qtys, constants

src/computational.tex

@@ -0,0 +1,131 @@
+\Part[
+    \eng{Computational Physics}
+    \ger{Computergestützte Physik}
+]{comp}
+\Section[
+    \eng{Many-body physics}
+    \ger{Vielteilchenphysik}
+]{mb}
+\TODO{TODO}
+    \Subsection[
+        \eng{Importance sampling}
+        \ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
+    ]{importance_sampling}
+    \TODO{Monte Carlo}
+
+    \Subsection[
+        \eng{Matrix product states}
+        \ger{Matrix Produktzustände}
+    ]{mps}
+
+\Section[
+    \eng{Misc}
+    \ger{Verschiedenes}
+]{misc}
+    \begin{formula}{mean_field}
+        \desc{Mean field approximation}{Replaces 2-particle operator by 1-particle operator}{Example for Coulumb interaction between many electrons}
+        \desc[german]{Molekularfeldnäherung}{Ersetzt 2-Teilchen Operator durch 1-Teilchen Operator}{Beispiel für Coulumb Wechselwirkung zwischen Elektronen}
+        \eq{
+            \frac{1}{2}\sum_{i\neq j} \frac{e^2}{\abs{\vec{r}_i - \vec{r}_j}} \approx \sum_{i} V_\text{eff}(\vec{r}_i)
+        }
+    \end{formula}
+
+
+\Section[
+    \eng{Tight-binding}
+    \ger{Tight-binding}
+]{tb}
+
+
+\Section[
+    \eng{Density functional theory (DFT)}
+    \ger{Dichtefunktionaltheorie (DFT)}
+]{dft}
+    \Subsection[
+        \eng{Hartree-Fock}
+        \ger{Hartree-Fock}
+    ]{hf}
+        \begin{ttext}
+            \eng{
+                \begin{itemize}
+                    \item \fqEqRef{comp:misc:mean_field} theory
+                    \item Self-interaction free: Self interaction is cancelled out by the Fock-term
+                \end{itemize}
+            }
+        \end{ttext}
+        \begin{formula}{equation}
+            \desc{Hartree-Fock equation}{}{
+                $\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
+                $\hat{T}$ kinetic electron energy,
+                $\hat{V}_{\text{en}}$ electron-nucleus attraction,
+                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential},
+            }
+            \desc[german]{Hartree-Fock Gleichung}{}{
+                $\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
+                $\hat{T}$ kinetische Energie der Elektronen,
+                $\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
+                $\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}
+            }
+            \eq{
+                \left(\hat{T} + \hat{V}_{\text{en}} + \hat{V}_{\text{HF}}^\xi\right)\varphi_\xi(x) = \epsilon_\xi \varphi_\xi(x)
+            }
+        \end{formula}
+        \begin{formula}{potential}
+            \desc{Hartree-Fock potential}{}{}
+            \desc[german]{Hartree Fock Potential}{}{}
+            \eq{
+                V_{\text{HF}}^\xi(\vecr) = 
+                \sum_{\vartheta} \int \d x' 
+                \frac{e^2}{\abs{\vecr - \vecr'}}
+                \left(
+                    \underbrace{\abs{\varphi_\xi(x')}^2}_{\text{Hartree-Term}}
+                    - \underbrace{\frac{\varphi_{\vartheta}^*(x') \varphi_{\xi}(x') \varphi_{\vartheta}(x)}{\varphi_\xi(x)}}_{\text{Fock-Term}}
+                \right)
+            }
+        \end{formula}
+        \begin{formula}{scf}
+            \desc{Self-consistend field}{}{}
+            % \desc[german]{}{}{}
+            \ttxt{
+                \eng{
+                    \begin{enumerate}
+                        \item Initial guess for $\psi$
+                        \item Solve SG for each particle
+                        \item Make new guess for $\psi$
+                    \end{enumerate}
+                }
+            }
+        \end{formula}
+
+    \Subsection[
+        \eng{Kohn-Sham}
+        \ger{Kohn-Sham}
+    ]{ks}
+    \TODO{TODO}
+
+    \Subsection[
+        \eng{Born-Oppenheimer Approximation}
+        \ger{Born-Oppenheimer Näherung}
+    ]{bo}
+        \TODO{TODO}
+
+    \Subsection[
+        \eng{Molecular Dynamics}
+        \ger{Molekulardynamik}
+    ]{md}
+        \begin{ttext}
+            \eng{Statistical method}
+            
+        \end{ttext}
+        
+
+
+
+\Section[
+    \eng{Gradient descent}
+    \ger{Gradientenverfahren}
+    ]{gd}
+    \TODO{TODO}
+
+
+

src/condensed_matter.tex

@@ -166,53 +166,6 @@ family of plane that are equivalent due to crystal symmetry
         \eq{\mu = \frac{q \tau}{m}}
     \end{formula}
 
