuitikz}
+            \end{tikzpicture}
 
             \begin{formula}{charging_energy}
                 \desc{Charging energy / electrostatic energy}{}{}
@@ -217,16 +219,14 @@
                         \baditem Sensibel für charge noise
                     \end{itemize}
                 }{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{circuitikz}
+                  \draw (0,0) to[sV=$V_\text{g}$] (0,2);
-                      \draw (0,0) to[sV=$V_\text{g}$] (0,2);
+                  % \draw (0,0) to (2,0);
-                      % \draw (0,0) to (2,0);
+                  \draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
-                      \draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
+                  \draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
-                      \draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
+                  \draw (0,0) to (2,0);
-                      \draw (0,0) to (2,0);
+                \end{tikzpicture}
-                    \end{circuitikz}
-                }
             \end{formula}
 
 
@@ -256,15 +256,13 @@
                         \baditem Geringe Anharmonizität $\alpha$
                     \end{itemize}
                 }{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{circuitikz}
+                    % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                    % to[capacitor=$C_\text{g}$] ++(2,0)
-                        % to[capacitor=$C_\text{g}$] ++(2,0)
+                    \draw (0,0) to ++(2,0) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to ++(0,-0.5) to ++(-2,0)
-                        \draw (0,0) to ++(2,0) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to ++(0,-0.5) to ++(-2,0)
+                     to[capacitor=$C_C$] ++(0,3);
-                         to[capacitor=$C_C$] ++(0,3);
+                \end{tikzpicture}
-                    \end{circuitikz}
-                }
             \end{formula}
 
             \begin{formula}{hamiltonian}
@@ -280,17 +278,14 @@
                 \begin{formula}{circuit}
                     \desc{Frequency tunable transmon}{By using a \fqSecRef{qc:scq:elements:squid} instead of a \fqSecRef{qc:scq:elements:josephson_junction}, the qubit is frequency tunable through an external field}{}
                     \desc[german]{}{Durch Nutzung eines \fqSecRef{qc:scq:elements:squid} anstatt eines \fqSecRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{}
-                    \content{
+                    \centering
-                        \centering
+                    \begin{tikzpicture}
-                        \begin{circuitikz}
+                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                            % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                        % to[capacitor=$C_\text{g}$] ++(2,0)
-                            % to[capacitor=$C_\text{g}$] ++(2,0)
+                        \draw (0,0) to ++(-2,0)
-                            \draw (0,0) to ++(-2,0)
+                        to ++(3,0) to ++(0,-0.5) \squidloop{loop}{SQUID} to ++(0,-0.5) to ++(-3,0)
-                            to ++(3,0) to ++(0,-0.5) \squidloop{loop}{SQUID} to ++(0,-0.5) to ++(-3,0)
+                        to[capacitor=$C_C$] ++(0,3);
-                            to[capacitor=$C_C$] ++(0,3);
+                    \end{tikzpicture}
-
-                        \end{circuitikz}
-                    }
                 \end{formula}
 
                 \begin{formula}{energy}
@@ -319,25 +314,23 @@
             \begin{formula}{circuit}
                 \desc{Phase qubit}{}{}
                 \desc[german]{Phase Qubit}{}{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{circuitikz}
+                    % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                    % to ++(2,0) coordinate(top1)
-                        % to ++(2,0) coordinate(top1)
+                    % to ++(2,0) coordinate(top2)
-                        % to ++(2,0) coordinate(top2)
+                    % to ++(2,0) coordinate(top3);
-                        % to ++(2,0) coordinate(top3);
+                    % \draw (0,0)
-                        % \draw (0,0)
+                    % to ++(2,0) coordinate(bot1)
-                        % to ++(2,0) coordinate(bot1)
+                    % to ++(2,0) coordinate(bot2)
-                        % to ++(2,0) coordinate(bot2)
+                    % to ++(2,0) coordinate(bot3);
-                        % to ++(2,0) coordinate(bot3);
+                    \draw[color=gray] (0,0) to[capacitor=$C_C$] (0,-2);
-                        \draw[color=gray] (0,0) to[capacitor=$C_C$] (0,-2);
+                    % \draw (top1) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to (bot2);
-                        % \draw (top1) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to (bot2);
+                    \draw(0,0) to ++(2,0) to[josephsoncap=$C_\text{J}$] ++(0,-2) to ++(-2,0);
-                        \draw(0,0) to ++(2,0) to[josephsoncap=$C_\text{J}$] ++(0,-2) to ++(-2,0);
+                    \draw (2,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-2) to ++(-2,0);
-                        \draw (2,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-2) to ++(-2,0);
+                    \node at (3,-1.5) {$\Phi_\text{ext}$};
-                        \node at (3,-1.5) {$\Phi_\text{ext}$};
+                \end{tikzpicture}
-                    \end{circuitikz}
+                \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                    \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                }
             \end{formula}
             \begin{formula}{hamiltonian}
                 \desc{Hamiltonian}{}{$\delta = \frac{\phi}{\phi_0}$}
@@ -359,17 +352,16 @@
             \begin{formula}{circuit}
                 \desc{Flux qubit / Persistent current qubit}{}{}
                 \desc[german]{Flux Qubit / Persistent current qubit}{}{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{circuitikz}
+                    \draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
-                        \draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
+                    \draw (0,0) to ++(3,0) 
-                        \draw (0,0) to ++(3,0) 
+                    to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
-                        to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
+                    to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
-                        to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
+                    to ++(-3,0);
-                        to ++(-3,0);
+                    \node at (1.5,-1.5) {$\Phi_\text{ext}$};
-                        \node at (1.5,-1.5) {$\Phi_\text{ext}$};
+                \end{tikzpicture}
-                    \end{circuitikz}
+                    % \begin{tikzpicture}
-                    % \begin{circuitikz}
                     %     \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
                     %     to ++(2,0) coordinate(top1)
                     %     to ++(2,0) coordinate(top2)
@@ -385,8 +377,7 @@
                     %     to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
                     %     to[josephsoncap=$E_\text{J}$] (bot3);
                     %     \node at (5,0.5) {$\Phi_\text{ext}$};
-                    % \end{circuitikz}
+                    % \end{tikzpicture}
-                }
             \end{formula}
 
 
@@ -404,18 +395,16 @@
                     Anstatt zu tunneln, können die Cooper-Paare über das induktive Element auf die Insel gelangen.
                     Das induktive Element besteht aus sehr vielen parallelen Josephson-Kontakten um parisitische Kapazitäten zu vermeiden.
                 }{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{circuitikz}
+                    % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                    % to ++(2,0) coordinate(top1);
-                        % to ++(2,0) coordinate(top1);
+                    \draw[color=gray] (0,0) to ++(-2,0) to[capacitor=$C_C$] ++(0,-3) to ++(2,0);
-                        \draw[color=gray] (0,0) to ++(-2,0) to[capacitor=$C_C$] ++(0,-3) to ++(2,0);
+                    \draw (0,0) to[josephsoncap=$C_\text{J}$] ++(-0,-3);
-                        \draw (0,0) to[josephsoncap=$C_\text{J}$] ++(-0,-3);
+                    \draw (0,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
-                        \draw (0,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
+                    \node at (1,-0.5) {$\Phi_\text{ext}$};
-                        \node at (1,-0.5) {$\Phi_\text{ext}$};
+                \end{tikzpicture}
-                    \end{circuitikz}
+                \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                    \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                }
             \end{formula}
 
             \def\temp{$E_\text{C} = \frac{(2e)^2}{2C}, E_\text{L} = \frac{\varphi_0^2}{2L}, \delta_\text{s} = \frac{\varphi_\text{s}}{\varphi_0}$}
@@ -448,7 +437,7 @@
         \begin{formula}{rabi_oscillation}
             \desc{Rabi oscillations}{}{$\omega_{21}$ resonance frequency of the energy transition, $\Omega$ Rabi frequency}
             \desc[german]{Rabi-Oszillationen}{}{$\omega_{21}$ Resonanzfrequenz des Energieübergangs, $\Omega$ Rabi-Frequenz}
-            \eq{\Omega_ TODO}
+            \eq{\Omega_ \text{\TODO{TODO}}}
         \end{formula}
 
         \Subsection[
@@ -471,7 +460,7 @@
             \eq{\Gamma_1 = \frac{1}{T_1} = \Gamma_{1\uparrow} + \Gamma_{1\downarrow}}
         \end{formula}
 
-        \begin{ttext}[long]
+        \begin{ttext}[longdesc]
             \eng{$\Gamma_{1\uparrow}$ is supressed at low temperatures because of detailed balance}
             \ger{$\Gamma_{1\uparrow}$ ist bei niedrigen Temperaturen unterdrückt wegen detailed balance}
         \end{ttext}

src/readme.md

@@ -1,46 +0,0 @@
-# Knowledge Collection
-This is supposed to be a compact, searchable collection of the most important stuff I had to during my physics studides,
-because it would be a shame if I forget it all!
-
-# LaTeX Guideline
-Here is some info to help myself remember why I did things the way I did.
-
-In general, most content should be written with macros, so that the behaviour can be changed later.
-
-## `fqname`
-All translation keys and LaTeX labels should use a structured approach:
-`<key type>:<partname>:<section name>:<subsection name>:<...>:<name>`
-
-The `<partname>:...:<lowest section name>` will be defined as `fqname` (fully qualified name) macro when using the `\Part`, `\Section`, ... macros.
-
-`<key type>` should be
-
-- equation: `eq`
-- table: `tab`
-- figure: `fig`
-- parts, (sub)sections: `sec`
-
-## Multilanguage
-All text should be defined as a translation (`translations` package, see `util/translation.tex`) and then used using the `gt` or `GT` macros.
-The english translation of any key must be defined, because it will also be used as fallback.
-
-Never make a macro that would have to be changed if a new language was added, eg dont do
-```tex
-% 1: key, 2: english version, 3: german version
-\newcommand{\mycmd}[3]{
-    \dosomestuff{english}{#1}{#2}
-    \dosomestuff{german}{#1}{#3}
-}
-
-\mycmd{key}{this is english}{das ist deutsch}
-```
-Instead, do
-```tex
-% [1]: lang, 2: key, 2: text
-\newcommand{\mycmd}[3][english]{
-    \dosomestuff{#1}{#2}{#3}
-}
-
-\mycmd{key}{this is english}
-\mycmd[german]{key}{das ist deutsch}
-```

src/scripts/plot.py

@@ -1,36 +0,0 @@
-import os
-import matplotlib.pyplot as plt
-import numpy as np
-import math
-import scipy as scp
-
-outdir = "../img/"
-filetype = ".pdf"
-skipasserts = False
-
-full = 8
-size_half_half = (full/2, full/2)
-size_third_half = (full/3, full/2)
-size_half_third = (full/2, full/3)
-
-def texvar(var, val, math=True):
-    s = "$" if math else ""
-    s += f"\\{var} = {val}"
-    if math: s += "$"
-    return s
-
-def export(fig, name, notightlayout=False):
-    if not skipasserts:
-        assert os.path.abspath(".").endswith("scripts"), "Please run from the `scripts` directory"
-    filename = os.path.join(outdir, name + filetype)
-    if not notightlayout:
-        fig.tight_layout()
-    fig.savefig(filename) #, bbox_inches="tight")
-
-
-@np.vectorize
-def smooth_step(x: float, left_edge: float, right_edge: float):
-    x = (x - left_edge) / (right_edge - left_edge)
-    if x <= 0: return 0.
-    elif x >= 1: return 1.
-    else: return 3*(x**2) - 2*(x**3)

