add periodic table

Makefile

@@ -0,0 +1,37 @@
+# Makefile for lualatex
+
+# Paths and filenames
+SRC_DIR  = src
+OUT_DIR  = out
+MAIN_TEX = $(SRC_DIR)/main.tex
+MAIN_PDF = $(OUT_DIR)/main.pdf
+
+# LaTeX and Biber commands
+
+LATEX = lualatex
+BIBER = biber
+
+LATEX_OPTS := -output-directory=$(OUT_DIR) -interaction=nonstopmode -shell-escape
+
+.PHONY: default release clean
+
+default: english
+release: german english
+# Default target
+english: 
+	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[english]{babel}/' $(MAIN_TEX)
+	-cd $(SRC_DIR) && latexmk -g
+	mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_en_formula_collection.pdf
+
+german:
+	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[german]{babel}/' $(MAIN_TEX)
+	-cd $(SRC_DIR) && latexmk -g
+	mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_formelsammlung.pdf
+
+# Clean auxiliary and output files
+clean:
+	rm -r $(OUT_DIR)
+
+# Phony targets
+.PHONY: all clean biber
+

scripts/periodic_table.py

@@ -0,0 +1,78 @@
+"""
+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 2024
+"""
+import json
+import os
+import re
+
+outdir = "../src/ch"
+
+
+def gen_periodic_table():
+    with open("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/plot.py

@@ -4,7 +4,7 @@ import numpy as np
 import math
 import scipy as scp
 
-outdir = "../img/"
+outdir = "../src/img/"
 filetype = ".pdf"
 skipasserts = False
 

src/.latexmkrc

@@ -0,0 +1,30 @@
+# 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'
+
+# 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/atom.tex

@@ -179,3 +179,17 @@
 ]{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/ch/ch.tex

@@ -0,0 +1,29 @@
+\Part[
+    \eng{Chemie}
+    \ger{Chemie}
+]{ch}
+    \Section[
+        \eng{Periodic table}
+        \ger{Periodensystem}
+    ]{ptable}
+        \drawPeriodicTable
+
+    \Section[
+        \eng{stuff}
+        \ger{stuff}
+    ]{stuff}
+        \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}
+
+    \Section[
+        \eng{List of elements}
+        \ger{Liste der Elemente}
+    ]{elements}
+        \printAllElements
+

src/cm/charge_transport.tex

@@ -0,0 +1,85 @@
+\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}{}{}
+        \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}
+        \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{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}

src/cm/cm.tex

@@ -1,12 +1,12 @@
 \Part[
     \eng{Condensed matter physics}
     \ger{Festkörperphysik}
-    ]{cm}
+]{cm}
     \TODO{Bonds, hybridized orbitals, tight binding}
 \Section[
     \eng{Bravais lattice}
     \ger{Bravais-Gitter}
-    ]{bravais}
+]{bravais}
 
     % \begin{ttext}
     %     \eng{
@@ -37,7 +37,7 @@
     \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
     \begin{table}[H]
         \centering
-        \caption{\gt{bravais_table2}}
+        \expandafter\caption\expandafter{\gt{bravais_table2}}
         \label{tab:bravais2}
     
         \begin{adjustbox}{width=\textwidth}
@@ -85,12 +85,70 @@
         \end{tabularx}
         \end{adjustbox}
     \end{table}
-    \TODO{FCC, BCC, diamond/Zincblende wurtzize cell/lattice vectors}
-    \TODO{primitive unit cell: contains one lattice point}\\
 
-family of plane that are equivalent due to crystal symmetry
+    \begin{quantity}{lattice_constant}{a}{}{s}
+        \desc{Lattice constant}{Parameter (length or angle) describing the smallest unit cell}{}
+        \desc[german]{Gitterkonstante}{Parameter (Länge oder Winkel) der die Einheitszelle beschreibt}{}
+    \end{quantity}
+
+    \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}
+
+    \TODO{primitive unit cell: contains one lattice point}\\
     \begin{formula}{miller}
-        \desc{Miller index}{}{}
+        \desc{Miller index}{}{Miller family: planes that are equivalent due to crystal symmetry}
         \desc[german]{Millersche Indizes}{}{}
         \eq{
             (hkl) & \text{\GT{plane}}\\
@@ -201,6 +259,7 @@ family of plane that are equivalent due to crystal symmetry
             \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}
@@ -209,9 +268,56 @@ family of plane that are equivalent due to crystal symmetry
 
         \TODO{TODO}
 
+\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{\GT{misc}}
     \ger{\GT{misc}}
 ]{misc}
 
+    \begin{formula}{exciton}
+        \desc{Exciton}{}{}
+        \desc[german]{Exziton}{}{}
+        \ttxt{
+            \eng{Quasi particle, excitation in condensed matter as bound electron-hole pair.}
+            \ger{Quasiteilchen, Anregung im Festkörper als gebundenes Elektron-Loch-Paar}
+        }
+    \end{formula}

src/cm/low_temp.tex

@@ -0,0 +1,141 @@
+\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{
+
+            }
+            
+        \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}
+    
+        \Subsection[
+            \eng{BCS-Theory}
+            \ger{BCS-Theorie}
+            ]{BCS}
+    
+

src/cm/semiconductors.tex

@@ -0,0 +1,58 @@
+\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{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}
+
+
+
+
+