-    \Subsection[
-        \eng{Drude model}
-        \ger{Drude-Modell}
-        ]{drude}
-        \begin{ttext}
-            \eng{Classical model describing the transport properties of electrons in materials (metals):
-                The material is assumed to be an ion lattice and with freely moving electrons (electron gas). The electrons are 
-                accelerated by an electric field and decelerated through collisions with the lattice ions.
-                The model disregards the Fermi-Dirac partition of the conducting electrons.
-            }
-            \ger{Ein klassisches Model zur Beschreibung der Transporteigenschaften von Elektronen in (v.a.) Metallen:
-                Der Festkörper wird als Ionenkristall mit frei beweglichen Elektronen (Elektronengas). 
-                Die Elektronen werden durch ein Elektrisches Feld $E$ beschleunigt und durch Stöße mit den Gitterionen gebremst.
-                Das Modell vernachlässigt die Fermi-Dirac Verteilung der Leitungselektronen.
-            }
-        \end{ttext}
-        \begin{formula}{motion}
-            \desc{Equation of motion}{}{$v$ electron speed, $\vec{v}_\text{D}$ drift velocity, $\tau$ mean free time between collisions}
-            \desc[german]{Bewegungsgleichung}{}{$v$ Elektronengeschwindigkeit, $\vec{v}_\text{D}$ Driftgeschwindigkeit, $\tau$ Stoßzeit}
-            \eq{\masse \odv{\vec{v}}{t} + \frac{\masse}{\tau} \vec{v}_\text{D} = -e \vec{E}}
-        \end{formula}
-        \begin{formula}{current_density}
-            \desc{Current density}{Ohm's law}{$n$ charge particle density}
-            \desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte}
-            \eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{E}}
-        \end{formula}
-        \begin{formula}{conductivity}
-            \desc{Drude-conductivity}{}{}
-            \desc[german]{Drude-Leitfähigkeit}{}{}
-            \eq{\sigma = \frac{\vec{j}}{\vec{E}} = \frac{e^2 \tau n}{\masse} = n e \mu}
-        \end{formula}
-
-    \Subsection[
-        \eng{Sommerfeld model}
-        \ger{Sommerfeld-Modell}
-        ]{sommerfeld}
-        \begin{ttext}
-            \eng{Assumes a gas of free fermions underlying the pauli-exclusion principle. Only electrons in an energy range of $\kB T$ around the Fermi energy $\EFermi$ participate in scattering processes.}
-            \ger{Annahme eines freien Fermionengases, welches dem Pauli-Prinzip unterliegt. Nur Elektronen in einem Energiebereich von $\kB T$ um die Fermi Energe $\EFermi$ nehmen an Streuprozessen teil.}
-        \end{ttext}
-        \begin{formula}{current_density}
-            \desc{Current density}{}{}
-            \desc[german]{Stromdichte}{}{}
-            \eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
-        \end{formula}
-        \TODO{The formula for the conductivity is the same as in the drude model?}
-
     \Subsection[
         \eng{2D electron gas}
         \ger{2D Elektronengas}
@@ -256,177 +209,9 @@ family of plane that are equivalent due to crystal symmetry
 
         \TODO{TODO}
 
-\Section[
-    \eng{Semiconductors}
-    \ger{Halbleiter}
-]{semic}
-    \begin{formula}{charge_density_eq}
-        \desc{Equilibrium charge densitites}{}{}
-        \desc[german]{Ladungsträgerdichte im Equilibrium}{}{}
-        \eq{
-            n_0 &\approx N_\text{c}(T) e^{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
-            p_0 &\approx N_\text{v}(T) e^{-\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)} e^{-\frac{E_\text{gap}}{2\kB T}}
-        }
-    \end{formula}
 
 \Section[
-    \eng{Measurement techniques}
+    \eng{\GT{misc}}
-    \ger{Messtechniken}
+    \ger{\GT{misc}}
-]{meas}
+]{misc}
-    \Subsection[
-        \eng{ARPES}
-        \ger{ARPES}
-        ]{arpes}
-        what?
-        in?
-        how?
-        plot
-
-    \Subsection[
-        \eng{Scanning probe microscopy SPM}
-        \ger{Rastersondenmikroskopie (SPM)}
-        ]{spm}
-        \begin{ttext}
-            \eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
-            \ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
-        \end{ttext}
-
-        \Eng[name]{Name}
-        \Ger[name]{Name}
-        \Eng[application]{Application}
-        \Ger[application]{Anwendung}
-
-
-        \begin{minipagetable}{amf}
-            \entry{name}{
-                \eng{Atomic force microscopy (AMF)}
-                \ger{Atomare Rasterkraftmikroskopie (AMF)}
-            }
-            \entry{application}{
-                \eng{Surface stuff}
-                \ger{Oberflächenzeug}
-            }
-            \entry{how}{
-                \eng{With needle}
-                \ger{Mit Nadel}
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
-                \caption{\cite{Bian2021}}
-            \end{figure}
-        \end{minipage}
-
-
-        \begin{minipagetable}{stm}
-            \entry{name}{
-                \eng{Scanning tunneling microscopy (STM)}
-                \ger{Rastertunnelmikroskop (STM)}
-            }
-            \entry{application}{
-                \eng{Surface stuff}
-                \ger{Oberflächenzeug}
-            }
-            \entry{how}{
-                \eng{With TUnnel}
-                \ger{Mit TUnnel}
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \begin{figure}[H]
-                \centering
-                \includegraphics[width=0.8\textwidth]{img/cm_stm.pdf}
-                \caption{\cite{Bian2021}}
-            \end{figure}
-        \end{minipage}
-
-\Section[
-    \eng{Fabrication techniques}
-    \ger{Herstellungsmethoden}
-    ]{fab}
-    \begin{minipagetable}{cvd}
-        \entry{name}{
-            \eng{Chemical vapor deposition (CVD)}
-            \ger{Chemische Gasphasenabscheidung (CVD)}
-        }
-        \entry{how}{
-            \eng{
-                A substrate is exposed to volatile precursors, which react and/or decompose on the heated substrate surface to produce the desired deposit.
-                By-products are removed by gas flow through the chamber.
-            }
-            \ger{
-                An der erhitzten Oberfläche eines Substrates wird aufgrund einer chemischen Reaktion mit einem Gas eine Feststoffkomponente abgeschieden.
-                Nebenprodukte werden durch den Gasfluss durch die Kammer entfernt.
-            }
-        }
-        \entry{application}{
-            \eng{
-                \begin{itemize}
-                    \item Polysilicon \ce{Si}
-                    \item Silicon dioxide \ce{SiO_2}     
-                    \item Graphene
-                    \item Diamond
-                \end{itemize}
-            }
-            \ger{
-                \begin{itemize}
-                    \item Poly-silicon \ce{Si}
-                    \item Siliziumdioxid \ce{SiO_2}     
-                    \item Graphen
-                    \item Diamant
-                \end{itemize}
-            }
-        }
-    \end{minipagetable}
-    \begin{minipage}{0.5\textwidth}
-        \centering
-        \includegraphics[width=\textwidth]{img/cm_cvd_english.pdf}
-    \end{minipage}
-
-
-    \Subsection[
-        \eng{Epitaxy}
-        \ger{Epitaxie}
-        ]{epitaxy}
-        \begin{ttext}
-            \eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
-            \ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
-        \end{ttext}
-
-        \begin{minipagetable}{mbe}
-            \entry{name}{
-                \eng{Molecular Beam Epitaxy (MBE)}
-                \ger{Molekularstrahlepitaxie (MBE)}
-            } 
-            \entry{how}{
-                \eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
-                \ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
-            }
-            \entry{application}{
-                \eng{
-                    \begin{itemize}
-                        \item Gallium arsenide \ce{GaAs}
-                    \end{itemize}
-                    \TODO{Link to GaAs}
-                }
-                \ger{
-                    \begin{itemize}
-                        \item Galliumarsenid \ce{GaAs}
-                    \end{itemize}
-                }
-            }
-        \end{minipagetable}
-        \begin{minipage}{0.5\textwidth}
-            \centering
-            \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
-        \end{minipage}
 