src/spv.tex

@@ -0,0 +1,41 @@
+\Section[
+    \eng{Surface-Photovoltage}
+    \ger{Oberflächen-Photospannung}
+]{spv}
+    Mechanisms: 
+    \begin{formula}{scr}
+        \desc{Space-charge regions}{}{}
+        % \desc[german]{}{}{}
+        \ttxt{
+            \eng{Under illumination, the potential of a space charge region is reduced through the separation of photogenerated charge carriers}
+        }
+    \end{formula}
+    \begin{formula}{dember}
+        \desc{Dember-Photovoltage}{}{\QtyRef{diffusion_coefficient}}
+        % \desc[german]{}{}{}
+        \ttxt{
+            \eng{Usually electrons diffuse faster than holes ($D_\txe > D_\txh$) \Rightarrow charge carrier separation}
+        }
+    \end{formula}
+
+    \begin{formula}{asymmetric_charge_transfer}
+        \desc{Asymmetric charge transfer}{}{}
+        % \desc[german]{}{}{}
+        \ttxt{
+            \eng{Asymmetric transfer rates from bulk to surface states and vice versa leads to charge carrier separation}
+        }
+    \end{formula}
+    \begin{formula}{exciton_dissociation}
+        \desc{Exciton dissociation}{Important in organic semiconductors with conjugated molecules}{}
+        % \desc[german]{}{}{}
+        \ttxt{
+            \eng{Excitons dissociate at donor-acceptor heterojunctions and the electron is transferred to the acceptor}
+        }
+    \end{formula}
+    \begin{formula}{surface_dipoles}
+        \desc{Surface dipoles}{}{}
+        % \desc[german]{}{}{}
+        \ttxt{
+            \eng{Light can excite electrons, which are then attracted to one part of the molecule. This leads to an orientation of surface dipoles}
+        }
+    \end{formula}

src/statistical_mechanics.tex

@@ -1,84 +1,84 @@
 \Part[
     \eng{Statistichal Mechanics}
     \ger{Statistische Mechanik}
-    ]{stat}
+]{stat}
 
-    \begin{ttext}
+\begin{ttext}
-        \eng{
+    \eng{
-            \textbf{Intensive quantities:} Additive for subsystems (system size dependent): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
+        \textbf{Extensive quantities:} Additive for subsystems (system size dependent): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
-            \textbf{Extensive quantities:} Independent of system size, ratio of two intensive quantities
+        \textbf{Intensive quantities:} Independent of system size, ratio of two extensive quantities
-        }
+    }
-        \ger{
+    \ger{
-            \textbf{Intensive Größen:} Additiv für Subsysteme (Systemgrößenabhänig): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
+        \textbf{Extensive Größen:} Additiv für Subsysteme (Systemgrößenabhänig): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
-            \textbf{Extensive Größen:} Unabhängig der Systemgröße, Verhältnis zweier intensiver Größen
+        \textbf{Intensive Größen:} Unabhängig der Systemgröße, Verhältnis zweier extensiver Größen
-        }
+    }
-    \end{ttext}
+\end{ttext}
 
-    \begin{formula}{liouville}
+\begin{formula}{liouville}
-        \desc{Liouville equation}{}{$\{\}$ poisson bracket}
+    \desc{Liouville equation}{}{$\{\}$ poisson bracket}
-        \desc[german]{Liouville-Gleichung}{}{$\{\}$ Poisson-Klammer}
+    \desc[german]{Liouville-Gleichung}{}{$\{\}$ Poisson-Klammer}
-        \eq{\pdv{\rho}{t} = - \sum_{i=1}^{N} \left(\pdv{\rho}{q_i} \pdv{H}{p_i} - \pdv{\rho}{p_i} \pdv{H}{q_i} \right) = \{H, \rho\}}
+    \eq{\pdv{\rho}{t} = - \sum_{i=1}^{N} \left(\pdv{\rho}{q_i} \pdv{H}{p_i} - \pdv{\rho}{p_i} \pdv{H}{q_i} \right) = \{H, \rho\}}
+\end{formula}
+
+\Section[
+    \eng{Entropy}
+    \ger{Entropie}
+]{entropy}
+
+    \begin{formula}{properties}
+        \desc{Positive-definite and additive}{}{}
+        \desc[german]{Positiv Definit und Additiv}{}{}
+        \eq{
+            S &\ge 0 \\
+            S(E_1, E_2) &= S_1 + S_2
+        }
     \end{formula}
 
-    \Section[
+    \begin{formula}{von_neumann}
-        \eng{Entropy}
+        \desc{Von-Neumann}{}{$\rho$ density matrix}
-        \ger{Entropie}
+        \desc[german]{Von-Neumann}{}{$\rho$ Dichtematrix}
-        ]{entropy}
+        \eq{S = - \kB \braket{\log \rho} = - \kB \tr(\rho \log\rho)}
+    \end{formula}
 
-        \begin{formula}{properties}
+    \begin{formula}{gibbs}
-            \desc{Positive-definite and additive}{}{}
+        \desc{Gibbs}{}{$p_n$ probability for micro state $n$}
-            \desc[german]{Positiv Definit und Additiv}{}{}
+        \desc[german]{Gibbs}{}{$p_n$ Wahrscheinlichkeit für Mikrozustand $n$}
-            \eq{
+        \eq{S = - \kB \sum_n p_n \log p_n}
-                S &\ge 0 \\
+    \end{formula}
-                S(E_1, E_2) &= S_1 + S_2
-            }
-        \end{formula}
 
-        \begin{formula}{von_neumann}
+    \begin{formula}{boltzmann}
-            \desc{Von-Neumann}{}{$\rho$ density matrix}
+        \desc{Boltzmann}{}{$\Omega$ \#micro states}
-            \desc[german]{Von-Neumann}{}{$\rho$ Dichtematrix}
+        \desc[german]{Boltzmann}{}{$\Omega$ \#Mikrozustände}
-            \eq{S = - \kB \braket{\log \rho} = - \kB \tr(\rho \log\rho)}
+        \eq{S = \kB \log\Omega}
-        \end{formula}
+    \end{formula}
 
-        \begin{formula}{gibbs}
+    \begin{formula}{temp}
-            \desc{Gibbs}{}{$p_n$ probability for micro state $n$}
+        \desc{Temperature}{}{}
-            \desc[german]{Gibbs}{}{$p_n$ Wahrscheinlichkeit für Mikrozustand $n$}
+        \desc[german]{Temperatur}{}{}
-            \eq{S = - \kB \sum_n p_n \log p_n}
+        \eq{\frac{1}{T} \coloneq \pdv{S}{E}_V}
-        \end{formula}
+    \end{formula}
 
-        \begin{formula}{boltzmann}
+    \begin{formula}{pressure}
-            \desc{Boltzmann}{}{$\Omega$ \#micro states}
+        \desc{Pressure}{}{}
-            \desc[german]{Boltzmann}{}{$\Omega$ \#Mikrozustände}
+        \desc[german]{Druck}{}{}
-            \eq{S = \kB \log\Omega}
+        \eq{p = T \pdv{S}{V}_E}
-        \end{formula}
+    \end{formula}
-
-        \begin{formula}{temp}
-            \desc{Temperature}{}{}
-            \desc[german]{Temperatur}{}{}
-            \eq{\frac{1}{T} \coloneq \pdv{S}{E}_V}
-        \end{formula}
-
-        \begin{formula}{pressure}
-            \desc{Pressure}{}{}
-            \desc[german]{Druck}{}{}
-            \eq{p = T \pdv{S}{V}_E}
-        \end{formula}
 
 \Part[
     \eng{Thermodynamics}
     \ger{Thermodynamik}
-    ]{td}
+]{td}
 
-    \begin{formula}{therm_wavelength}
+\begin{formula}{therm_wavelength}
-        \desc{Thermal wavelength}{}{}
+    \desc{Thermal wavelength}{}{}
-        \desc[german]{Thermische Wellenlänge}{}{}
+    \desc[german]{Thermische Wellenlänge}{}{}
-        \eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
+    \eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
-    \end{formula}
+\end{formula}
 
-    \Section[
+\Section[
-        \eng{Processes}
+    \eng{Processes}
-        \ger{Prozesse}
+    \ger{Prozesse}
-    ]{process}
+]{process}
     \begin{ttext}
         \eng{
             \begin{itemize}
@@ -111,27 +111,32 @@
         \ger{Irreversible Gasexpansion (Gay-Lussac-Versuch)}
         ]{gay}
 
-        \begin{minipage}{0.6\textwidth}
+        \begin{bigformula}{experiment}
-            \vfill
+            \desc{Gay-Lussac experiment}{}{}
-            \begin{ttext}
+            \desc[german]{Gay-Lussac-Versuch}{}{}
-                \eng{
+            \begin{minipage}{0.6\textwidth}
-                    A classical gas in a system with volume $V_1$ is separated from another system with volume $V_2$. 
+                \vfill
-                    In the Gay-Lussac experiment, the separation is removed and the gas flows into $V_2$.
+                \begin{ttext}
-                }
+                    \eng{
-                \ger{
+                        A classical gas in a system with volume $V_1$ is separated from another system with volume $V_2$. 
-                    Ein klassisches Gas in einem System mit Volumen $V_1$ ist getrennt von einem zweiten System mit Volumen $V_2$.
+                        In the Gay-Lussac experiment, the separation is removed and the gas flows into $V_2$.
-                    Beim Gay-Lussac Versuch wird die Trennwand entfern und das Gas fließt in das Volumen $V_2$.
+                    }
-                }
+                    \ger{
-            \end{ttext}
+                        Ein klassisches Gas in einem System mit Volumen $V_1$ ist getrennt von einem zweiten System mit Volumen $V_2$.
-            \vfill
+                        Beim Gay-Lussac Versuch wird die Trennwand entfern und das Gas fließt in das Volumen $V_2$.
-        \end{minipage}
+                    }
-        \hfill
+                \end{ttext}
-        \begin{minipage}{0.3\textwidth}
+                \vfill
-            \begin{figure}[H]
+            \end{minipage}
-                \centering
+            \hfill
-                \includegraphics[width=\textwidth]{img/td_gay_lussac.pdf}
+            \begin{minipage}{0.3\textwidth}
-            \end{figure}
+                \begin{figure}[H]
-        \end{minipage}
+                    \centering
+                    \includegraphics[width=\textwidth]{img/td_gay_lussac.pdf}
+                \end{figure}
+            \end{minipage}
+        \end{bigformula}
+
 
         \begin{formula}{entropy}
             \desc{Entropy change}{}{}
@@ -149,7 +154,7 @@
     \Section[
         \eng{Phase transitions}
         \ger{Phasenübergänge}
-        ]{phases}
+    ]{phases}
 
         \begin{ttext}
             \eng{
@@ -187,7 +192,7 @@
         \Subsubsection[
             \eng{Osmosis}
             \ger{Osmose}
-            ]{osmosis}
+        ]{osmosis}
             \begin{ttext}
                 \eng{
                     Osmosis is the spontaneous net movement or diffusion of solvent molecules 
@@ -213,7 +218,7 @@
     \Subsection[
         \eng{Material properties}
         \ger{Materialeigenschaften}
-        ]{}
+    ]{props}
         \begin{formula}{heat_cap}
             \desc{Heat capacity}{}{$Q$ heat}
             \desc[german]{Wärmekapazität}{}{$Q$ Wärme}
@@ -266,12 +271,12 @@
 \Section[
     \eng{Laws of thermodynamics}
     \ger{Hauptsätze der Thermodynamik}
-    ]{laws}
+]{laws}
 