src/cm/techniques.tex

@@ -0,0 +1,154 @@
+\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

@@ -6,5 +6,31 @@
         \desc{Planck Constant}{}{}
         \desc[german]{Plancksches Wirkumsquantum}{}{}
         \val{6.62607015\cdot 10^{-34}}{\joule\s}
-        \val{4.135667969\dots\cdot 10^{-15}}{\eV\s}
+        \val{4.135667969\dots\xE{-15}}{\eV\s}
+    \end{constant}
+
+    \begin{constant}{universal_gas}{R}{def}
+        \desc{Universal gas constant}{Proportionality factor for ideal gases}{\ConstRef{avogadro}, \ConstRef{boltzmann}}
+        \desc[german]{Universelle Gaskonstante}{Proportionalitätskonstante für ideale Gase}{}
+        \val{8.31446261815324}{\joule\per\mol\kelvin}
+        \val{\NA \cdot \kB}{}
+    \end{constant}
+
+    \begin{constant}{avogadro}{\NA}{def}
+        \desc{Avogadro constant}{Number of molecules per mole}{}
+        \desc[german]{Avogadro-Konstante}{Anzahl der Moleküle pro mol}{}
+        \val{6.02214076 \xE{23}}{1\per\mole}
+    \end{constant}
+
+    \begin{constant}{boltzmann}{\kB}{def}
+        \desc{Boltzmann constant}{Temperature-Energy conversion factor}{}
+        \desc[german]{Boltzmann-Konstante}{Temperatur-Energie Umrechnungsfaktor}{}
+        \val{1.380649 \xE{-23}}{\joule\per\kelvin}
+    \end{constant}
+
+    \begin{constant}{faraday}{F}{def}
+        \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}{}
+        \val{9.64853321233100184}{\coulomb\per\mol}
+        \val{\NA\,e}{}
     \end{constant}

src/electrodynamics.tex

@@ -5,33 +5,9 @@
 ]{ed}
 
 
-\Section[
+% pure electronic stuff in el
-    \eng{Maxwell-Equations}
+% pure magnetic stuff in mag
-    \ger{Maxwell-Gleichungen}
+% electromagnetic stuff in em
-]{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}
-    \TODO{Polarization}
-
 
 \Section[
     \eng{Electric field}
@@ -40,47 +16,104 @@
     \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}}
+        \eq{\PhiE = \iint_S \vec{\E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}}
+    \end{formula}
+
+    \begin{quantity}{permittivity}{\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}{}
+        \desc{Permittivity}{Electric polarizability of a dielectric material}{}
+        \desc[german]{Permitivität}{Dielektrische Konstante\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{}
+    \end{quantity}
+    \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{constant}{vacuum_permittivity}{\epsilon_0}{exp}
+        \desc{Vacuum permittivity}{Electric constant}{}
+        \desc[german]{Vakuum Permittivität}{Elektrische Feldkonstante}{}
+        \val{8.8541878188(14)\E{-1}}{\ampere\s\per\volt\m}
+    \end{constant}
+
+    \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}{}
+        \eq{
+            \epsilon_\txr = 1 + \chi_\txe
+        }
+    \end{formula}
+    \begin{formula}{dielectric_polarization_density}
+        \desc{Dielectric polarization density}{}{\ConstRef{vacuum_permittivity}, $\fqEqRef{ed:el:electric_susceptibility}$, \QtyRef{electric_field}}
+        \desc[german]{Dielektrische Polarisationsdichte}{}{}
+        \eq{\vec{P} = \epsilon_0 \chi_\txe \vec{\E}}
     \end{formula}
 
 \Section[
     \eng{Magnetic field}
     \ger{Magnetfeld}
 ]{mag}
-    \begin{constant}{h_joule}{\hbar}{def}
-        \desc{Planck Constant}{}{}
-        \desc[german]{Plancksches Wirkumsquantum}{}{}
-        \val{6.62607015\cdot 10^{-34}}{\joule\s}
-        \val{4.135667969\dots\cdot 10^{-15}}{\eV\s}
-    \end{constant}
 
     \Eng[magnetic_flux]{Magnetix flux density}
     \Ger[magnetic_flux]{Magnetische Flussdichte}
 
     \begin{quantity}{magnetic_flux}{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
-        \desc{Magnetic flux}{}
+        \desc{Magnetic flux}{Test desc}{Test def}
-        \desc[german]{Magnetischer Fluss}{}
+        \desc[german]{Magnetischer Fluss}{Test desc}{Test def}
     \end{quantity}
 
     \begin{quantity}{magnetic_flux_density}{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{}
-        \desc{Magnetic flux density}{}
+        \desc{Magnetic flux density}{}{}
-        \desc[german]{Magnetische Flussdichte}{}
+        \desc[german]{Magnetische Flussdichte}{}{}
     \end{quantity}
     \begin{formula}{magnetic_flux_density}
-        \desc{\qtyRef{magnetic_flux_density}}{}{$\vec{H}$ \qtyRef{magnetic_field_density}, $\vec{M}$ \qtyRef{magnetization}, $\mu_0$ \constRef{vacuum_permeability}}
+        \desc{\qtyRef{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]{}{}{}
+        \desc[german]{}{Definiert über \fqEqRef{ed:mag:lorentz}}{}
         \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
     \end{formula}
 