src/constants.tex

@@ -0,0 +1,10 @@
+\Section[
+    \eng{Constants}
+    \ger{Konstanten}
+]{constants}
+    \begin{constant}{planck}{h}{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}

src/electrodynamics.tex

@@ -1,5 +1,3 @@
-\def\PhiB{\Phi_\text{B}}
-\def\PhiE{\Phi_\text{E}}
 
 \Part[
     \eng{Electrodynamics}
@@ -10,7 +8,7 @@
 \Section[
     \eng{Maxwell-Equations}
     \ger{Maxwell-Gleichungen}
-    ]{Maxwell}
+]{Maxwell}
     \begin{formula}{vacuum}
         \desc{Vacuum}{microscopic formulation}{}
         \desc[german]{Vakuum}{Mikroskopische Formulierung}{}
@@ -32,38 +30,60 @@
             \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
         }
     \end{formula}
-    \TODO{Polarization, Magnetisation}
+    \TODO{Polarization}
+
 
 \Section[
-    \eng{Fields}
-    \ger{Felder}
-    ]{fields}
-
-    \Subsection[
     \eng{Electric field}
     \ger{Elektrisches Feld}
-        ]{el}
+]{el}
     \begin{formula}{gauss_law}
         \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface}
         \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche}
         \eq{\PhiE = \iint_S \vec{E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}}
     \end{formula}
 
-    \Subsection[
+\Section[
     \eng{Magnetic field}
     \ger{Magnetfeld}
-        ]{mag}
+]{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}{mag_flux}{\Phi}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
+    \begin{quantity}{magnetic_flux}{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
         \desc{Magnetic flux}{}
         \desc[german]{Magnetischer Fluss}{}
     \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[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[german]{}{}{}
+        \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}
+        \desc{Magnetic permeability}{}
+        \desc[german]{Magnetisch Permeabilität}{}
+    \end{quantity}
+    \begin{constant}{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}{magnetic_flux}
-            \desc{Magnetic flux}{}{}
+        \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
         \desc[german]{Magnetischer Fluss}{}{}
         \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
     \end{formula}
@@ -74,15 +94,24 @@
         \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
     \end{formula}
 
+    \begin{quantity}{magnetization}{\vec{M}}{\ampere\per\m}{vector}
+        \desc{Magnetization}{Vector field describing the density of magnetic dipoles}
+        \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{Magnetization}{}{$m$ mag. moment, $V$ volume}
+        \desc{\qtyRef{magnetization}}{}{$m$ \qtyRef{magnetic_moment}, $V$ \qtyRef{volume}}
-            \desc[german]{Magnetisierung}{}{$m$ mag. Moment, $V$ Volumen}
+        \desc[german]{}{}{}
         \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\text{m} \cdot \vec{H}}
     \end{formula}
 
     \begin{formula}{angular_torque}
-            \desc{Torque}{}{$m$ mag. moment}
+        \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}}
-            \desc[german]{Drehmoment}{}{$m$ mag. Moment}
+        \desc[german]{Drehmoment}{}{}
         \eq{\vec{\tau} = \vec{m} \times \vec{B}}
     \end{formula}
 
@@ -99,7 +128,11 @@
         \eq{\vec{S} = \vec{E} \times \vec{H}}
     \end{formula}
 