     \Subsection[
         \eng{Zeroeth law}
         \ger{Nullter Hauptsatz}
-        ]{law0}
+    ]{law0}
         \begin{ttext}
             \eng{If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.}
             \ger{Wenn sich zwei Siesteme jeweils im thermischen Gleichgewicht mit einem dritten befinden, befinden sie sich auch untereinander im thermischen Gleichgewicht.}
@@ -307,7 +312,7 @@
     \Subsection[
         \eng{Second law}
         \ger{Zweiter Hauptsatz}
-        ]{law2}
+    ]{law2}
         \begin{ttext}
             \eng{
                 \textbf{Clausius}: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.\\
@@ -321,7 +326,7 @@
     \Subsection[
         \eng{Third law}
         \ger{Dritter Hauptsatz}
-        ]{law3}
+    ]{law3}
         \begin{ttext}
             \eng{It is impussible to cool a system to absolute zero.}
             \ger{Es ist unmöglich, ein System bis zum absoluten Nullpunkt abzukühlen.}
@@ -332,7 +337,7 @@
             \desc[german]{Entropiedichte}{}{$s = \frac{S}{N}$}
             \eq{
                 \lim_{T\to 0} s(T) &= 0 \\
-                \shortintertext{\GT{and_therefore_also}} \\
+                \shortintertext{\GT{and_therefore_also}}
                 \lim_{T\to 0} c_V &= 0
             }
         \end{formula}   
@@ -340,25 +345,77 @@
 \Section[
     \eng{Ensembles}
     \ger{Ensembles}
-    ]{ensembles}
+]{ensembles}
+    \Eng[const_variables]{Constant variables}
+    \Ger[const_variables]{Konstante Variablen}
 
+    \begin{bigformula}{nve} \absLabel[mc_ensemble]
+        \desc{Microcanonical ensemble}{}{}
+        \desc[german]{Mikrokanonisches Ensemble}{}{}
+        \begin{minipagetable}{nve}
+            \entry{const_variables} {$E$, $V,$ $N$           }
+            \entry{partition_sum}   {$\Omega = \sum_n 1$     }
+            \entry{probability}     {$p_n = \frac{1}{\Omega}$}
+            \entry{td_pot}          {$S = \kB\ln\Omega$      }
+            \entry{pressure}        {$p = T \pdv{S}{V}_{E,N}$}
+            \entry{entropy}         {$S = \kB = \ln\Omega$   }
+        \end{minipagetable}
+    \end{bigformula}
 
+    \begin{bigformula}{nvt} \absLabel[c_ensemble]
+        \desc{Canonical ensemble}{}{}
+        \desc[german]{Kanonisches Ensemble}{}{}
+        \begin{minipagetable}{nvt}
+            \entry{const_variables} {$T$, $V$, $N$                    }
+            \entry{partition_sum}   {$Z = \sum_n \e^{-\beta E_n}$     }
+            \entry{probability}     {$p_n = \frac{\e^{-\beta E_n}}{Z}$}
+            \entry{td_pot}          {$F = - \kB T \ln Z$              }
+            \entry{pressure}        {$p = -\pdv{F}{V}_{T,N}$          }
+            \entry{entropy}         {$S = -\pdv{F}{T}_{V,N}$          }
+        \end{minipagetable}
+    \end{bigformula}
+
+    \begin{bigformula}{mvt} \absLabel[gc_ensemble]
+        \desc{Grand canonical ensemble}{}{}
+        \desc[german]{Grosskanonisches Ensemble}{}{}
+        \begin{minipagetable}{mvt}
+            \entry{const_variables} {$T$, $V$, $\mu$                                      }
+            \entry{partition_sum}   {$Z_\text{g} = \sum_{n} \e^{-\beta(E_n - \mu N_n)}$   }
+            \entry{probability}     {$p_n = \frac{\e^{-\beta (E_n - \mu N_n}}{Z_\text{g}}$}
+            \entry{td_pot}          {$ \Phi = - \kB T \ln Z$                              }
+            \entry{pressure}        {$p = -\pdv{\Phi}{V}_{T,\mu} = -\frac{\Phi}{V}$       }
+            \entry{entropy}         {$S = -\pdv{\Phi}{T}_{V,\mu}$                         }
+        \end{minipagetable}
+    \end{bigformula}
+
+    \begin{bigformula}{npt}
+        \desc{Isobaric-isothermal}{Gibbs ensemble}{}
+        % \desc[german]{Kanonisches Ensemble}{}{}
+        \begin{minipagetable}{npt}
+            \entry{const_variables} {$N$, $p$, $T$}
+            \entry{partition_sum}   {}
+            \entry{probability}     {$p_n ? \frac{\e^{-\beta(E_n + pV_n)}}{Z}$}
+            \entry{td_pot}          {}
+            \entry{pressure}        {}
+            \entry{entropy}         {}
+        \end{minipagetable}
+    \end{bigformula}
+
+    \begin{bigformula}{nph}
+        \desc{Isonthalpic-isobaric ensemble}{Enthalpy ensemble}{}
+        % \desc[german]{Kanonisches Ensemble}{}{}
+        \begin{minipagetable}{nph}
+            \entry{const_variables} {}
+            \entry{partition_sum}   {}
+            \entry{probability}     {}
+            \entry{td_pot}          {}
+            \entry{pressure}        {}
+            \entry{entropy}         {}
+        \end{minipagetable}
+    \end{bigformula}
+
+    \TODO{complete, link potentials}
 
-    \begin{table}[H]
-        \centering
-        \caption{caption}
-        \label{tab:\fqname}
-    
-        \begin{tabular}{l|c|c|c}
-             &  \gt{mk} & \gt{k}  & \gt{gk}  \\ \hline
-            \GT{variables} & $E$, $V,$ $N$ & $T$, $V$, $N$ & $T$, $V$, $\mu$ \\ \hline
-            \GT{partition_sum} & $\Omega = \sum_n 1$ & $Z = \sum_n \e^{-\beta E_n}$ & $Z_\text{g} = \sum_{n} \e^{-\beta(E_n - \mu N_n)}$ \\ \hline
-            \GT{probability} & $p_n = \frac{1}{\Omega}$ & $p_n = \frac{\e^{-\beta E_n}}{Z}$ & $p_n = \frac{\e^{-\beta (E_n - \mu N_n}}{Z_\text{g}}$ \\ \hline
-            \GT{td_pot} & $S = \kB\ln\Omega$ & $F = - \kB T \ln Z$ & $ \Phi = - \kB T \ln Z$ \\ \hline
-            \GT{pressure} & $p = T \pdv{S}{V}_{E,N}$ &$p = -\pdv{F}{V}_{T,N}$ & $p = -\pdv{\Phi}{V}_{T,\mu} = -\frac{\Phi}{V}$ \\ \hline
-            \GT{entropy} & $S = \kB = \ln\Omega$ & $S = -\pdv{F}{T}_{V,N}$ & $S = -\pdv{\Phi}{T}_{V,\mu}$ \\ \hline
-        \end{tabular}
-    \end{table}
 
     \begin{formula}{ergodic_hypo}
         \desc{Ergodic hypothesis}{Over a long periode of time, all accessible microstates in the phase space are equiprobable}{$A$ Observable}
@@ -370,27 +427,27 @@
     \Subsection[
         \eng{Potentials}
         \ger{Potentiale}
-        ]{pots}
+    ]{pots}
         \begin{formula}{internal_energy}
             \desc{Internal energy}{}{}
             \desc[german]{Innere Energie}{}{}
             \eq{\d U(S,V,N) = T\d S -p\d V + \mu\d N}
         \end{formula}
+        \begin{formula}{free_energy}
+            \desc{Free energy / Helmholtz energy }{}{}
+            \desc[german]{Freie Energie / Helmholtz Energie}{}{}
+            \eq{\d F(T,V,N) = -S\d T -p\d V + \mu\d N}
+        \end{formula}
         \begin{formula}{enthalpy}
             \desc{Enthalpy}{}{}
             \desc[german]{Enthalpie}{}{}
             \eq{\d H(S,p,N) = T\d S +V\d p + \mu\d N}
         \end{formula}
         \begin{formula}{gibbs_energy}
-            \desc{Gibbs energy}{}{}
+            \desc{Free enthalpy / Gibbs energy}{}{}
-            \desc[german]{Gibbsche Energie}{}{}
+            \desc[german]{Freie Entahlpie / Gibbs-Energie}{}{}
             \eq{\d G(T,p,N) = -S\d T + V\d p + \mu\d N}
         \end{formula}
-        \begin{formula}{free_energy}
-            \desc{Free energy / Helmholtz energy }{}{}
-            \desc[german]{Freie Energie / Helmholtz Energie}{}{}
-            \eq{\d F(T,V,N) = -S\d T -p\d V + \mu\d N}
-        \end{formula}
         \begin{formula}{grand_canon_pot}
             \desc{Grand canonical potential}{}{}
             \desc[german]{Großkanonisches Potential}{}{}
@@ -398,11 +455,32 @@
         \end{formula}
 
         \TODO{Maxwell Relationen, TD Quadrat}
+        \begin{formula}{td-square}
+            \desc{Thermodynamic squre}{}{}
+            \desc[german]{Themodynamisches Quadrat}{Guggenheim Quadrat}{}
+            \begin{minipage}{0.3\textwidth}
+                \begin{tikzpicture}
+                    \draw[thick] (0,0) grid (3,3);
+                    \node at (0.5, 2.5) {$-S$};
+                    \node at (1.5, 2.5) {\color{blue}$U$};
+                    \node at (2.5, 2.5) {$V$};
+                    \node at (0.5, 1.5) {\color{blue}$H$};
+                    \node at (2.5, 1.5) {\color{blue}$F$};
+                    \node at (0.5, 0.5) {$-p$};
+                    \node at (1.5, 0.5) {\color{blue}$G$};
+                    \node at (2.5, 0.5) {$T$};
+                \end{tikzpicture}
+            \end{minipage}
+            \begin{ttext}
+                \eng{The corners opposite from the potential are the coefficients and each coefficients differential is opposite to it.}
+                \ger{Die Ecken gegenüber des Potentials sind die Koeffizienten, das Differential eines Koeffizienten ist in der Ecke gegenüber.}
+            \end{ttext}
+        \end{formula}
 
 \Section[
     \eng{Ideal gas}
     \ger{Ideales Gas}
-    ]{id_gas}
+]{id_gas}
     \begin{ttext}
         \eng{The ideal gas consists of non-interacting, undifferentiable particles.}
         \ger{Das ideale Gas besteht aus nicht-wechselwirkenden, ununterscheidbaren Teilchen.}
@@ -467,20 +545,18 @@
         \begin{formula}{desc}
             \desc{Molecule gas}{2 particles of mass $M$ connected by a ``spring'' with distance $L$}{}
             \desc[german]{Molekülgas}{2 Teilchen der Masse $M$ sind verbunden durch eine ``Feder'' mit Länge $L$}{}
-            \content{
+            % \begin{figure}[h]
-                % \begin{figure}[h]
+            \centering
-                \centering
+            \tikzstyle{spring}=[thick,decorate,decoration={coil,aspect=0.8,amplitude=5,pre length=0.1cm,post length=0.1cm,segment length=10}]
-                \tikzstyle{spring}=[thick,decorate,decoration={coil,aspect=0.8,amplitude=5,pre length=0.1cm,post length=0.1cm,segment length=10}]
+            \begin{tikzpicture}
-                \begin{tikzpicture}
+                \def\radius{0.5}
-                    \def\radius{0.5}
+                \coordinate (left) at (-3, 0);
-                    \coordinate (left) at (-3, 0);
+                \coordinate (right) at (3, 0);
-                    \coordinate (right) at (3, 0);
+                \draw (left) circle (\radius);
-                    \draw (left) circle (\radius);
+                \draw[spring] ($(left) + (\radius,0)$)  -- ($(right) - (\radius,0)$);
-                    \draw[spring] ($(left) + (\radius,0)$)  -- ($(right) - (\radius,0)$);
+                \draw (right) circle (\radius);
-                    \draw (right) circle (\radius);
+            \end{tikzpicture}
-                \end{tikzpicture}
                 % \end{figure}
-            }
         \end{formula}
 
         \begin{formula}{translation}
@@ -506,7 +582,7 @@
 \Section[
     \eng{Real gas}
     \ger{Reales Gas}
-    ]{real_gas}
+]{real_gas}
 