-    \begin{quantity}{magnetic_permeability}{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
+    \begin{quantity}{magnetic_field_intensity}{\vec{H}}{\ampere\per\m}{vector}
-        \desc{Magnetic permeability}{}
+        \desc{Magnetic field intensity}{}{}
-        \desc[german]{Magnetisch Permeabilität}{}
+        \desc[german]{Magnetische Feldstärke}{}{}
     \end{quantity}
-    \begin{constant}{vacuum_permeability}{\mu_0}{exp}
+    \begin{formula}{magnetic_field_intensity}
+        \desc{\qtyRef{magnetic_field_intensity}}{}{}
+        \desc[german]{}{}{}
+        \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{quantity}{magnetic_permeability}{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
+        \desc{Magnetic permeability}{}{}
+        \desc[german]{Magnetisch Permeabilität}{}{}
+    \end{quantity}
+    \begin{formula}{magnetic_permeability}
+        \desc{\qtyRef{magnetic_permeability}}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
+        \desc[german]{}{}{}
+        \eq{\mu=\frac{B}{H}}
+    \end{formula}
+    \begin{constant}{magnetic_vacuum_permeability}{\mu_0}{exp}
         \desc{Magnetic vauum permeability}{}{}
         \desc[german]{Magnetische Vakuumpermeabilität}{}{}
         \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2}
     \end{constant}
+    \begin{formula}{relative_permeability}
+        \desc{Relative permeability}{}{}
+        \desc[german]{Realtive Permeabilität}{}{}
+        \eq{
+            \mu_\txr = \frac{\mu}{\mu_0}
+        }
+    \end{formula}
 
     \begin{formula}{magnetic_flux}
         \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
@@ -95,45 +128,115 @@
     \end{formula}
 
     \begin{quantity}{magnetization}{\vec{M}}{\ampere\per\m}{vector}
-        \desc{Magnetization}{Vector field describing the density of magnetic dipoles}
+        \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{}
-        \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}
+        \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{}
     \end{quantity}
-    \begin{quantity}{magnetic_moment}{\vec{m}}{\ampere\m^2}{vector}
-        \desc{Magnetic moment}{Strength and direction of a magnetic dipole}
-        \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}
-    \end{quantity}
-
     \begin{formula}{magnetization}
         \desc{\qtyRef{magnetization}}{}{$m$ \qtyRef{magnetic_moment}, $V$ \qtyRef{volume}}
         \desc[german]{}{}{}
-        \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\text{m} \cdot \vec{H}}
+        \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}}
     \end{formula}
 
+    \begin{quantity}{magnetic_moment}{\vec{m}}{\ampere\m^2}{vector}
+        \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{}
+        \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{}
+    \end{quantity}
+
     \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}{suceptibility}
+    \begin{formula}{magnetic_susceptibility}
-        \desc{Susceptibility}{}{}
+        \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}}
         \desc[german]{Suszeptibilität}{}{}
-        \eq{\chi_\text{m} = \pdv{M}{B} = \frac{\mu}{\mu_0} - 1 }
+        \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}
+
+\Section[
+    \eng{Electromagnetism}
+    \ger{Elektromagnetismus}
+]{em}
+    \begin{constant}{speed_of_light}{c}{exp}
+        \desc{Speed of light}{in the vacuum}{}
+        \desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
+        \val{299792458}{\m\per\s}
+    \end{constant}
+    \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}, $\phi$}
+        \desc[german]{Poisson Gleichung in der Elektrostatik}{}{}
+        \eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}}
+    \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}{magnetic_permeability}
+    \Subsection[
-        \desc{\qtyRef{magnetic_permeability}}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
+        \eng{Maxwell-Equations}
-        \desc[german]{}{}{}
+        \ger{Maxwell-Gleichungen}
-        \eq{\mu=\frac{B}{H}}
+    ]{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}
+        \TODO{Polarization}
+
     \Subsection[
         \eng{Induction}
         \ger{Induktion}
@@ -157,15 +260,7 @@
             }
         \end{formula}
 
-    \Subsection[
+
-        \eng{Magnetic materials}
-        \ger{Magnetische Materialien}
-    ]{materials}
-        \begin{formula}{paramagnetism}
-            \desc{Paramagnetism}{}{$\mu$ \fqEqRef{ed:mag:permeability}, $\chi$ \fqEqRef{ed:mag:susecptibility}}
-            \desc[german]{Paramagnetismus}{}{}
-            \eq{\mu &> 1 \\ \chi > 0}
-        \end{formula}
 
 
 \Section[

src/main.tex

@@ -40,6 +40,7 @@
 % SCIENCE PACKAGES
 \usepackage{mathtools}
 \usepackage{MnSymbol}  % for >>> \ggg sign
+\usepackage{chemmacros}  % for orbitals
 % \usepackage{esdiff} % derivatives
 % esdiff breaks when taking \dot{q} has argument
 \usepackage{derivative}
@@ -108,31 +109,71 @@
     \label{sec:\fqname}
 }
 