-
+    \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}
 
     \Subsection[
         \eng{Induction}
@@ -124,6 +157,17 @@
             }
         \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[
     \eng{Hall-Effect}
     \ger{Hall-Effekt}
@@ -152,9 +196,9 @@
         \end{formula}
 
         \begin{formula}{coefficient}
-            \desc{Hall coefficient}{}{}
+            \desc{Hall coefficient}{Sometimes $R_\txH$}{}
-            \desc[german]{Hall-Koeffizient}{}{}
+            \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
-            \eq{R_\text{H} = -\frac{Eg}{j_x Bg} = \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
+            \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
         \end{formula}
 
         \begin{formula}{resistivity}
@@ -240,7 +284,7 @@
 \Section[
     \eng{Dipole-stuff}
     \ger{Dipol-zeug}
-    ]{dipole}
+]{dipole}
 
     \begin{formula}{poynting}
         \desc{Dipole radiation Poynting vector}{}{}

src/main.tex

@@ -1,6 +1,6 @@
 \documentclass[11pt, a4paper]{article}
 % \usepackage[utf8]{inputenc}
-\usepackage[english]{babel}
+\usepackage[german]{babel}
 \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
 % ENVIRONMENTS etc
 \usepackage{adjustbox}
@@ -15,23 +15,19 @@
 \usepackage{expl3} % switch case and other stuff
 \usepackage{substr}
 \usepackage{xcolor}
-\usepackage{float}
+% FORMATING
+\usepackage{float}  % float barrier
+\usepackage{subcaption} % subfigure
 \usepackage[hidelinks]{hyperref}
-\usepackage{subcaption}
-
 \usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
-\hypersetup{colorlinks   = true,    % Colours links instead of ugly boxes
+\usepackage{titlesec}  % colored titles
-            urlcolor     = blue,    % Colour for external hyperlinks
+\usepackage{array}
-            linkcolor    = cyan,    % Colour of internal links
+\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type
-            citecolor    = red      % Colour of citations 
+% \usepackage{sectsty}
-            }
+% TRANSLATION
 \usepackage{translations}
 \input{util/translation.tex}
-
-\usepackage{sectsty}
-\usepackage{titlesec}
 \input{util/colorscheme.tex}
-
 % GRAPHICS
 \usepackage{tikz} % drawings
 \usetikzlibrary{decorations.pathmorphing}
@@ -40,9 +36,7 @@
 % \usetikzlibrary{external}
 % \tikzexternalize[prefix=tikz_figures]
 % \tikzexternalize
-
 \usepackage{circuitikz}
-
 % SCIENCE PACKAGES
 \usepackage{mathtools}
 \usepackage{MnSymbol}  % for >>> \ggg sign
@@ -57,23 +51,21 @@
 \sisetup{separate-uncertainty}
 \sisetup{per-mode = power}
 \sisetup{exponent-product=\ensuremath{\cdot}}
-
+% DUMB STUFF
-
+% \usepackage{emoji}
+% \newcommand\temoji[1]{\text{\emoji{#1}}}
+% \def\sigma{\temoji{shark}}
+% \def\lambda{\temoji{sheep}}
+% \def\psi{\temoji{pickup-truck}}
+% \def\pi{\temoji{birthday-cake}}
+% \def\Pi{\temoji{hospital}}
+% \def\rho{\temoji{rhino}}
+% \def\nu{\temoji{unicorn}}
+% \def\mu{\temoji{mouse}}
 
 \newcommand{\TODO}[1]{{\color{bright_red}TODO:#1}}
 \newcommand{\ts}{\textsuperscript}
 
-% put an explanation above an equal sign
-% [1]: equality sign (or anything else)
-% 2: text (not in math mode!)
-\newcommand{\explUnderEq}[2][=]{%
-    \underset{\substack{\uparrow\\\mathrlap{\text{\hspace{-1em}#2}}}}{#1}}
-\newcommand{\explOverEq}[2][=]{%
-    \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}}
-    
-
-
-
 % "automate" sectioning
 % start <section>, get heading from translation, set label
 % fqname is the fully qualified name: the keys of all previous sections joined with a ':'
@@ -118,37 +110,57 @@
 
 % Make the translation of #1 a reference to a equation
 % 1: key
-\newcommand{\fqEqRef}[1]{
+\newrobustcmd{\fqEqRef}[1]{%
-    \edef\fqeqrefname{\GT{#1}}
+    % \edef\fqeqrefname{\GT{#1}}
-    \hyperref[eq:#1]{\fqeqrefname}
+    % \hyperref[eq:#1]{\fqeqrefname}
+    \hyperref[eq:#1]{\GT{#1}}%
 }
-\newcommand{\qtyRef}[1]{
+\newrobustcmd{\qtyRef}[1]{%
-    % using temp edef so that underscores in undefined trasnlation keys are printed as characters
+    \hyperref[qty:#1]{\GT{#1}}%
-    \edef\qtyrefname{\GT{qty:#1}}
+}
-    \hyperref[qty:#1]{\qtyrefname}
+\newrobustcmd{\constRef}[1]{%
+    \hyperref[const:#1]{\GT{#1}}%
 }
 % Make the translation of #1 a reference to a section
 % 1: key
-\newcommand{\fqSecRef}[1]{
+\newrobustcmd{\fqSecRef}[1]{%
-    \hyperref[sec:#1]{\GT{#1}}
+    \hyperref[sec:#1]{\GT{#1}}%
 }
 
 % \usepackage{xstring}
 
 
 \input{circuit.tex}
+\input{util/macros.tex}
+\input{util/environments.tex}  % requires util/translation.tex to be loaded first
 
-% some translations
+\def\inputOnlyFile{\relax}
+\newcommand\Input[1]{
+    \ifstrequal{\relax}{\inputOnlyFile}{
+        \input{#1}
+    }{
+        \ifstrequal{#1}{\inputOnlyFile}{
+            \input{#1}
+        }{}
+    }
+}
+
+% \includeonly{mechanics}
+% \includeonly{low_temp}
 
 \title{Formelsammlung}
 \author{Matthias Quintern}
 \date{\today}
-
-\input{util/macros.tex}
-\input{util/environments.tex}
-
-% \includeonly{computational}
 \begin{document}
+\IfFileExists{\jobname.translations.aux}{%
+  \input{\jobname.translations.aux}
+}{}
+
+
+\newwrite\translationsaux
+\immediate\openout\translationsaux=\jobname.translations.aux
+\immediate\write\translationsaux{\noexpand\def\noexpand\MYVAR{AUSM AUX}}%
+\AtEndDocument{\immediate\closeout\translationsaux}
 