     \Subsection[
         \eng{Virial expansion}
@@ -536,10 +612,11 @@
             % b - \frac{a}{\kB T}}
         \end{formula}
 
-        \begin{formula}{lennard_jones}
+        \begin{formula}{lennard_jones} \absLabel
-            \desc{Lennard-Jones potential}{Potential between two molecules. Attractive for $r > \sigma$, repulsive for $r < \sigma$}{}
+            \desc{Lennard-Jones potential}{Potential between two molecules. Attractive for $r > \sigma$, repulsive for $r < \sigma$.\\ In condensed matter: Attraction due to Landau Dispersion \TODO{verify} and repulsion due to Pauli exclusion principle.}{}
-            \desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$}{}
+            \desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$.\\ In Festkörpern: Anziehung durch Landau-Dispersion und Abstoßung durch Pauli-Prinzip.}{}
-            \figeq{img/potential_lennard_jones.pdf}{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
+            \fig[0.7]{img/potential_lennard_jones.pdf}
+            \eq{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
         \end{formula}
 
     \Subsection[
@@ -566,7 +643,7 @@
 \Section[
     \eng{Ideal quantum gas}
     \ger{Ideales Quantengas}
-    ]{id_qgas}
+]{id_qgas}
     \def\bosfer{$\pm$: {$\text{bos} \atop \text{fer}$}}
 
     \begin{formula}{fugacity}
@@ -611,7 +688,8 @@
     \begin{formula}{occupation_number}
         \desc{Occupation number}{}{\bosfer}
         \desc[german]{Besetzungszahl}{}{\bosfer}
-        \figeq{img/td_id_qgas_distributions.pdf}{%
+        \fig[0.7]{img/td_id_qgas_distributions.pdf}
+        \eq{
             \braket{n(\epsilon)} &= \frac{1}{\e^{\beta(\epsilon - \mu)} \mp 1} \\
             \shortintertext{\GT{for} $\epsilon - \mu \gg \kB T$}
                         &= \frac{1}{\e^{\beta(\epsilon - \mu)}}
@@ -639,7 +717,7 @@
         \eq{
             pV &= \kB T \ln Z_g \\
             \shortintertext{\GT{after} \GT{td:real_gas:virial}}
-               &= N \kB T \left[1 \mp \frac{\lambda^3}{2^{5/2} g v} + \Order\left(\left(\frac{\lambda^3}{v}\right)^2\right)\right]
+               &= N \kB T \left[1 \mp \frac{\lambda^3}{2^{5/2} g v} + \Order{\left(\frac{\lambda^3}{v}\right)^2}\right]
         }
     \end{formula}
     \begin{formula}{relevance}
@@ -657,8 +735,8 @@
     \Subsection[
         \eng{Bosons}
         \ger{Bosonen}
-        ]{bos}
+    ]{bos}
-        \begin{formula}{partition_sum}
+        \begin{formula}{partition-sum}
             \desc{Partition sum}{}{$p \in\N_0$}
             \desc[german]{Zustandssumme}{}{$p \in\N_0$}
             \eq{Z_\text{g} = \prod_{p} \frac{1}{1-\e^{-\beta(\epsilon_p - \mu)}}}
@@ -673,7 +751,7 @@
     \Subsection[
         \eng{Fermions}
         \ger{Fermionen}
-        ]{fer}
+    ]{fer}
         \begin{formula}{partition_sum}
             \desc{Partition sum}{}{$p = 0,\,1$}
             \desc[german]{Zustandssumme}{}{$p = 0,\,1$}
@@ -682,7 +760,8 @@
         \begin{formula}{occupation}
             \desc{Occupation number}{Fermi-Dirac distribution. At $T=0$ \textit{Fermi edge} at $\epsilon=\mu$}{}
             \desc[german]{Besetzungszahl}{Fermi-Dirac Verteilung}{Bei $T=0$ \textit{Fermi-Kante} bei $\epsilon=\mu$}
-            \figeq{img/td_fermi_occupation.pdf}{\braket{n_p} = \frac{1}{\e^{\beta(\epsilon-\mu)}+1}}
+            \fig[0.7]{img/td_fermi_occupation.pdf}
+            \eq{\braket{n_p} = \frac{1}{\e^{\beta(\epsilon-\mu)}+1}}
         \end{formula}
 
         \begin{formula}{slater_determinant}
@@ -725,7 +804,7 @@
         \Subsubsection[
             \eng{Strong degeneracy}
             \ger{Starke Entartung}
-            ]{degenerate}
+        ]{degenerate}
             \eng[low_temps]{for low temperatures $T \ll T_\text{F}$}
             \ger[low_temps]{für geringe Temperaturen $T\ll T_\text{F}$}
 
@@ -748,7 +827,8 @@
             \begin{formula}{heat_cap}
                 \desc{Heat capacity}{\gt{low_temps}}{differs from \fqEqRef{td:TODO:petit_dulong}}
                 \desc[german]{Wärmecapacity}{\gt{low_temps}}{weicht ab vom \fqEqRef{td:TODO:petit_dulong}}
-                \figeq{img/td_fermi_heat_capacity.pdf}{C_V = \pdv{E}{T}_V = N\kB \frac{\pi}{2} \left(\frac{T}{T_\text{F}}\right)}
+                \fig[0.7]{img/td_fermi_heat_capacity.pdf}
+                \eq{C_V = \pdv{E}{T}_V = N\kB \frac{\pi}{2} \left(\frac{T}{T_\text{F}}\right)}
             \end{formula}
 
             

src/test.tex

@@ -0,0 +1,102 @@
+\part{Testing}
+
+% \directlua{tex.sprint("Compiled in directory: \\detokenize{" .. lfs.currentdir() .. "}")} \\
+% \directlua{tex.sprint("Jobname: " .. tex.jobname)} \\
+% \directlua{tex.sprint("Output directory \\detokenize{" .. os.getenv("TEXMF_OUTPUT_DIRECTORY") .. "}")} \\
+% \directlua{tex.sprint("String sanitize \\detokenize{" .. string.sanitize("m_a^th?") .. "}")}
+
+\languagename
+
+\paragraph{File loading}
+\noindent Lua Aux loaded? \luaAuxLoaded\\
+% Translations Aux loaded? \translationsAuxLoaded\\
+Input only: \inputOnlyFile
+
+\paragraph{Testing GT, GetTranslation, IfTranslationExists, IfTranslation}
+\addtranslation{english}{ttest}{This is the english translation of \texttt{ttest}}
+\noindent
+GT: ttest = \GT{ttest}\\
+% GetTranslation: ttest = \GetTranslation{ttest}\\
+% Is english? = \IfTranslation{english}{ttest}{yes}{no} \\
+% Is german? = \IfTranslation{german}{ttest}{yes}{no} \\
+Is defined = \IfTranslationExists{ttest}{yes}{no} \\
+
+\paragraph{Testing translation keys containing macros}
+\def\ttest{NAME}
+% \addtranslation{english}{\ttest:name}{With variable}
+% \addtranslation{german}{\ttest:name}{Mit Variable}
+% \addtranslation{english}{NAME:name}{Without variable}
+% \addtranslation{german}{NAME:name}{Without Variable}
+\DT[\ttest:name]{english}{DT With variable}
+\DT[\ttest:name]{german}{DT Mit Variable}
+\noindent
+GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\
+% GetTranslation: {\textbackslash}ttest:name = \GetTranslation{\ttest:name}\\
+% Is english? = \IfTranslation{english}{\ttest:name}{yes}{no} \\
+% Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\
+% Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\
+% Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
+
+\paragraph{Testing relative translations}
+\begingroup
+    \edef\prevFqname{\fqname}
+    \edef\fqname{\prevFqname:test}
+    \eng{English, relative}
+    \ger{Deutsch, relativ}
+\endgroup
+\dt[testkey]{english}{Testkey}
+{\textbackslash}gt\{test\}: \gt{test}\\
+{\textbackslash}gt\{test\}: \gt{testkey}
+
+% \DT[qty:test]{english}{HAHA}
+
+\paragraph{Testing hyperrefs}
+\noindent{This text is labeled with "test" \label{test}}\\
+\hyperref[test]{This should refer to the line above}\\
+Link to quantity which is defined after the reference: \qtyRef{test}\\
+\DT[eq:test]{english}{If you read this, then the translation for eq:test was expandend!}
+Link to defined quantity: \qtyRef{mass}
+\\ Link to element with name: \ElRef{H}
+\begin{equation}
+    \label{eq:test}
+    E = mc^2
+\end{equation}
+
+\paragraph{Testing translation keys with token symbols like undescores}
+\noindent
+\GT{absolute_undefined_translation_with_underscors}\\
+\gt{relative_undefined_translation_with_underscors}\\
+\GT{absolute_undefined_translation_with_&ampersand}
+
+
+\paragraph{Testing formula2}
+\begin{formula}{test}
+    \desc{Test}{Test Description}{Defs}
+    \desc[german]{Test (DE)}{Beschreibung}{Defs (DE)}
+    \eq{
+        \text{equationwith}_{\alpha} \delta \E \left[yo\right]
+    }
+    \quantity{\tau}{\m\per\s}{iv}
+\end{formula}
+\begin{formula}{test2}
+    \desc{Test2}{Test Description}{Defs}
+    \desc[german]{Test2 (DE)}{Beschreibung}{Defs (DE)}
+    \ttxt{
+        \eng{This text is english}
+        \ger{Dieser Text ist deutsch}
+    }
+    \ttxt[moretext]{
+        \eng{This text is english, again}
+        \ger{Dieser Text ist wieder deutsch}
+    }
+    \begin{equation}
+        M\omega\rho\epsilon
+    \end{equation}
+\end{formula}
+\begin{formula}{test3}
+    \desc{Test2}{Test Description}{Defs}
+    \desc[german]{Test2 (DE)}{Beschreibung}{Defs (DE)}
+    Formula  with just plain text.
+\end{formula}
+
+

src/util/colors.tex

@@ -0,0 +1,37 @@
+
+% \redefinecolor{black}{HTML}{fg0}
+% Dark mode
+\pagecolor{bg0}
+\color{fg0}
+
+% \pagecolor{dark0_hard}
+% \color{light0_hard}
+
+% section headings in bright colors, \titleformat from titlesec package
+\titleformat{\section}
+  {\color{fg-purple}\normalfont\Large\bfseries}
+  {\color{fg-purple}\thesection}{1em}{}
+
+\titleformat{\subsection}
+  {\color{fg-blue}\normalfont\large\bfseries}
+  {\color{fg-blue}\thesubsection}{1em}{}
+
+\titleformat{\subsubsection}
+  {\color{fg-aqua}\normalfont\normalsize\bfseries}
+  {\color{fg-aqua}\thesubsubsection}{1em}{}
+
+\titleformat{\paragraph}
+  {\color{fg-green}\normalfont\normalsize\bfseries}
+  {\color{fg-green}\theparagraph}{1em}{}
+
+\titleformat{\subparagraph}
+  {\color{fg-purple}\normalfont\normalsize\bfseries}
+  {\color{fg-purple}\thesubparagraph}{1em}{}
+
+\hypersetup{
+  colorlinks=true,
+  linkcolor=fg-purple,
+  citecolor=fg-green,
+  filecolor=fg-blue,
+  urlcolor=fg-orange
+}