-% Make the translation of #1 a reference to a equation
+% REFERENCES
-% 1: key
+% 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
+% <name>
 \newrobustcmd{\fqEqRef}[1]{%
     % \edef\fqeqrefname{\GT{#1}}
     % \hyperref[eq:#1]{\fqeqrefname}
     \hyperref[eq:#1]{\GT{#1}}%
 }
-\newrobustcmd{\qtyRef}[1]{%
+% Section
-    \hyperref[qty:#1]{\GT{#1}}%
+% <name>
-}
-\newrobustcmd{\constRef}[1]{%
-    \hyperref[const:#1]{\GT{#1}}%
-}
-% Make the translation of #1 a reference to a section
-% 1: key
 \newrobustcmd{\fqSecRef}[1]{%
     \hyperref[sec:#1]{\GT{#1}}%
 }
+% Quantities
+% <symbol>
+\newrobustcmd{\qtyRef}[1]{%
+    \hyperref[qty:#1]{\GT{qty:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\QtyRef}[1]{%
+    ${\luavar{quantities["#1"]["symbol"]}}$ \hyperref[qty:#1]{\GT{qty:#1}}%
+}
+% Constants
+% <name>
+\newrobustcmd{\constRef}[1]{%
+    \hyperref[const:#1]{\GT{const:#1}}%
+}
+% <symbol> <name>
+\newrobustcmd{\ConstRef}[1]{%
+    $\luavar{constants["#1"]["symbol"]}$ \hyperref[const:#1]{\GT{const:#1}}%
+}
+% Element from periodic table
+% <symbol>
+\newrobustcmd{\elRef}[1]{%
+    \hyperref[el:#1]{{\color{dark0_hard}#1}}%
+}
+% <name>
+\newrobustcmd{\ElRef}[1]{%
+    \hyperref[el:#1]{\GT{el:#1}}%
+}
 
 % \usepackage{xstring}
 
+% LUA sutff
+\newcommand\luavar[1]{\directlua{tex.sprint(#1)}}
+% Write directlua command to aux and run it as well
+\newcommand\directLuaAux[1]{
+    \immediate\write\luaauxfile{\noexpand\directlua{\detokenize{#1}}}
+    \directlua{#1}
+}
+\newwrite\luaauxfile
+\immediate\openout\luaauxfile=\jobname.lua.aux
+\immediate\write\luaauxfile{\noexpand\def\noexpand\luaAuxLoaded{lua aux loaded}}%
+\AtEndDocument{\immediate\closeout\luaauxfile}
+\IfFileExists{\jobname.lua.aux}{%
+  \input{\jobname.lua.aux}
+}{}
 
 \input{circuit.tex}
 \input{util/macros.tex}
 \input{util/environments.tex}   % requires util/translation.tex to be loaded first
+\input{util/periodic_table.tex} % requires util/translation.tex to be loaded first
 
 \def\inputOnlyFile{\relax}
 \newcommand\Input[1]{
@@ -159,9 +200,11 @@
 
 \newwrite\translationsaux
 \immediate\openout\translationsaux=\jobname.translations.aux
-\immediate\write\translationsaux{\noexpand\def\noexpand\MYVAR{AUSM AUX}}%
+\immediate\write\translationsaux{\noexpand\def\noexpand\translationsAuxLoaded{translations aux loaded}}%
 \AtEndDocument{\immediate\closeout\translationsaux}
 
+\makeatletter\let\percentchar\@percentchar\makeatother
+
 \maketitle
 \tableofcontents
 \newpage
@@ -169,10 +212,14 @@
 
 \input{util/translations.tex}
 
-% \include{maths/linalg}
+\Part[
-% \include{maths/geometry}
+    \eng{Mathematics}
-\input{maths/analysis.tex}
+    \ger{Mathematik}
-% \include{maths/probability_theory}
+]{math}
+% \include{math/linalg}
+% \include{math/geometry}
+% \input{math/calculus.tex}
+% \include{math/probability_theory}
 
 \include{mechanics}
 
@@ -183,7 +230,7 @@
 % \include{quantum_mechanics}
 % \include{atom}
 
-\include{condensed_matter}
+\input{cm/cm.tex}
 \input{cm/charge_transport.tex}
 \input{cm/low_temp.tex}
 \input{cm/semiconductors.tex}
@@ -198,6 +245,9 @@
 \include{quantities}
 \include{constants}
 
+\input{ch/periodic_table.tex}  % only definitions
+\input{ch/ch.tex}
+
 \newpage
 % \DT[english]{ttest}{TESTT EN}
 % \DT[german]{ttest}{TESTT DE}
@@ -235,6 +285,7 @@ Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
 Link to quantity which is defined after the reference: \qtyRef{test}\\
 \DT[qty:test]{english}{If you read this, then the translation for qty:test was expandend!}
 Link to defined quantity: \qtyRef{mass}
+\\ Link to element with name: \ElRef{H}
 \begin{equation}
     \label{qty:test}
     E = mc^2
@@ -246,9 +297,9 @@ Link to defined quantity: \qtyRef{mass}
 \gt{relative_undefined_translation_with_underscors}\\
 \GT{absolute_undefined_translation_with_&ampersand}
 
-
+\paragraph{Aux files}
-
+\noindent Lua Aux loaded? \luaAuxLoaded\\
-
+Translations Aux loaded? \translationsAuxLoaded\\
 
 
 \newpage
@@ -261,4 +312,5 @@ Link to defined quantity: \qtyRef{mass}
 \listoftables
 % \bibliographystyle{plain}
 % \bibliography{ref}
+
 \end{document}

src/math/calculus.tex

@@ -1,7 +1,7 @@
-\Part[
+\Section[
     \eng{Calculus}
     \ger{Analysis}
-    ]{cal}
+]{cal}
 
     % \begin{formula}{shark}
     %     \desc{Shark-midnight formula}{\emoji{shark}-s}{}
@@ -148,10 +148,10 @@
         \end{formula}
 