 \maketitle
 \tableofcontents
@@ -159,7 +171,7 @@
 
 % \include{maths/linalg}
 % \include{maths/geometry}
-% \include{maths/analysis}
+\input{maths/analysis.tex}
 % \include{maths/probability_theory}
 
 \include{mechanics}
@@ -168,25 +180,30 @@
 
 \include{electrodynamics}
     
-\include{quantum_mechanics}
+% \include{quantum_mechanics}
-\include{atom}
+% \include{atom}
 
 \include{condensed_matter}
-\include{low_temp}
+\input{cm/charge_transport.tex}
+\input{cm/low_temp.tex}
+\input{cm/semiconductors.tex}
+% \include{cm/techniques}
 
 \include{topo}
 
-\include{quantum_computing}
+% \include{quantum_computing}
 
 \include{computational}
 
 \include{quantities}
+\include{constants}
 
 \newpage
 % \DT[english]{ttest}{TESTT EN}
 % \DT[german]{ttest}{TESTT DE}
 
-\addtranslation{english}{ttest}{JA MOIN}
+\paragraph{Testing GT, GetTranslation, IfTranslationExists, IfTranslation}
+\addtranslation{english}{ttest}{This is the english translation of \texttt{ttest}}
 \noindent
 GT: ttest = \GT{ttest}\\
 GetTranslation: ttest = \GetTranslation{ttest}\\
@@ -194,6 +211,7 @@ Is english? = \IfTranslation{english}{ttest}{yes}{no} \\
 Is german? = \IfTranslation{german}{ttest}{yes}{no} \\
 Is defined = \IfTranslationExists{ttest}{yes}{no} \\
 
+\paragraph{Testing translation keys containing macros}
 \def\ttest{NAME}
 % \addtranslation{english}{\ttest:name}{With variable}
 % \addtranslation{german}{\ttest:name}{Mit Variable}
@@ -211,17 +229,27 @@ Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
 
 % \DT[qty:test]{english}{HAHA}
 
-{blablabla \label{test}}
+\paragraph{Testing hyperrefs}
+\noindent{This text is labeled with "test" \label{test}}\\
+\hyperref[test]{This should refer to the line above}\\
+Link to quantity which is defined after the reference: \qtyRef{test}\\
+\DT[qty:test]{english}{If you read this, then the translation for qty:test was expandend!}
+Link to defined quantity: \qtyRef{mass}
+\begin{equation}
+    \label{qty:test}
+    E = mc^2
+\end{equation}
+
+\paragraph{Testing translation keys with token symbols like undescores}
+\noindent
+\GT{absolute_undefined_translation_with_underscors}\\
+\gt{relative_undefined_translation_with_underscors}\\
+\GT{absolute_undefined_translation_with_&ampersand}
+
+
 
-\hyperref[test]{TEST reference}
-\qtyRef{test}
-
-\DT[qty:test]{english}{HAHA}
 
 
-\qtyRef{mass}
-\GT{qty:#1}
-\GT{\qtyname}
 
 \newpage
 \Eng[appendix]{Appendix}

src/maths/analysis.tex

@@ -3,6 +3,13 @@
     \ger{Analysis}
     ]{cal}
 
+    % \begin{formula}{shark}
+    %     \desc{Shark-midnight formula}{\emoji{shark}-s}{}
+    %     \desc[german]{Shark-Mitternachtformel}{}{}
+    %     \eq{
+    %         \temoji{seal}_{1,2} = \frac{-\temoji{shark}\pm \sqrt{\temoji{shark}^2-4\temoji{octopus}\temoji{tropical-fish}}}{2\temoji{octopus}}
+    %     }
+    % \end{formula}
 
     \Subsection[
         \eng{Convolution}
@@ -15,7 +22,7 @@
         \begin{formula}{def}
             \desc{Definition}{}{}
             \desc[german]{Definition}{}{}
-            \eq{(f*g)(t) = f(t) * g(t) = int_{-\infty}^\infty f(\tau) g(t-\tau) \d \tau}
+            \eq{(f*g)(t) = f(t) * g(t) = \int_{-\infty}^\infty f(\tau) g(t-\tau) \d \tau}
         \end{formula}
         \begin{formula}{notation}
             \desc{Notation}{}{}
@@ -134,6 +141,12 @@
             }
         \end{formula}
 
+        \begin{formula}{delta_of_function}
+            \desc{Dirac-Delta of a function}{}{$g(x_0) = 0$}
+            \desc[german]{Dirac-Delta einer Funktion}{}{}
+            \eq{\delta(f(x)) = \frac{\delta(x-x_0)}{\abs{g'(x_0)}}}
+        \end{formula}
+
 
 \Section[
     \eng{Logarithm}
@@ -150,12 +163,23 @@
             x^{\log(y)} &= y^{\log(x)}
         }
     \end{formula}
+    \begin{formula}{intergral}
+        \desc{Integral of natural logarithm}{}{}
+        \desc[german]{Integral des natürluchen Logarithmus}{}{}
+        \eq{
+            \int \ln(x) \d x &= x \left(\ln(x) -1\right) \\
+            \int \ln(ax + b) \d x &= \frac{ax+b}{a} \left(\ln(ax + b) -1\right)
+        }
+    \end{formula}
 
 \Section[
     \eng{List of common integrals}
     \ger{Liste nützlicher Integrale}
     ]{integrals}
 