src/util/colorscheme.tex

@@ -1,73 +1,38 @@
-% Define Gruvbox colors
+% This file was generated by scripts/formulary.py
-\definecolor{dark0_hard}{HTML}{1d2021}
+% Do not edit it directly, changes will be overwritten
-\definecolor{dark0}{HTML}{282828}
+\definecolor{fg-blue}{HTML}{072140}
-\definecolor{dark0_soft}{HTML}{32302f}
+\definecolor{bg-blue}{HTML}{5E94D4}
-\definecolor{dark1}{HTML}{3c3836}
+\definecolor{alt-blue}{HTML}{3070B3}
-\definecolor{dark2}{HTML}{504945}
+\definecolor{bg-yellow}{HTML}{FED702}
-\definecolor{dark3}{HTML}{665c54}
+\definecolor{fg-yellow}{HTML}{CBAB01}
-\definecolor{dark4}{HTML}{7c6f64}
+\definecolor{alt-yellow}{HTML}{FEDE34}
-\definecolor{medium}{HTML}{928374}
+\definecolor{bg-orange}{HTML}{F7811E}
-\definecolor{light0_hard}{HTML}{f9f5d7}
+\definecolor{fg-orange}{HTML}{D99208}
-\definecolor{light0}{HTML}{fbf1c7}
+\definecolor{alt-orange}{HTML}{F9BF4E}
-\definecolor{light0_soft}{HTML}{f2e5bc}
+\definecolor{bg-purple}{HTML}{B55CA5}
-\definecolor{light1}{HTML}{ebdbb2}
+\definecolor{fg-purple}{HTML}{9B468D}
-\definecolor{light2}{HTML}{d5c4a1}
+\definecolor{alt-purple}{HTML}{C680BB}
-\definecolor{light3}{HTML}{bdae93}
+\definecolor{bg-red}{HTML}{EA7237}
-\definecolor{light4}{HTML}{a89984}
+\definecolor{fg-red}{HTML}{D95117}
-\definecolor{bright_red}{HTML}{fb4934}
+\definecolor{alt-red}{HTML}{EF9067}
-\definecolor{bright_green}{HTML}{b8bb26}
+\definecolor{bg-green}{HTML}{9FBA36}
-\definecolor{bright_yellow}{HTML}{fabd2f}
+\definecolor{fg-green}{HTML}{7D922A}
-\definecolor{bright_blue}{HTML}{83a598}
+\definecolor{alt-green}{HTML}{B6CE55}
-\definecolor{bright_purple}{HTML}{d3869b}
+\definecolor{bg-gray}{HTML}{475058}
-\definecolor{bright_aqua}{HTML}{8ec07c}
+\definecolor{fg-gray}{HTML}{20252A}
-\definecolor{bright_orange}{HTML}{fe8019}
+\definecolor{alt-gray}{HTML}{333A41}
-\definecolor{neutral_red}{HTML}{cc241d}
+\definecolor{bg-aqua}{HTML}{689d6a}
-\definecolor{neutral_green}{HTML}{98971a}
+\definecolor{fg-aqua}{HTML}{427b58}
-\definecolor{neutral_yellow}{HTML}{d79921}
+\definecolor{fg0-hard}{HTML}{000000}
-\definecolor{neutral_blue}{HTML}{458588}
+\definecolor{fg0}{HTML}{000000}
-\definecolor{neutral_purple}{HTML}{b16286}
+\definecolor{fg0-soft}{HTML}{20252A}
-\definecolor{neutral_aqua}{HTML}{689d6a}
+\definecolor{fg1}{HTML}{072140}
-\definecolor{neutral_orange}{HTML}{d65d0e}
+\definecolor{fg2}{HTML}{333A41}
-\definecolor{faded_red}{HTML}{9d0006}
+\definecolor{fg3}{HTML}{475058}
-\definecolor{faded_green}{HTML}{79740e}
+\definecolor{fg4}{HTML}{6A757E}
-\definecolor{faded_yellow}{HTML}{b57614}
+\definecolor{bg0-hard}{HTML}{FFFFFF}
-\definecolor{faded_blue}{HTML}{076678}
+\definecolor{bg0}{HTML}{FBF9FA}
-\definecolor{faded_purple}{HTML}{8f3f71}
+\definecolor{bg0-soft}{HTML}{EBECEF}
-\definecolor{faded_aqua}{HTML}{427b58}
+\definecolor{bg1}{HTML}{DDE2E6}
-\definecolor{faded_orange}{HTML}{af3a03}
+\definecolor{bg2}{HTML}{E3EEFA}
-
+\definecolor{bg3}{HTML}{F0F5FA}
-% Use Gruvbox colors for various elements
-% \pagecolor{light0_hard}
-% \color{dark0_hard}
-% \pagecolor{dark0_hard}
-% \color{light0_hard}
-
-% Section headings in bright colors
-\titleformat{\section}
-  {\color{neutral_purple}\normalfont\Large\bfseries}
-  {\color{neutral_purple}\thesection}{1em}{}
-
-\titleformat{\subsection}
-  {\color{neutral_blue}\normalfont\large\bfseries}
-  {\color{neutral_blue}\thesubsection}{1em}{}
-
-\titleformat{\subsubsection}
-  {\color{neutral_aqua}\normalfont\normalsize\bfseries}
-  {\color{neutral_aqua}\thesubsubsection}{1em}{}
-
-\titleformat{\paragraph}
-  {\color{neutral_green}\normalfont\normalsize\bfseries}
-  {\color{neutral_green}\theparagraph}{1em}{}
-
-\titleformat{\subparagraph}
-  {\color{neutral_purple}\normalfont\normalsize\bfseries}
-  {\color{neutral_purple}\thesubparagraph}{1em}{}
-
-% Links in neutral colors
-\hypersetup{
-  colorlinks=true,
-  linkcolor=neutral_red,
-  citecolor=neutral_green,
-  filecolor=neutral_blue,
-  urlcolor=neutral_orange
-}

src/util/environments.tex

@@ -1,195 +1,36 @@
-% use this to define text in different languages for the key <env arg>
-% the translation for <env arg> when the environment ends.
-% (temporarily change fqname to the \fqname:<env arg> to allow
-% the use of \eng and \ger without the key parameter)
-% [1]: key
-\newenvironment{ttext}[1][desc]{
-    \edef\realfqname{\fqname}
-    \edef\fqname{\fqname:#1}
-}{
-    \expandafter\GT\expandafter{\fqname} \\
-    \edef\fqname{\realfqname}
-}
-
-
 \def\descwidth{0.3\textwidth}
 \def\eqwidth{0.6\textwidth}
 
-% [1]: minipage width
+\newcommand\separateEntries{
-% 2: fqname of name
-% 3: fqname of a translation that holds the explanation
-\newcommand{\NameWithExplanation}[3][\descwidth]{
-    \begin{minipage}{#1}
-        \iftranslation{#2}{
-            \raggedright
-            \gt{#2}
-        }{} 
-        \iftranslation{#3}{
-           \\ {\color{dark1} \gt{#3}}
-        }{}
-    \end{minipage}
-}
-
-% [1]: minipage width
-% 2: content
-% 3: fqname of a translation that holds the explanation
-\newcommand{\ContentBoxWithExplanation}[3][\eqwidth]{
-    \fbox{
-    \begin{minipage}{#1}
-        % \vspace{-\baselineskip}  % remove the space that comes from starting a new paragraph
-        #2
-        \noindent\iftranslation{#3}{
-            \begingroup
-                \color{dark1} 
-                \gt{#3}
-                % \edef\temp{\GT{#1_defs}}
-                % \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
-            \endgroup
-        }{}
-        % \vspace{-\baselineskip}  % remove the space that comes from starting a new paragraph
-    \end{minipage}
-    }
-
-}
-
-% 1: fqname, optional with #1_defs and #1_desc defined
-% 2: content
-\newcommand{\NameLeftContentRight}[2]{
-    \par\noindent\ignorespaces
-    % \textcolor{gray}{\hrule}
     \vspace{0.5\baselineskip}
-    \NameWithExplanation[\descwidth]{#1}{#1_desc}
+    \textcolor{fg3}{\hrule}
-    \hfill
-    \ContentBoxWithExplanation[\eqwidth]{#2}{#1_defs}
-    \textcolor{dark3}{\hrule}
     \vspace{0.5\baselineskip}
-    % \par
-    % \hrule
-}
-
-\newcommand{\insertEquation}[2]{
-    \NameLeftContentRight{#1}{
-        \begin{align}
-            \label{eq:\fqname:#1}
-            #2
-        \end{align}
-    }
-}
-
-\newcommand{\insertFLAlign}[2]{  % eq name, #cols, eq
-    \NameLeftContentRight{#1}{%
-        \begin{flalign}%
-            % dont place label when one is provided
-            % \IfSubStringInString{label}\unexpanded{#3}{}{
-            %     \label{eq:#1}
-            % }
-            #2%
-        \end{flalign}
-    }
-}
-
-\newcommand{\insertAlignedAt}[3]{  % eq name, #cols, eq
-    \NameLeftContentRight{#1}{%
-        \begin{alignat}{#2}%
-            % dont place label when one is provided
-            % \IfSubStringInString{label}\unexpanded{#3}{}{
-            %     \label{eq:#1}
-            % }
-            #3%
-        \end{alignat}
-    }
-}
-
-\newcommand\luaexpr[1]{\directlua{tex.sprint(#1)}}
-% 1: fqname
-% 2: file path
-% 3: equation
-\newcommand{\insertEquationWithFigure}[4][0.55]{
-    \par\noindent\ignorespaces
-    % \textcolor{gray}{\hrule}
-    \vspace{0.5\baselineskip}
-    \begin{minipage}{#1\textwidth}
-        \NameWithExplanation[\textwidth]{#2}{#2_desc}
-        % TODO: why is this ignored
-        \vspace{1.0cm}
-        % TODO: fix box is too large without 0.9
-        \ContentBoxWithExplanation[0.90\textwidth]{
-            \begin{align}
-                \label{eq:\fqname:#2}
-                #4
-            \end{align}
-        }{#2_defs}
-    \end{minipage}
-    \hfill
-    \begin{minipage}{\luaexpr{1.0-#1}\textwidth}
-        \begin{figure}[H]
-            \centering
-            \includegraphics[width=\textwidth]{#3}
-            \label{fig:\fqname:#2}
-        \end{figure}
-    \end{minipage}
-    \textcolor{dark3}{\hrule}
-    \vspace{0.5\baselineskip}
-
-}
-
-\newenvironment{formula}[1]{
-    % key
-    \newcommand{\desc}[4][english]{
-        % language, name, description, definitions
-        \dt[#1]{##1}{##2}
-        \ifblank{##3}{}{\dt[#1_desc]{##1}{##3}}
-        \ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
-    }
-    \newcommand{\eq}[1]{
-        \insertEquation{#1}{##1}
-    }
-    \newcommand{\eqAlignedAt}[2]{
-        \insertAlignedAt{#1}{##1}{##2}
-    }
-    \newcommand{\eqFLAlign}[1]{
-        \insertFLAlign{#1}{##1}
-    }
-    \newcommand{\figeq}[2]{
-        \insertEquationWithFigure{#1}{##1}{##2}
-    }
-    \newcommand{\content}[1]{
-        \NameLeftContentRight{#1}{##1}
-    }
-}{\ignorespacesafterend}
-
-
-\newenvironment{quantity}[5]{
-    % key, symbol, si unit, si base units, comment (key to translation)
-    \newcommand{\desc}[3][english]{
-        % language, name, description
-        \DT[qty:#1]{}{##1}{##2}
-        \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
-    }
-    \newcommand{\eq}[1]{
-        \insertEquation{#1}{##1}
-    }
-    \newcommand{\eqAlignedAt}[2]{
-        \insertAlignedAt{#1}{##1}{##2}
-    }
-    \newcommand{\eqFLAlign}[1]{
-        \insertFLAlign{#1}{##1}
-    }
-
-    \edef\qtyname{#1}
-    \edef\qtysign{#2}
-    \edef\qtyunit{#3}
-    \edef\qtybaseunits{#4}
-    \edef\qtycomment{#5}
-}
-{
-    Quantity: \expandafter\GT\expandafter{qty:\qtyname}: \GT{qty:\qtyname_desc} \\
-    $\qtysign$ $[\SI{\qtyunit}] = [\SI{\qtybaseunits}]$ - \qtycomment \\
-    \ignorespacesafterend
 }
 