 
-\Section[
+    \Subsection[
         \eng{Logarithm}
         \ger{Logarithmus}
-]{log}
+    ]{log}
         \begin{formula}{identities}
             \desc{Logarithm identities}{}{}
             \desc[german]{Logarithmus Identitäten}{Logarithmus Rechenregeln}{}
@@ -172,7 +172,7 @@
             }
         \end{formula}
 
-\Section[
+    \Subection[
         \eng{List of common integrals}
         \ger{Liste nützlicher Integrale}
     ]{integrals}

src/math/geometry.tex

@@ -1,50 +1,50 @@
-\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[german]{Exponentialfunktion}{}{}
         \eq{\exp(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}}
-\end{formula}
+    \end{formula}
 
-\begin{formula}{sine}
+    \begin{formula}{sine}
         \desc{Sine}{}{}
         \desc[german]{Sinus}{}{}
         \eq{\sin(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{(2n+1)}}{(2n+1)!} \\
                     &= \frac{e^{ix}-e^{-ix}}{2i}}
-\end{formula}
+    \end{formula}
 
-\begin{formula}{cosine}
+    \begin{formula}{cosine}
         \desc{Cosine}{}{}
         \desc[german]{Kosinus}{}{}
         \eq{\cos(x) &= \sum_{n=0}^{\infty} (-1)^{n} \frac{x^{(2n)}}{(2n)!} \\
                     &= \frac{e^{ix}+e^{-ix}}{2}}
-\end{formula}
+    \end{formula}
 
 
-\begin{formula}{hyperbolic_sine}
+    \begin{formula}{hyperbolic_sine}
         \desc{Hyperbolic sine}{}{}
         \desc[german]{Sinus hyperbolicus}{}{}
         \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[german]{Kosinus hyperbolicus}{}{}
         \eq{\cosh(x) &= \cos{ix} \\ &= \frac{e^{x}+e^{-x}}{2}}
-\end{formula}
+    \end{formula}
 
-    \Subsection[
+\Subsection[
     \eng{Various theorems}
     \ger{Verschiedene Theoreme}
-    ]{theorems}
+]{theorems}
     \begin{formula}{sum}
         \desc{}{}{}
         \desc[german]{}{}{}
@@ -78,7 +78,7 @@
     \end{formula}
 
 
-    \Subsection[
+    \Subsubsection[
         \eng{Table of values}
         \ger{Wertetabelle}
     ]{value_table}

src/math/linalg.tex

@@ -1,11 +1,9 @@
-\def\id{\mathbb{1}}
+\Section[
-
-\Part[
     \eng{Linear algebra}
     \ger{Lineare Algebra}
     ]{linalg}
 
-    \Section[
+    \Subsection[
         \eng{Determinant}
         \ger{Determinante}
         ]{determinant}
@@ -43,7 +41,7 @@
         \end{formula}
 
 
-    \Section[
+    \Subsection[
         
     ]{zeug}
 
@@ -95,7 +93,7 @@
         \end{formula}
 
 
-    \Section[
+    \Subection[
         \eng{Eigenvalues}
         \ger{Eigenwerte}
     ]{eigen}

src/math/probability_theory.tex

@@ -0,0 +1,241 @@
+\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}{autocorrelation}
+        \desc{Autocorrelation}{Correlation of $f$ to itself at an earlier point in time, $C$ is a covariance function}{}
+        \desc[german]{Autokorrelation}{Korrelation vonn $f$ zu sich selbst zu einem früheren Zeitpunkt. $C$ ist auch die Kovarianzfunktion}{}
+        \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}
+
+    \Subsection[
+        \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}
+
+    \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}
+
+

src/maths/probability_theory.tex

@@ -1,241 +0,0 @@
-\Part[
-    \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{pt:std-deviation}}{}
-        \desc[german]{Varianz}{Quadrat der\fqEqRef{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}{autocorrelation}
-        \desc{Autocorrelation}{Correlation of $f$ to itself at an earlier point in time, $C$ is a covariance function}{}
-        \desc[german]{Autokorrelation}{Korrelation vonn $f$ zu sich selbst zu einem früheren Zeitpunkt. $C$ ist auch die Kovarianzfunktion}{}
-        \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}
-
-\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}
-
-\Section[
-    \eng{Propagation of uncertainty / error}
-    \ger{Fehlerfortpflanzung}
-]{error}
-    \begin{formula}{generalised}
-        \desc{Generalized error propagation}{}{$V$ \fqEqRef{pt:covariance} matrix, $J$ \fqEqRef{ana:jacobi-matrix}}
-        \desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fqEqRef{pt:covariance} Matrix, $J$ \fqEqRef{ana: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{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{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{pt:error:weight}}
-        \desc[german]{Varianz des gewichteten Mittelwertes}{}{}
-        \eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
-    \end{formula}
-
-

src/quantities.tex

@@ -6,72 +6,72 @@
 \paragraph{\GT{si_base_units}}
 
     \begin{quantity}{time}{t}{\second}{}
-        \desc{Time}{}
+        \desc{Time}{}{}
-        \desc[german]{Zeit}{}
+        \desc[german]{Zeit}{}{}
     \end{quantity}
 
     \begin{quantity}{Length}{l}{\m}{e}
-        \desc{Length}{}
+        \desc{Length}{}{}
-        \desc[german]{Länge}{}
+        \desc[german]{Länge}{}{}
     \end{quantity}
 