+    % Put links to other integrals here
+    \fqEqRef{cal:log:integral}
+
     \begin{formula}{spherical-coordinates}
         \desc{Spherical coordinates}{}{}
         \desc[german]{Kugelkoordinaten}{}{}
@@ -179,3 +203,4 @@
 
 
 
+

src/maths/probability_theory.tex

@@ -47,6 +47,12 @@
         \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}

src/quantities.tex

@@ -0,0 +1,77 @@
+% if this causes a compilation error, check that none of the units have been redefined
+
+\Eng[si_base_units]{SI base units}
+\Ger[si_base_units]{SI Basisgrößen}
+
+\paragraph{\GT{si_base_units}}
+
+    \begin{quantity}{time}{t}{\second}{}
+        \desc{Time}{}
+        \desc[german]{Zeit}{}
+    \end{quantity}
+
+    \begin{quantity}{Length}{l}{\m}{e}
+        \desc{Length}{}
+        \desc[german]{Länge}{}
+    \end{quantity}
+
+    \begin{quantity}{mass}{m}{\kg}{es}
+        \desc{Mass}{}
+        \desc[german]{Masse}{}
+    \end{quantity}
+
+    \begin{quantity}{temperature}{T}{\kelvin}{is}
+        \desc{Temperature}{}
+        \desc[german]{Temperatur}{}
+    \end{quantity}
+
+    \begin{quantity}{current}{I}{\ampere}{es}
+        \desc{Electric current}{}
+        \desc[german]{Elektrischer Strom}{}
+    \end{quantity}
+
+    \begin{quantity}{amount}{n}{\mol}{es}
+        \desc{Amount of substance}{}
+        \desc[german]{Stoffmenge}{}
+    \end{quantity}
+
+    \begin{quantity}{luminous_intensity}{I_\text{V}}{\candela}{s}
+        \desc{Luminous intensity}{}
+        \desc[german]{Lichtstärke}{}
+    \end{quantity}
+
+\paragraph{\GT{other}}
+    \begin{quantity}{volume}{V}{\m^d}{}
+        \desc{Volume}{$d$ dimensional Volume}
+        \desc[german]{Volumen}{$d$ dimensionales Volumen}
+    \end{quantity}
+
+    \begin{quantity}{force}{\vec{F}}{\newton=\kg\m\per\second^2}{ev}
+        \desc{Force}{}
+        \desc[german]{Kraft}{}
+    \end{quantity}
+
+    \begin{quantity}{spring_constant}{k}{\newton\per\m=\kg\per\second^2}{s}
+        \desc{Spring constant}{}
+        \desc[german]{Federkonstante}{}
+    \end{quantity}
+
+    \begin{quantity}{velocity}{\vec{v}}{\m\per\s}{v}
+        \desc{Velocity}{}
+        \desc[german]{Geschwindigkeit}{}
+    \end{quantity}
+
+    \begin{quantity}{torque}{\tau}{\newton\m=\kg\m^2\per\s^2}{v}
+        \desc{Torque}{}
+        \desc[german]{Drehmoment}{}
+    \end{quantity}
+
+    \begin{quantity}{heat_capacity}{C}{\joule\per\kelvin}{}
+        \desc{Heat capacity}{}
+        \desc[german]{Wärmekapazität}{}
+    \end{quantity}
+
+    \begin{quantity}{charge}{q}{\coulomb=\ampere\s}{}
+        \desc{Charge}{}
+        \desc[german]{Ladung}{}
+    \end{quantity}

src/quantum_mechanics.tex

@@ -53,6 +53,43 @@
                 \eq{\hat{A} = \hat{A}^\dagger}
             \end{formula}
 
+            \Subsubsection[
+                \eng{Measurement}
+                \ger{Messung}
+            ]{measurement}  
+                \begin{ttext}
+                    \eng{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}
+                    \ger{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}
+                \end{ttext}
+                \begin{formula}{name}
+                    \desc{Measurement probability}{Probability to measure $\psi$ in state $\lambda$}{}
+                    \desc[german]{Messwahrscheinlichkeit}{Wahrscheinlichkeit, $\psi$ im Zustand $\lambda$ zu messen}{}
+                    \eq{p(\lambda) = \braket{\psi|\hat{P}_\lambda|\psi}}
+                \end{formula}
+                \begin{formula}{state_after}
+                    \desc{State after measurement}{}{}
+                    \desc[german]{Zustand nach der Messung}{}{}
+                    \eq{\ket{\psi}_\text{post} = \frac{1}{\sqrt{p(\lambda)}}\hat{P}_\lambda \ket{\psi}}
+                \end{formula}
+                
+            
+            \Subsubsection[
+                \eng{Pauli matrices}
+                \ger{Pauli-Matrizen}
+            ]{pauli_matrices}
+                \begin{formula}{pauli_matrices}
+                    \desc{Pauli matrices}{}{}
+                    \desc[german]{Pauli Matrizen}{}{}
+                    \eqAlignedAt{2}{
+                        \sigma_x &= \sigmaxmatrix &&= \sigmaxbraket \label{eq:pauli_x} \\
+                        \sigma_y &= \sigmaymatrix &&= \sigmaybraket \label{eq:pauli_y} \\
+                        \sigma_z &= \sigmazmatrix &&= \sigmazbraket \label{eq:pauli_z}
+                    }
+                \end{formula}
+            % $\sigma_x$ NOT
+            % $\sigma_y$ PHASE
+            % $\sigma_z$ Sign
+
         \Subsection[
             \ger{Wahrscheinlichkeitstheorie}
             \eng{Probability theory}
@@ -85,23 +122,6 @@
                 }
             \end{formula}
 