 
 
+% Custon environment with table of contents, requires etoolbox?
+% Define a custom list
+\newcommand{\listofmyenv}{%
+    \section*{List of My Environments}%
+    \addcontentsline{toc}{section}{List of My Environments}%
+    \par\noindent\hrule\par\vspace{0.5\baselineskip}\@starttoc{myenv}%
+}
+\newcommand{\addmyenv}[1]{\addcontentsline{myenv}{subsection}{\protect\numberline{\themyenv}#1}}
+% Define the custom environment
+\newcounter{myenv}
+\newenvironment{myenv}[1]{%
+  \refstepcounter{myenv}%
+  \addmyenv{#1}%
+  \noindent\textbf{My Environment \themyenv: #1}\par%
+}{\par\vspace{0.5\baselineskip}}
+
+
+
+
+%
+% DISTRIBUTION
+%
 \def\distrightwidth{0.45\textwidth}
 \def\distleftwidth{0.45\textwidth}
 
@@ -202,11 +43,12 @@
         % add links to some names
         \directlua{
             local cases = {
-                pdf         = "eq:pt:distributions:pdf",
+                pdf         = "f:math:pt:pdf",
-                pmf         = "eq:pt:distributions:pdf",
+                pmf         = "f:math:pt:pmf",
-                cdf         = "eq:pt:distributions:cdf",
+                cdf         = "f:math:pt:cdf",
-                mean        = "eq:pt:mean",
+                mean        = "f:math:pt:mean",
-                variance    = "eq:pt:variance"
+                variance    = "f:math:pt:variance",
+                median      = "f:math:pt:median",
             }
             if cases["\luaescapestring{##1}"] \string~= nil then
                 tex.sprint("\\hyperref["..cases["\luaescapestring{##1}"].."]{\\GT{##1}}")
@@ -239,22 +81,34 @@
     \edef\tmpMinipagetableWidth{#1}
     \edef\tmpMinipagetableName{#2}
     \directlua{
+        table_name = "\luaescapestring{#2}"
         entries = {}
     }
 
+    % Normal entry
+    % 1: field name (translation key)
+    % 2: entry text
+    \newcommand{\entry}[2]{
+        \directlua{
+            table.insert(entries, {key = "\luaescapestring{##1}", value = [[\detokenize{##2}]]})
+        }
+    }
+    % Translation entry
     % 1: field name (translation key)
     % 2: translation define statements (field content)
-    \newcommand{\entry}[2]{
+    \newcommand{\tentry}[2]{
         % temporarily set fqname so that the translation commands dont need an explicit key
         \edef\fqname{\tmpFqname:#2:##1}
         ##2
         \edef\fqname{\tmpFqname}
         \directlua{
-            table.insert(entries, "\luaescapestring{##1}")
+            table.insert(entries, {key = "\luaescapestring{##1}", value = "\\gt{" .. table_name .. ":\luaescapestring{##1}}"})
         }
     }
 }{
     % \hfill
+    % reset the fqname
+    \edef\fqname{\tmpFqname}
     \begin{minipage}{\tmpMinipagetableWidth}
         \begingroup
             \setlength{\tabcolsep}{0.9em}  % horizontal
@@ -262,13 +116,12 @@
             \begin{tabularx}{\textwidth}{|l|X|}
             \hline
             \directlua{
-                for _, k in ipairs(entries) do
+                for _, kv in ipairs(entries) do
-                    tex.print("\\GT{" .. k .. "} & \\gt{\tmpMinipagetableName:" .. k .. "}\\\\")
+                    tex.print("\\GT{" .. kv.key .. "} & " .. kv.value .. "\\\\")
                 end
             }
             \hline
             \end{tabularx}
         \endgroup
     \end{minipage}
-    % reset the fqname
 }

src/util/fqname.tex

@@ -0,0 +1,180 @@
+% Everything related to referencing stuff
+
+\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
+
+% SECTIONING
+% start <section>, get heading from translation, set label
+% secFqname is the fully qualified name of sections: the keys of all previous sections joined with a ':'
+% fqname is secFqname:<key> where <key> is the key/id of some environment, like formula
+% [1]: code to run after setting \fqname, but before the \part, \section etc
+% 2: key
+\newcommand{\Part}[2][desc]{
+    \newpage
+    \def\partName{#2}
+    \def\sectionName{}
+    \def\subsectionName{}
+    \def\subsubsectionName{}
+    \edef\fqname{\partName}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \part{\fqnameText} 
+    \label{sec:\fqname}
+}
+\newcommand{\Section}[2][]{
+    \def\sectionName{#2}
+    \def\subsectionName{}
+    \def\subsubsectionName{}
+    \edef\fqname{\partName:\sectionName}
+    \edef\secFqname{\fqname}
+    #1
+    % this is necessary so that \section takes the fully expanded string. Otherwise the pdf toc will have just the fqname
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \section{\fqnameText}
+    \label{sec:\fqname}
+}
+% \newcommand{\Subsection}[1]{\Subsection{#1}{}}
+\newcommand{\Subsection}[2][]{
+    \def\subsectionName{#2}
+    \def\subsubsectionName{}
+    \edef\fqname{\partName:\sectionName:\subsectionName}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \subsection{\fqnameText}
+    \label{sec:\fqname}
+}
+\newcommand{\Subsubsection}[2][]{
+    \def\subsubsectionName{#2}
+    \edef\fqname{\partName:\sectionName:\subsectionName:\subsubsectionName}
+    \edef\secFqname{\fqname}
+    #1
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \subsubsection{\fqnameText}
+    \label{sec:\fqname}
+}
+\edef\fqname{NULL}
+
+\newcommand\luaDoubleFieldValue[3]{%
+    \directlua{
+        if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
+            tex.sprint(#1[#2][#3])
+            return
+        end
+        luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
+        tex.sprint("???")
+    }%
+}
+% REFERENCES
+% All xyzRef commands link to the key using the translated name
+% Uppercase (XyzRef) commands have different link texts, but the same link target
+% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
+
+% Equations/Formulas
+% \newrobustcmd{\fqEqRef}[1]{%
+\newrobustcmd{\fqEqRef}[1]{%
+    % \edef\fqeqrefname{\GT{#1}}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[f:#1]{\GT{#1}}%
+}
+% Formula in the current section
+\newrobustcmd{\secEqRef}[1]{%
+    % \edef\fqeqrefname{\GT{#1}}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[f:\secFqname:#1]{\GT{\secFqname:#1}}%
+}
+
+% Section
+% <name>
+\newrobustcmd{\fqSecRef}[1]{%
+    \hyperref[sec:#1]{\GT{#1}}%
+}
+% Quantities
+% <symbol>
+\newrobustcmd{\qtyRef}[1]{%
+    \edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"fqname"}}%
+    \hyperref[qty:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\QtyRef}[1]{%
+    $\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
+}
+% Constants
+% <name>
+\newrobustcmd{\constRef}[1]{%
+    \edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"fqname"}}%
+    \hyperref[const:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\ConstRef}[1]{%
+    $\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
+}
+% Element from periodic table
+% <symbol>
+\newrobustcmd{\elRef}[1]{%
+    \hyperref[el:#1]{{\color{fg0}#1}}%
+}
+% <name>
+\newrobustcmd{\ElRef}[1]{%
+    \hyperref[el:#1]{\GT{el:#1}}%
+}
+
+
+
+% "LABELS"
+% These currently do not place a label,
+% instead they provide an alternative way to reference an existing label
+\directLuaAux{
+    if absLabels == nil then
+        absLabels = {}
+    end
+}
+% [1]: target (fqname to point to)
+% 2: key
+\newcommand{\absLink}[2][sec:\fqname]{
+    \directLuaAuxExpand{
+        absLabels["#2"] = [[#1]] 
+    } 
+}
+\directLuaAux{
+    if abbrLabels == nil then
+        abbrLabels = {}
+    end
+}
+% [1]: target (fqname to point to)
+% 2: key
+% 3: label (abbreviation)
+\newcommand{\abbrLink}[3][sec:\fqname]{
+    \directLuaAuxExpand{
+        abbrLabels["#2"] = {}
+        abbrLabels["#2"]["abbr"] = [[#3]] 
+        abbrLabels["#2"]["fqname"] = [[#1]] 
+    } 
+}
+% [1]: 
+\newrobustcmd{\absRef}[2][\relax]{%
+    \directlua{
+        if absLabels["#2"] == nil then
+            tex.sprint("\\detokenize{#2}???")
+        else
+            if "#1" == "" then  %-- if [#1]  is not given, use translation of key as text, else us given text
+                tex.sprint("\\hyperref[" .. absLabels["#2"] .. "]{\\GT{" .. absLabels["#2"] .. "}}")
+            else
+                tex.sprint("\\hyperref[" .. absLabels["#2"] .. "]{\luaescapestring{#1}}")
+            end
+        end
+    }
+}
+\newrobustcmd{\abbrRef}[1]{%
+    \directlua{
+        if abbrLabels["#1"] == nil then
+            tex.sprint("\\detokenize{#1}???")
+        else
+            tex.sprint("\\hyperref[" .. abbrLabels["#1"]["fqname"] .. "]{" .. abbrLabels["#1"]["abbr"] .. "}")
+        end
+    }
+}
+
+
+
+

src/util/macros.tex

@@ -1,50 +1,198 @@
-\def\gooditem{\item[{$\color{neutral_red}\bullet$}]}
+% use \newcommand instead of \def because we want to throw an error if a command gets redefined
-\def\baditem{\item[{$\color{neutral_green}\bullet$}]}
+\newcommand\smartnewline[1]{\ifhmode\\\fi}  % newline only if there in horizontal mode
+\newcommand\gooditem{\item[{$\color{fg-green}\bullet$}]}
+\newcommand\baditem{\item[{$\color{fg-red}\bullet$}]}
 
-\def\Grad{\vec{\nabla}}
+% Functions with (optional) paranthesis
-\def\Div{\vec{\nabla} \cdot}
+% 1: The function (like \exp, \sin etc.)
-\def\Rot{\vec{\nabla} \times}
+% 2: The argument (optional)
-\def\vecr{\vec{r}}
+% If an argument is provided, it is wrapped in paranthesis.
+\newcommand\CmdWithParenthesis[2]{
+    \ifstrequal{#2}{\relax}{
+        #1
+    }{
+        #1\left(#2\right)
+    }
+}
+\newcommand\CmdInParenthesis[2]{
+    \ifstrequal{#2}{\relax}{
+        #1
+    }{
+        \left(#1 #2\right)
+    }
+}
 