     \begin{quantity}{mass}{m}{\kg}{es}
-        \desc{Mass}{}
+        \desc{Mass}{}{}
-        \desc[german]{Masse}{}
+        \desc[german]{Masse}{}{}
     \end{quantity}
 
     \begin{quantity}{temperature}{T}{\kelvin}{is}
-        \desc{Temperature}{}
+        \desc{Temperature}{}{}
-        \desc[german]{Temperatur}{}
+        \desc[german]{Temperatur}{}{}
     \end{quantity}
 
     \begin{quantity}{current}{I}{\ampere}{es}
-        \desc{Electric current}{}
+        \desc{Electric current}{}{}
-        \desc[german]{Elektrischer Strom}{}
+        \desc[german]{Elektrischer Strom}{}{}
     \end{quantity}
 
     \begin{quantity}{amount}{n}{\mol}{es}
-        \desc{Amount of substance}{}
+        \desc{Amount of substance}{}{}
-        \desc[german]{Stoffmenge}{}
+        \desc[german]{Stoffmenge}{}{}
     \end{quantity}
 
     \begin{quantity}{luminous_intensity}{I_\text{V}}{\candela}{s}
-        \desc{Luminous intensity}{}
+        \desc{Luminous intensity}{}{}
-        \desc[german]{Lichtstärke}{}
+        \desc[german]{Lichtstärke}{}{}
     \end{quantity}
 
 \paragraph{\GT{other}}
     \begin{quantity}{volume}{V}{\m^d}{}
-        \desc{Volume}{$d$ dimensional Volume}
+        \desc{Volume}{$d$ dimensional Volume}{}
-        \desc[german]{Volumen}{$d$ dimensionales Volumen}
+        \desc[german]{Volumen}{$d$ dimensionales Volumen}{}
     \end{quantity}
 
     \begin{quantity}{force}{\vec{F}}{\newton=\kg\m\per\second^2}{ev}
-        \desc{Force}{}
+        \desc{Force}{}{}
-        \desc[german]{Kraft}{}
+        \desc[german]{Kraft}{}{}
     \end{quantity}
 
     \begin{quantity}{spring_constant}{k}{\newton\per\m=\kg\per\second^2}{s}
-        \desc{Spring constant}{}
+        \desc{Spring constant}{}{}
-        \desc[german]{Federkonstante}{}
+        \desc[german]{Federkonstante}{}{}
     \end{quantity}
 
     \begin{quantity}{velocity}{\vec{v}}{\m\per\s}{v}
-        \desc{Velocity}{}
+        \desc{Velocity}{}{}
-        \desc[german]{Geschwindigkeit}{}
+        \desc[german]{Geschwindigkeit}{}{}
     \end{quantity}
 
     \begin{quantity}{torque}{\tau}{\newton\m=\kg\m^2\per\s^2}{v}
-        \desc{Torque}{}
+        \desc{Torque}{}{}
-        \desc[german]{Drehmoment}{}
+        \desc[german]{Drehmoment}{}{}
     \end{quantity}
 
     \begin{quantity}{heat_capacity}{C}{\joule\per\kelvin}{}
-        \desc{Heat capacity}{}
+        \desc{Heat capacity}{}{}
-        \desc[german]{Wärmekapazität}{}
+        \desc[german]{Wärmekapazität}{}{}
     \end{quantity}
 
     \begin{quantity}{charge}{q}{\coulomb=\ampere\s}{}
-        \desc{Charge}{}
+        \desc{Charge}{}{}
-        \desc[german]{Ladung}{}
+        \desc[german]{Ladung}{}{}
     \end{quantity}

src/topo.tex

@@ -1,8 +1,11 @@
-\Part{Topo}
+\Part[
+    \eng{Topological Materials}
+    \ger{Topologische Materialien}
+]{topo}
 \Section[
     \eng{Berry phase / Geometric phase}
     \ger{Berry-Phase / Geometrische Phase}
-     ]{berry_phase}
+]{berry_phase}
 
     \begin{ttext}[desc]
         \eng{

src/util/environments.tex

@@ -25,7 +25,7 @@
 % [1]: minipage width
 % 2: fqname of name
 % 3: fqname of a translation that holds the explanation
-\newcommand{\NameWithExplanation}[3][\descwidth]{
+\newcommand{\NameWithDescription}[3][\descwidth]{
     \begin{minipage}{#1}
         \IfTranslationExists{#2}{
             \raggedright
@@ -45,6 +45,7 @@
     \begin{minipage}{#1}
         % \vspace{-\baselineskip}  % remove the space that comes from starting a new paragraph
         #2
+        \smartnewline
         \noindent\IfTranslationExists{#3}{
             \begingroup
                 \color{dark1} 
@@ -65,7 +66,7 @@
     \par\noindent\ignorespaces
     % \textcolor{gray}{\hrule}
     \vspace{0.5\baselineskip}
-    \NameWithExplanation[\descwidth]{#1}{#1_desc}
+    \NameWithDescription[\descwidth]{#1}{#1_desc}
     \hfill
     \ContentBoxWithExplanation[\eqwidth]{#2}{#1_defs}
     \textcolor{dark3}{\hrule}
@@ -107,7 +108,6 @@
     }
 }
 