-            \Subsubsection[
-                \eng{Pauli matrices}
-                \ger{Pauli-Matrizen}
-            ]{pauli_matrices}
-                \begin{formula}{pauli_matrices}
-                    \desc{Pauli matrices}{}{}
-                    \desc[german]{Pauli Matrizen}{}{}
-                    \eqAlignedAt{2}{
-                        \sigma_x &= \sigmaxmatrix &&= \sigmaxbraket \label{eq:pauli_x} \\
-                        \sigma_y &= \sigmaymatrix &&= \sigmaybraket \label{eq:pauli_y} \\
-                        \sigma_z &= \sigmazmatrix &&= \sigmazbraket \label{eq:pauli_z}
-                    }
-                \end{formula}
-            % $\sigma_x$ NOT
-            % $\sigma_y$ PHASE
-            % $\sigma_z$ Sign
-
 
         \Subsection[
             \eng{Commutator}

src/readme.md

@@ -27,7 +27,11 @@ Functions that create a hyperlink (and use the translation of the target element
 
 
 ## Multilanguage
-All text should be defined as a translation (`translations` package, see `util/translation.tex`) and then used using the `gt` or `GT` macros.
+All text should be defined as a translation (`translations` package, see `util/translation.tex`).
+Use `\dt` or `\DT` or the the shorthand language commands `\eng`, `\Eng` etc. to define translations.
+These commands also be write the translations to an auxiliary file, which is read after the document begins.
+This means (on subsequent compilations) that the translation can be resolved before they are defined.  
+Use the `gt` or `GT` macros to retrieve translations.
 The english translation of any key must be defined, because it will also be used as fallback.
 
 Lower case macros are relative to the current `fqname`, while upper case macros are absolute.

src/statistical_mechanics.tex

@@ -5,12 +5,12 @@
 
     \begin{ttext}
         \eng{
-            \textbf{Intensive quantities:} Additive for subsystems (system size dependent): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
+            \textbf{Extensive quantities:} Additive for subsystems (system size dependent): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
-            \textbf{Extensive quantities:} Independent of system size, ratio of two intensive quantities
+            \textbf{Intensive quantities:} Independent of system size, ratio of two extensive quantities
         }
         \ger{
-            \textbf{Intensive Größen:} Additiv für Subsysteme (Systemgrößenabhänig): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
+            \textbf{Extensive Größen:} Additiv für Subsysteme (Systemgrößenabhänig): $S(\lambda E, \lambda V, \lambda N)  = \lambda S(E, V, N)$\\
-            \textbf{Extensive Größen:} Unabhängig der Systemgröße, Verhältnis zweier intensiver Größen
+            \textbf{Intensive Größen:} Unabhängig der Systemgröße, Verhältnis zweier extensiver Größen
         }
     \end{ttext}
 
@@ -660,7 +660,7 @@
         \eq{
             pV &= \kB T \ln Z_g \\
             \shortintertext{\GT{after} \GT{td:real_gas:virial}}
-               &= N \kB T \left[1 \mp \frac{\lambda^3}{2^{5/2} g v} + \Order\left(\left(\frac{\lambda^3}{v}\right)^2\right)\right]
+               &= N \kB T \left[1 \mp \frac{\lambda^3}{2^{5/2} g v} + \Order{\left(\frac{\lambda^3}{v}\right)^2}\right]
         }
     \end{formula}
     \begin{formula}{relevance}

src/util/colorscheme.tex

@@ -1,4 +1,4 @@
-% Define Gruvbox colors
+% Gruvbox colors
 \definecolor{dark0_hard}{HTML}{1d2021}
 \definecolor{dark0}{HTML}{282828}
 \definecolor{dark0_soft}{HTML}{32302f}
@@ -36,13 +36,13 @@
 \definecolor{faded_aqua}{HTML}{427b58}
 \definecolor{faded_orange}{HTML}{af3a03}
 
-% Use Gruvbox colors for various elements
+% Dark mode
 % \pagecolor{light0_hard}
 % \color{dark0_hard}
 % \pagecolor{dark0_hard}
 % \color{light0_hard}
 
-% Section headings in bright colors
+% section headings in bright colors, \titleformat from titlesec package
 \titleformat{\section}
   {\color{neutral_purple}\normalfont\Large\bfseries}
   {\color{neutral_purple}\thesection}{1em}{}
@@ -63,10 +63,9 @@
   {\color{neutral_purple}\normalfont\normalsize\bfseries}
   {\color{neutral_purple}\thesubparagraph}{1em}{}
 
-% Links in neutral colors
 \hypersetup{
   colorlinks=true,
-  linkcolor=neutral_red,
+  linkcolor=neutral_purple,
   citecolor=neutral_green,
   filecolor=neutral_blue,
   urlcolor=neutral_orange

src/util/environments.tex

@@ -7,7 +7,7 @@
     \edef\realfqname{\fqname}
     \edef\fqname{\fqname:#1}
 }{
-    \expandafter\GT\expandafter{\fqname} \\
+    \expandafter\GT\expandafter{\fqname}% \\
     \edef\fqname{\realfqname}
 }
 