-\def\kB{k_\text{B}}
-\def\EFermi{E_\text{F}}
 
-\def\masse{m_\textrm{e}}
+% COMMON SYMBOLS WITH SUPER/SUBSCRIPTS, VECTOR ARROWS ETC.
+% \def\laplace{\Delta} % Laplace operator
+\newcommand\laplace{\bigtriangleup} % Laplace operator
+% symbols
+\newcommand\Grad{\vec{\nabla}}       
+\newcommand\Div {\vec{\nabla} \cdot} 
+\newcommand\Rot {\vec{\nabla} \times}
+% symbols with parens
+\newcommand\GradS[1][\relax]{\CmdInParenthesis{\Grad}{#1}}
+\newcommand\DivS [1][\relax]{\CmdInParenthesis{\Div} {#1}}
+\newcommand\RotS [1][\relax]{\CmdInParenthesis{\Rot} {#1}}
+% text with parens
+\newcommand\GradT[1][\relax]{\CmdWithParenthesis{\text{grad}\,}{#1}}
+\newcommand\DivT[1][\relax] {\CmdWithParenthesis{\text{div}\,} {#1}}
+\newcommand\RotT[1][\relax] {\CmdWithParenthesis{\text{rot}\,} {#1}}
+\newcommand\kB{k_\text{B}}         % boltzmann
+\newcommand\NA{N_\text{A}}         % avogadro
+\newcommand\EFermi{E_\text{F}}     % fermi energy
+\newcommand\Efermi{E_\text{F}}     % fermi energy
+\newcommand\Evalence{E_\text{v}}   % val vand energy
+\newcommand\Econd{E_\text{c}}      % cond. band nergy
+\newcommand\Egap{E_\text{gap}}     % band gap energy
+\newcommand\Evac{E_\text{vac}}     % vacuum energy
+\newcommand\masse{m_\text{e}}      % electron mass
+\newcommand\Four{\mathcal{F}}      % Fourier transform
+\newcommand\Lebesgue{\mathcal{L}}  % Lebesgue
+% \newcommand\O{\mathcal{O}}         % order
+\newcommand\PhiB{\Phi_\text{B}}    % mag. flux
+\newcommand\PhiE{\Phi_\text{E}}    % electric flux
+\newcommand\nreal{n^{\prime}}            % refraction real part
+\newcommand\ncomplex{n^{\prime\prime}}        % refraction index complex part
+\newcommand\I{i}                   % complex/imaginary unit
+\newcommand\crit{\text{crit}}      % crit (for subscripts)
+\newcommand\muecp{\overline{\mu}}  % electrochemical potential
+% \newcommand\pH{\text{pH}}          % pH, already defined by one of the chem packages
+\newcommand\rfactor{\text{rf}}     % rf roughness_factor
 
-\def\R{\mathbb{R}}
-\def\C{\mathbb{C}}
-\def\Z{\mathbb{Z}}
-\def\N{\mathbb{N}}
 
-\def\Four{\mathcal{F}}  % Fourier transform
+% SYMBOLS
-\def\Lebesgue{\mathcal{L}}  % Lebesgue
+\newcommand\R{\mathbb{R}}
-\def\Order{\mathcal{O}} 
+\newcommand\C{\mathbb{C}}
+\newcommand\Z{\mathbb{Z}}
+\newcommand\N{\mathbb{N}}
+\newcommand\id{\mathbb{1}}
+% caligraphic
+\newcommand\E{\mathcal{E}}  % electric field
+% upright, vector
+\newcommand\txA{\text{A}}  \newcommand\vecA{\vec{A}}  
+\newcommand\txB{\text{B}}  \newcommand\vecB{\vec{B}}
+\newcommand\txC{\text{C}}  \newcommand\vecC{\vec{C}}
+\newcommand\txD{\text{D}}  \newcommand\vecD{\vec{D}}
+\newcommand\txE{\text{E}}  \newcommand\vecE{\vec{E}}
+\newcommand\txF{\text{F}}  \newcommand\vecF{\vec{F}}
+\newcommand\txG{\text{G}}  \newcommand\vecG{\vec{G}}
+\newcommand\txH{\text{H}}  \newcommand\vecH{\vec{H}}
+\newcommand\txI{\text{I}}  \newcommand\vecI{\vec{I}}
+\newcommand\txJ{\text{J}}  \newcommand\vecJ{\vec{J}}
+\newcommand\txK{\text{K}}  \newcommand\vecK{\vec{K}}
+\newcommand\txL{\text{L}}  \newcommand\vecL{\vec{L}}
+\newcommand\txM{\text{M}}  \newcommand\vecM{\vec{M}}
+\newcommand\txN{\text{N}}  \newcommand\vecN{\vec{N}}
+\newcommand\txO{\text{O}}  \newcommand\vecO{\vec{O}}
+\newcommand\txP{\text{P}}  \newcommand\vecP{\vec{P}}
+\newcommand\txQ{\text{Q}}  \newcommand\vecQ{\vec{Q}}
+\newcommand\txR{\text{R}}  \newcommand\vecR{\vec{R}}
+\newcommand\txS{\text{S}}  \newcommand\vecS{\vec{S}}
+\newcommand\txT{\text{T}}  \newcommand\vecT{\vec{T}}
+\newcommand\txU{\text{U}}  \newcommand\vecU{\vec{U}}
+\newcommand\txV{\text{V}}  \newcommand\vecV{\vec{V}}
+\newcommand\txW{\text{W}}  \newcommand\vecW{\vec{W}}
+\newcommand\txX{\text{X}}  \newcommand\vecX{\vec{X}}
+\newcommand\txY{\text{Y}}  \newcommand\vecY{\vec{Y}}
+\newcommand\txZ{\text{Z}}  \newcommand\vecZ{\vec{Z}}
+                           
+\newcommand\txa{\text{a}}  \newcommand\veca{\vec{a}}
+\newcommand\txb{\text{b}}  \newcommand\vecb{\vec{b}}
+\newcommand\txc{\text{c}}  \newcommand\vecc{\vec{c}}
+\newcommand\txd{\text{d}}  \newcommand\vecd{\vec{d}}
+\newcommand\txe{\text{e}}  \newcommand\vece{\vec{e}}
+\newcommand\txf{\text{f}}  \newcommand\vecf{\vec{f}}
+\newcommand\txg{\text{g}}  \newcommand\vecg{\vec{g}}
+\newcommand\txh{\text{h}}  \newcommand\vech{\vec{h}}
+\newcommand\txi{\text{i}}  \newcommand\veci{\vec{i}}
+\newcommand\txj{\text{j}}  \newcommand\vecj{\vec{j}}
+\newcommand\txk{\text{k}}  \newcommand\veck{\vec{k}}
+\newcommand\txl{\text{l}}  \newcommand\vecl{\vec{l}}
+\newcommand\txm{\text{m}}  \newcommand\vecm{\vec{m}}
+\newcommand\txn{\text{n}}  \newcommand\vecn{\vec{n}}
+\newcommand\txo{\text{o}}  \newcommand\veco{\vec{o}}
+\newcommand\txp{\text{p}}  \newcommand\vecp{\vec{p}}
+\newcommand\txq{\text{q}}  \newcommand\vecq{\vec{q}}
+\newcommand\txr{\text{r}}  \newcommand\vecr{\vec{r}}
+\newcommand\txs{\text{s}}  \newcommand\vecs{\vec{s}}
+\newcommand\txt{\text{t}}  \newcommand\vect{\vec{t}}
+\newcommand\txu{\text{u}}  \newcommand\vecu{\vec{u}}
+\newcommand\txv{\text{v}}  \newcommand\vecv{\vec{v}}
+\newcommand\txw{\text{w}}  \newcommand\vecw{\vec{w}}
+\newcommand\txx{\text{x}}  \newcommand\vecx{\vec{x}}
+\newcommand\txy{\text{y}}  \newcommand\vecy{\vec{y}}
+\newcommand\txz{\text{z}}  \newcommand\vecz{\vec{z}}
 
-% complex, may be changed later to idot or upright...
+% SPACES
-\def\I{i}
+\newcommand\sdots{\,\dots\,}
+\newcommand\qdots{\quad\dots\quad}
+\newcommand\qRarrow{\quad\Rightarrow\quad}
 
-\def\sdots{\,\dots\,}
+% ANNOTATIONS
-\def\qdots{\quad\dots\quad}
+% put an explanation above an equal sign
-\def\qRarrow{\quad\Rightarrow\quad}
+% [1]: equality sign (or anything else)
+% 2: text (not in math mode!)
+\newcommand{\explUnderEq}[2][=]{%
+    \underset{\substack{\uparrow\\\mathrlap{\text{\hspace{-1em}#2}}}}{#1}}
+\newcommand{\explOverEq}[2][=]{%
+    \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}}
+\newcommand{\eqnote}[1]{
+    \text{\color{fg2}#1}
+}
 
-\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
-\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
-\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
 
+% DELIMITERS
+% not using DeclarePairedDelmiter to always get scaling
+\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
+\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
+\newcommand{\ceil}[1]{\left\lceil#1\right\rceil}
+
+% OPERATORS
+% * places subset under the word instead of next to it
 \DeclareMathOperator{\e}{e}
-\DeclareMathOperator{\T}{T}  % transposed
+\def\T{\text{T}}  % transposed
 \DeclareMathOperator{\sgn}{sgn}
 \DeclareMathOperator{\tr}{tr}
 \DeclareMathOperator{\const}{const}
 \DeclareMathOperator{\erf}{erf}
+\DeclareMathOperator{\erfc}{erfc}
+\DeclareMathOperator{\cov}{cov}
+
+\DeclareMathOperator*{\argmin}{arg\,min}
+\DeclareMathOperator*{\argmax}{arg\,max}
+% \DeclareMathOperator{\div}{div}
+% \DeclareMathOperator{\grad}{grad}
+% \DeclareMathOperator{\rot}{rot}
+% \DeclareMathOperator{\arcsin}{arcsin}
+% \DeclareMathOperator{\arccos}{arccos}
+% \DeclareMathOperator{\arctan}{arctan}
+\DeclareMathOperator{\arccot}{arccot}
+\DeclareMathOperator{\arsinh}{arsinh}
+\DeclareMathOperator{\arcosh}{arcosh}
+\DeclareMathOperator{\artanh}{artanh}
+\DeclareMathOperator{\arcoth}{arcoth}
 % diff, for integrals and stuff
 % \DeclareMathOperator{\dd}{d}
 \renewcommand*\d{\mathop{}\!\mathrm{d}}
-
+% times 10^{x}
-% functions with paranthesis
+\newcommand\xE[1]{\cdot 10^{#1}}
-\newcommand\CmdWithParenthesis[2]{
-    #1\left(#2\right)
-}
 \newcommand\Exp[1]{\CmdWithParenthesis{\exp}{#1}}
 \newcommand\Sin[1]{\CmdWithParenthesis{\sin}{#1}}
 \newcommand\Cos[1]{\CmdWithParenthesis{\cos}{#1}}
+\newcommand\Ln[1]{\CmdWithParenthesis{\ln}{#1}}
+\newcommand\Log[1]{\CmdWithParenthesis{\log}{#1}}
+\newcommand\Order[1]{\CmdWithParenthesis{\mathcal{O}}{#1}}
+
+% VECTOR, MATRIX and TENSOR
+% use vecAr to force an arrow
+\NewCommandCopy{\vecAr}{\vec}
+% extra {} assure they can b directly used after _
+%% arrow/underline
+\newcommand\mat[1]{{\ensuremath{\underline{#1}}}}
+\renewcommand\vec[1]{{\ensuremath{\vecAr{#1}}}}
+\newcommand\ten[1]{{\ensuremath{[#1]}}}
+\newcommand\complex[1]{{\ensuremath{\tilde{#1}}}}
+%% bold
+% \newcommand\mat[1]{{\ensuremath{\bm{#1}}}}
+% \renewcommand\vec[1]{{\ensuremath{\bm{#1}}}}