-\newcommand\luaexpr[1]{\directlua{tex.sprint(#1)}}
 % [1]: width
 % 2: fqname
 % 3: file path
@@ -117,7 +117,7 @@
     % \textcolor{gray}{\hrule}
     \vspace{0.5\baselineskip}
     \begin{minipage}{#1\textwidth}
-        \NameWithExplanation[\textwidth]{\fqname:#2}{#2_desc}
+        \NameWithDescription[\textwidth]{\fqname:#2}{#2_desc}
         % TODO: why is this ignored
         \vspace{1.0cm}
         % TODO: fix box is too large without 0.9
@@ -129,7 +129,7 @@
         }{#2_defs}
     \end{minipage}
     \hfill
-    \begin{minipage}{\luaexpr{1.0-#1}\textwidth}
+    \begin{minipage}{\luavar{1.0-#1}\textwidth}
         \begin{figure}[H]
             \centering
             \includegraphics[width=\textwidth]{#3}
@@ -138,7 +138,6 @@
     \end{minipage}
     \textcolor{dark3}{\hrule}
     \vspace{0.5\baselineskip}
-
 }
 
 % 1: key
@@ -255,7 +254,42 @@
 %     % \addquantity{\expandafter\gt\expandafter{\qtyname}}%
 %     % \noindent\textbf{My Environment \themyenv: #1}\par%
 % }
+\directLuaAux{
+    if constants == nil then
+        constants = {}
+    end
+}
+\newcommand\printConstant[1]{
+    \edef\constName{const:#1}
+    \NameLeftContentRight{\constName}{
+        \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}
+% 1: key - must expand to a valid lua string!
+% 2: symbol
+% 3: either exp or def; experimentally or defined constant
 \newenvironment{constant}[3]{
     % [1]: language
     % 2: name
@@ -267,89 +301,76 @@
         \ifblank{##3}{}{\DT[const:#1_desc]{##1}{##3}}
         \ifblank{##4}{}{\DT[const:#1_defs]{##1}{##4}}
     }
-    \directlua{
+    \directLuaAux{
-        constVals = {}
+        constants["#1"] = {};
-        constUnits = {}
+        constants["#1"]["symbol"]  = [[\detokenize{#2}]];
+        constants["#1"]["exp_or_def"]   = [[\detokenize{#3}]];
+        constants["#1"]["values"] = {} -- array of {value, unit};
     }
-    % 1: equation for align environment
+    % 1: value
+    % 2: unit
     \newcommand{\val}[2]{
-        \directlua{
+        \directLuaAux{
-            %--table.insert(constVals, "LOL")
+            table.insert(constants["#1"]["values"], { value = [[\detokenize{##1}]], unit = [[\detokenize{##2}]] })
-            table.insert(constVals, [[##1]])
-            table.insert(constUnits, [[##2]])
-            %--table.insert(constUnits, "\luaescapestring{##2}")
         }
-        \def\constValue{##1}
-        \def\constUnit{##2}
     }
-    \edef\constName{const:#1}
+    \edef\lastConstName{#1}
-    \edef\constDesc{const:#1_desc}
-    \def\constSymbol{#2}
-    \edef\constExpOrDef{\GT{const:#3}}
 }{
-    \NameLeftContentRight{\constName}{
+    \expandafter\printConstant{\lastConstName}
-        \begingroup  % for label
-            Symbol: $\constSymbol$
-            \IfTranslationExists{\constDesc}{
-                \\Description: \GT{\constDesc}
-            }{}
-            % TODO manage multiple values
-            % \\Value: $\constValue\,\si{\constUnit}$
-            \\\constExpOrDef:
-            \directlua{
-                %--tex.sprint("Hier steht Luatext" .. ":", #constVals)
-                for i, v in ipairs(constVals) do
-                tex.sprint("\\\\\\hspace*{1cm}${", constVals[i], "}\\,\\si{", constUnits[i], "}$")
-                    %--tex.sprint("VALUE ", i, v)
-                end
-            }
-            \label{\constName}
-        \endgroup
-    }
     \ignorespacesafterend
 }
 
 
 
-% 1: key
+\directLuaAux{
+    if quantities == nil then
+        quantities = {}
+    end
+}
+\newcommand\printQuantity[1]{
+    \edef\qtyName{qty:#1}
+    \NameLeftContentRight{\qtyName}{
+        \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
+    }
+
+}
+% 1: key - must expand to a valid lua string!
 % 2: symbol
 % 3: units
 % 4: comment key to translation
 \newenvironment{quantity}[4]{
-    % language, name, description
+    % language, name, description, definitions
-    \newcommand{\desc}[3][english]{
+    \newcommand{\desc}[4][english]{
         \ifblank{##2}{}{\DT[qty:#1]{##1}{##2}}
         \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
+        \ifblank{##4}{}{\DT[qty:#1_defs]{##1}{##4}}
     }
     % TODO put these in long term key - value storage for generating a full table and global referenes \qtyRef
     % for references, there needs to be a label somwhere
-    \edef\qtyname{qty:#1}
+    \directLuaAux{
-    \edef\qtydesc{qty:#1_desc}
+        quantities["#1"] = {} 
-    \def\qtysymbol{#2}
+        quantities["#1"]["symbol"]  = [[\detokenize{#2}]]
-    \def\qtyunits{#3}
+        quantities["#1"]["units"]   = [[\detokenize{#3}]]
-    \edef\qtycomment{#4}
+        quantities["#1"]["comment"] = [[\detokenize{#4}]]
-    % Unit: $\directlua{split_and_print_units([[\m\per\kg]])}$
+    }
+    \def\lastQtyName{#1}
 }
 {
-    \NameLeftContentRight{\qtyname}{
+    \expandafter\printQuantity{\lastQtyName}
-        \begingroup
-            Symbol: $\qtysymbol$
-            \IfTranslationExists{\qtydesc}{
-                \\Description: \GT{\qtydesc}
-            }{}
-            \\Unit: $\directlua{split_and_print_units([[\qtyunits]])}$
-            \expandafter\IfTranslationExists\expandafter\qtycomment{
-                \\Comment: \GT\qtycomment
-            }{}%{\\No comment \color{gray}}
-            \label{\qtyname}
-        \endgroup
-    }
     \ignorespacesafterend
-
     % for TOC
     \refstepcounter{quantity}%
     % \addquantity{\expandafter\gt\expandafter{\qtyname}}%
-    % \noindent\textbf{My Environment \themyenv: #1}\par%
 }
 \newcounter{quantity}
 \newcommand{\listofquantities}{%