src/util/tikz_macros.tex

@@ -0,0 +1,114 @@
+
+\tikzset{
+  % bands
+  sc band con/.style={   draw=fg0, thick},
+  sc band val/.style={   draw=fg0, thick},
+  sc band vac/.style={   draw=fg1, thick},
+  sc band/.style={       draw=fg0, thick},
+  sc fermi level/.style={draw=fg-aqua,dashed,thick},
+  % electron filled
+  sc occupied/.style={
+    pattern=north east lines,
+    pattern color=fg-aqua,
+    draw=none
+  },
+  % materials
+  sc p type/.style={     draw=none,fill=bg-yellow!20},
+  sc n type/.style={     draw=none,fill=bg-blue!20},
+  sc metal/.style={      draw=none,fill=bg-purple!20},
+  sc oxide/.style={      draw=none,fill=bg-green!20},
+  sc separate/.style={   draw=fg0,dotted},
+}
+
+\newcommand\drawDArrow[4]{
+    \draw[<->] (#1,#2) -- (#1,#3) node[midway,right] () {#4};
+}
+% Band bending down at L-R interface: BendH must be negative
+% need two functions for different out= angles, or use if else on the sign of BendH
+\newcommand\leftBandAuto[2]{
+  \directlua{
+    if \tkLBendH == 0 then
+      tex.print([[(\tkLx,#2) \ifblank{#1}{}{node[anchor=east] \detokenize{{#1}}} -- (\tkLW,#2) ]])
+    else
+      if \tkLBendH > 0 then
+        angle = 180+45
+      else
+        angle = 180-45
+      end
+      tex.sprint([[(\tkLx,#2) \ifblank{#1}{}{node[anchor=east] \detokenize{{#1}}}
+        -- (\tkLW-\tkLBendW,#2) to[out=0,in=]], angle, [[](\tkLW,#2+\tkLBendH)]])
+    end
+  }
+  % % \ifthenelse{\equal{\tkLBendH}{0}}%
+  %   % {%
+  %     \ifthenelse{\tkLBendH > 0}%
+  %     {\pgfmathsetmacro{\angle}{-45}}%
+  %     {\pgfmathsetmacro{\angle}{45}}%
+  %   % }
+}
+\newcommand\rightBandAuto[2]{
+  \directlua{
+    if \tkRBendH == 0 then
+      %-- tex.print([[\rightBand{#1}{#2}]])
+    tex.print([[(\tkRx,#2) -- (\tkW,#2)]]) %-- \ifblank{#1}{}{node[anchor=west] \{#1\}}]])
+    else
+      if \tkRBendH > 0 then
+        angle = -45
+      else
+        angle = 45
+      end
+      tex.sprint([[(\tkRx,#2+\tkRBendH) to[out=]], angle, [[,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2) ]])
+        %-- \ifblank{#1}{}{node[anchor=west] \{#1\}} ]])
+    end
+    if "\luaescapestring{#1}" \string~= "" then
+      tex.print([[node[anchor=west] \detokenize{{#1}} ]])
+    end
+  }
+  % \ifthenelse{\equal{\tkRBendH}{0}}%
+  %   {\rightBand{#1}{#2}}
+  %   {%
+  %     \ifthenelse{\tkRBendH > 0}%
+  %     {\pgfmathsetmacro{\angle}{-45}}%
+  %     {\pgfmathsetmacro{\angle}{45}}%
+  %     (\tkRx,#2+\tkRBendH) to[out=45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2) 
+  %     \ifblank{#1}{}{node[anchor=west]{#1}} 
+  %   }
+}
+\newcommand\leftBandDown[2]{
+    (\tkRx,#2+\tkRBendH) to[out=45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2) 
+    \ifblank{#1}{}{node[anchor=west]{#1}} 
+}
+\newcommand\rightBandDown[2]{
+    (\tkRx,#2+\tkRBendH) to[out=45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2) 
+    \ifblank{#1}{}{node[anchor=west]{#1}} 
+}
+% Band bending down at L-R interface: BendH must be positive
+\newcommand\leftBandUp[2]{
+    (\tkLx,#2) \ifblank{#1}{}{node[anchor=east]{#1}} 
+    -- (\tkLW-\tkLBendW,#2) to[out=0,in=180+45] (\tkLW,#2+\tkLBendH) 
+}
+\newcommand\rightBandUp[2]{
+    (\tkRx,#2+\tkRBendH) to[out=-45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2) 
+    \ifblank{#1}{}{node[anchor=west]{#1}} 
+}
+% Straight band
+\newcommand\leftBand[2]{
+    (\tkLx,#2) \ifblank{#1}{}{node[anchor=east]{#1}} -- (\tkLW,#2) 
+}
+\newcommand\rightBand[2]{
+    (\tkRx,#2) -- (\tkW,#2) \ifblank{#1}{}{node[anchor=west]{#1}} 
+}
+
+\newcommand\drawAxes{
+  \draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
+  \draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east] {$E$};
+}
+
+\newcommand\tkXTick[2]{
+  \pgfmathsetmacro{\tickwidth}{0.1}
+  \draw (#1, -\tickwidth/2) -- (#1, \tickwidth/2) node[anchor=north] {#2};
+}
+\newcommand\tkYTick[2]{
+  \pgfmathsetmacro{\tickwidth}{0.1}
+  \draw (-\tickwidth/2, #1) -- (\tickwidth/2,#1) node[anchor=east] {#2};
+}

src/util/translation.tex

@@ -1,66 +0,0 @@
-%
-% TRANSLATION COMMANDS
-%
-% The lower case commands use \fqname based keys, the upper case absolute keys.
-% Example:
-%   \dt[example]{german}{Beispiel}  % defines the key \fqname:example
-%   \ger[example]{Beispiel}         % defines the key \fqname:example
-%   \DT[example]{german}{Beispiel}  % defines the key example
-%   \Ger[example]{Beispiel}         % defines the key example
-%
-% For ease of use in the ttext environment and the optional argument of the \Part, \Section, ... commands,
-% all "define translation" commands use \fqname as default key
-
-% Get a translation
-% expandafter required because the translation commands dont expand anything
-% shortcuts for translations
-% 1: key
-\newcommand{\gt}[1]{\expandafter\GetTranslation\expandafter{\fqname:#1}}
-\newcommand{\GT}[1]{\expandafter\GetTranslation\expandafter{#1}}
-
-\newcommand{\IfTranslationExists}{
-    % \IfTranslation{\languagename}
-    \IfTranslation{english}  % only check english. All translations must be defined for english
-}
-\newcommand{\iftranslation}[1]{\expandafter\IfTranslationExists\expandafter{\fqname:#1}}
-
-% Define a translation and also make the fallback if it is the english translation
-% 1: lang, 2: key, 3: translation
-\newcommand{\addtranslationcustom}[3]{
-    \ifstrequal{#1}{english}{
-            \addtranslationfallback{#2}{#3}
-        }{}
-    \addtranslation{#1}{#2}{#3}
-}
-
-% Define a new translation
-% [1]: key, 2: lang, 3: translation
-\newcommand{\dt}[3][\fqname]{
-    \ifstrempty{#3}{}{ % dont add empty translations so that the fallback will be used instead
-        % hack because using expandafter on the second arg didnt work
-        \def\tempaddtranslation{\addtranslationcustom{#2}}
-        \ifstrequal{#1}{\fqname}{
-            \expandafter\tempaddtranslation\expandafter{\fqname}{#3}
-        }{
-            \expandafter\tempaddtranslation\expandafter{\fqname:#1}{#3}
-        }
-    }
-}
-\newcommand{\DT}[3][\fqname]{
-    \ifstrempty{#3}{}{ % dont add empty translations so that the fallback will be used instead
-        % hack because using expandafter on the second arg didnt work
-        \def\tempaddtranslation{\addtranslationcustom{#2}}
-        \ifstrequal{#1}{\fqname}{
-            \expandafter\tempaddtranslation\expandafter{\fqname}{#3}
-        }{
-            \expandafter\tempaddtranslation\expandafter{#1}{#3}
-        }
-    }
-}
-% [1]: key, 2: translation
-\newcommand{\ger}[2][\fqname]{\dt[#1]{german}{#2}}
-\newcommand{\eng}[2][\fqname]{\dt[#1]{english}{#2}}
-
-\newcommand{\Ger}[2][\fqname]{\DT[#1]{german}{#2}}
-\newcommand{\Eng}[2][\fqname]{\DT[#1]{english}{#2}}
-

src/util/translations.tex

@@ -1,27 +1,78 @@
+% WORDS
+\Eng[even]{even}
+\Ger[even]{gerade}
+
+\Eng[odd]{odd}
+\Ger[odd]{ungerade}
+
+% SCIENTIFIC
 \Eng[angle_deg]{Degree}
 \Ger[angle_deg]{Grad}
 
 \Eng[angle_rad]{Radian}
 \Ger[angle_rad]{Rad}
 
-\Eng[see_also]{See also}
-\Ger[see_also]{Siehe auch}
-
-\Eng[and_therefore]{and therefore}
-\Ger[and_therefore]{und damit}
-
-\Eng[and_therefore_also]{and therefore also}
-\Ger[and_therefore_also]{und damit auch}
-
 \Eng[time]{Time}
 \Ger[time]{Zeit}
 
 \Eng[ensemble]{Ensemble}
 \Ger[ensemble]{Ensemble}
 
-\Eng[even]{even}
+\Eng[area]{area}
-\Ger[even]{gerade}
+\Ger[area]{Fläche}
+
+% SPECIFIC
+\Eng[diamond]{Diamond}
+\Ger[diamond]{Diamant}
+
+\Eng[metal]{Metal}
+\Ger[metal]{Metall}
+
+\Eng[semiconductor]{Semiconductor}
+\Ger[semiconductor]{Halbleiter}
+
+
+\Eng[creation_annihilation_ops]{Creation / Annihilation operators}
+\Ger[creation_annihilation_ops]{Erzeugungs / Vernichtungs-Operatoren}
+
+% FORMATING
+\Eng[list_of_quantitites]{List of quantitites}
+\Ger[list_of_quantitites]{Liste von Größen}
+
+\Eng[other]{Others}
+\Ger[other]{Sonstige}
+
+\Eng[sometimes]{sometimes}
+\Ger[sometimes]{manchmal}
+
+\Eng[see_also]{See also}
+\Ger[see_also]{Siehe auch}
+
+\Eng[for]{for}
+\Ger[for]{für}
+
+\Eng[and_therefore]{and therefore}
+\Ger[and_therefore]{und damit}
+
+\Eng[and_therefore_also]{and therefore also}
+\Ger[and_therefore_also]{und damit auch}
+
+\Eng[const:exp]{Experimental value}
+\Ger[const:exp]{Experimenteller Wert}
+\Eng[const:def]{Defined value}
+\Ger[const:def]{Definierter Wert}
+
+% PERIODIC TABLE
+\Eng[symbol]{Symbol}
+\Ger[symbol]{Symbol}
+
+\Eng[atomic_number]{Number}
+\Ger[atomic_number]{Ordnungszahl}
+
+\Eng[electron_config]{Electronic configuration}
+\Ger[electron_config]{Elektronenkonfiguration}
+
+\Eng[crystal_structure]{Crystal structure}
+\Ger[crystal_structure]{Kristallstruktur}
 
-\Eng[odd]{odd}
-\Ger[odd]{ungerade}