src/util/macros.tex

@@ -1,3 +1,4 @@
+\newcommand\smartnewline[1]{\ifhmode\\\fi}  % newline only if there in horizontal mode
 \def\gooditem{\item[{$\color{neutral_red}\bullet$}]}
 \def\baditem{\item[{$\color{neutral_green}\bullet$}]}
 
@@ -10,12 +11,15 @@
     \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}}
 
 % COMMON SYMBOLS WITH SUPER/SUBSCRIPTS, VECTOR ARROWS ETC.
+% \def\laplace{\Delta} % Laplace operator
+\def\laplace{\bigtriangleup} % Laplace operator
 \def\Grad{\vec{\nabla}}
 \def\Div{\vec{\nabla} \cdot}
 \def\Rot{\vec{\nabla} \times}
 \def\vecr{\vec{r}}
 \def\vecx{\vec{x}}
-\def\kB{k_\text{B}}
+\def\kB{k_\text{B}}  % boltzmann
+\def\NA{N_\text{A}}  % avogadro
 \def\EFermi{E_\text{F}}
 \def\Evalence{E_\text{v}}
 \def\Econd{E_\text{c}}
@@ -33,8 +37,9 @@
 \def\C{\mathbb{C}}
 \def\Z{\mathbb{Z}}
 \def\N{\mathbb{N}}
+\def\id{\mathbb{1}}
 % caligraphic
-\def\calE{\mathcal{E}}
+\def\E{\mathcal{E}}  % electric field
 % upright
 \def\txA{\text{A}}
 \def\txB{\text{B}}
@@ -114,6 +119,8 @@
 % diff, for integrals and stuff
 % \DeclareMathOperator{\dd}{d}
 \renewcommand*\d{\mathop{}\!\mathrm{d}}
+% times 10^{x}
+\newcommand\xE[1]{\cdot 10^{#1}}
 % functions with paranthesis
 \newcommand\CmdWithParenthesis[2]{
     #1\left(#2\right)

src/util/periodic_table.tex

@@ -0,0 +1,162 @@
+% 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}
+    \NameLeftContentRight{\elementName}{
+        \begingroup % for label
+            \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
+            }
+            % label it only once
+            \directlua{ 
+                if elements["#1"]["labeled"] == nil then
+                    elements["#1"]["labeled"] = true
+                    tex.print("\\label{el:#1}")
+                end
+            }
+        \endgroup
+    }
+}
+\newcommand{\printAllElements}{
+    \directlua{
+            %-- tex.sprint("\\printElement{"..val.."}")
+        for key, val in ipairs(elementsOrder) do
+            %-- tex.sprint(key, val);
+            tex.sprint("\\printElement{"..val.."}")
+        end
+    }
+}
+
+% PERIODIC TABLE
+\directlua{
+    category2color = {
+        metal               = "neutral_blue",
+        metalloid           = "bright_orange",
+        transitionmetal     = "bright_blue",
+        lanthanoide         = "neutral_orange",
+        alkalimetal         = "bright_red",
+        alkalineearthmetal  = "bright_purple",
+        nonmetal            = "bright_aqua",
+        halogen             = "bright_yellow",
+        noblegas            = "neutral_purple"
+    }
+}
+\directlua{
+    function getColor(cat) 
+        local color = category2color[cat]
+        if color == nil then
+            return "light3"
+        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,faded_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/util/translation.tex

@@ -21,15 +21,16 @@
     \def\tempiftranslation{\IfTranslation{english}}%
     \expandafter\tempiftranslation\expandafter{#1}%
 }
-\newcommand{\iftranslation}[3]{%
+\newcommand{\iftranslation}[1]{%
-    \IfTranslationExists{\fqname:#1}{#2}{#3}%
+    \IfTranslation{english}{\fqname:#1}
+    % \expandafter\IfTranslationExists\expandafter{\fqname:#1}
 }
 
 \newcommand{\gt}[1]{%
     \iftranslation{#1}{%
         \expandafter\GetTranslation\expandafter{\fqname:#1}%
     }{%
-        \fqname:\detokenize{#1}%
+        \detokenize{\fqname}:\detokenize{#1}%
     }%
 }
 \newrobustcmd{\GT}[1]{%\expandafter\GetTranslation\expandafter{#1}}

src/util/translations.tex

@@ -46,3 +46,17 @@
 \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}
+
+