@@ -149,7 +149,7 @@
     % 4: definitions/links
     \newcommand{\desc}[4][english]{
         % language, name, description, definitions
-        \dt[#1]{##1}{##2}
+        \ifblank{##2}{}{\dt[#1]{##1}{##2}}
         \ifblank{##3}{}{\dt[#1_desc]{##1}{##3}}
         \ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
     }
@@ -211,13 +211,114 @@
         tex.print(result)
     end
 }
+
+% 1: key
+% 2: symbol
+% 3: value
+% 4: units
+% 5: exp or def
+% \newenvironment{constant}[5]{
+%     % key, symbol, si unit(s), comment (key to global translation)
+%     \newcommand{\desc}[3][english]{
+%         % language, name, description
+%         % \DT[qty:#1]{##1}{##2}
+%         % \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
+%         \ifblank{##2}{}{\DT[const:#1]{##1}{##2}}
+%         \ifblank{##3}{}{\DT[const:#1_desc]{##1}{##3}}
+%     }
+%     % TODO put these in long term key - value storage for generating a full table and global referenes \constRef
+%     % for references, there needs to be a label somwhere
+%     \edef\constName{const:#1}
+%     \edef\constDesc{const:#1_desc}
+%     \def\constSymbol{#2}
+%     \edef\constValue{#3}
+%     \def\constUnits{#4}
+%     \edef\constExpOrDef{const:#5}
+% }
+% {
+%     \NameLeftContentRight{\constName}{
+%         \begingroup
+%             Symbol: $\constSymbol$
+%             \IfTranslationExists{\constDesc}{
+%                 \\Description: \GT{\constDesc}
+%             }{}
+%             \\Value: $\constValue$
+%             \\Unit: $\directlua{split_and_print_units([[\constUnits]])}$
+%             \GT{\constExpOrDef}
+%             \label{\constName}
+%         \endgroup
+%     }
+%     \ignorespacesafterend
+
+%     % for TOC
+%     \refstepcounter{constant}%
+%     % \addquantity{\expandafter\gt\expandafter{\qtyname}}%
+%     % \noindent\textbf{My Environment \themyenv: #1}\par%
+% }
+\newcounter{constant}
+\newenvironment{constant}[3]{
+    % [1]: language
+    % 2: name
+    % 3: description
+    % 4: definitions/links
+    \newcommand{\desc}[4][english]{
+        % language, name, description, definitions
+        \ifblank{##2}{}{\DT[const:#1]{##1}{##2}}
+        \ifblank{##3}{}{\DT[const:#1_desc]{##1}{##3}}
+        \ifblank{##4}{}{\DT[const:#1_defs]{##1}{##4}}
+    }
+    \directlua{
+        constVals = {}
+        constUnits = {}
+    }
+    % 1: equation for align environment
+    \newcommand{\val}[2]{
+        \directlua{
+            %--table.insert(constVals, "LOL")
+            table.insert(constVals, [[##1]])
+            table.insert(constUnits, [[##2]])
+            %--table.insert(constUnits, "\luaescapestring{##2}")
+        }
+        \def\constValue{##1}
+        \def\constUnit{##2}
+    }
+    \edef\constName{const:#1}
+    \edef\constDesc{const:#1_desc}
+    \def\constSymbol{#2}
+    \edef\constExpOrDef{\GT{const:#3}}
+}{
+    \NameLeftContentRight{\constName}{
+        \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
+% 2: symbol
+% 3: units
+% 4: comment key to translation
 \newenvironment{quantity}[4]{
-    % key, symbol, si unit(s), comment (key to global translation)
-    \newcommand{\desc}[3][english]{
     % language, name, description
-        % \DT[qty:#1]{##1}{##2}
+    \newcommand{\desc}[3][english]{
-        % \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
+        \ifblank{##2}{}{\DT[qty:#1]{##1}{##2}}
-        \DT[qty:#1]{##1}{##2}
         \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
     }
     % TODO put these in long term key - value storage for generating a full table and global referenes \qtyRef
@@ -227,6 +328,7 @@
     \def\qtysymbol{#2}
     \def\qtyunits{#3}
     \edef\qtycomment{#4}
+    % Unit: $\directlua{split_and_print_units([[\m\per\kg]])}$
 }
 {
     \NameLeftContentRight{\qtyname}{
@@ -238,7 +340,7 @@
             \\Unit: $\directlua{split_and_print_units([[\qtyunits]])}$
             \expandafter\IfTranslationExists\expandafter\qtycomment{
                 \\Comment: \GT\qtycomment
-            }{\\No comment \color{gray}}
+            }{}%{\\No comment \color{gray}}
             \label{\qtyname}
         \endgroup
     }
@@ -246,12 +348,10 @@
 
     % for TOC
     \refstepcounter{quantity}%
-    \addquantity{\expandafter\gt\expandafter{\qtyname}}%
+    % \addquantity{\expandafter\gt\expandafter{\qtyname}}%
     % \noindent\textbf{My Environment \themyenv: #1}\par%
 }
 \newcounter{quantity}
-\Eng[list_of_quantitites]{List of quantitites}
-\Ger[list_of_quantitites]{Liste von Größen}
 \newcommand{\listofquantities}{%
     \section*{\GT{list_of_quantitites}}%
     \addcontentsline{toc}{section}{\GT{list_of_quantitites}}%

src/util/macros.tex

@@ -1,38 +1,108 @@
 \def\gooditem{\item[{$\color{neutral_red}\bullet$}]}
 \def\baditem{\item[{$\color{neutral_green}\bullet$}]}
 
+% put an explanation above an equal sign
+% [1]: equality sign (or anything else)
+% 2: text (not in math mode!)
+\newcommand{\explUnderEq}[2][=]{%
+    \underset{\substack{\uparrow\\\mathrlap{\text{\hspace{-1em}#2}}}}{#1}}
+\newcommand{\explOverEq}[2][=]{%
+    \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}}
+
+% COMMON SYMBOLS WITH SUPER/SUBSCRIPTS, VECTOR ARROWS ETC.
 \def\Grad{\vec{\nabla}}
 \def\Div{\vec{\nabla} \cdot}
 \def\Rot{\vec{\nabla} \times}
-% common vectors
 \def\vecr{\vec{r}}
 \def\vecx{\vec{x}}
-
 \def\kB{k_\text{B}}
 \def\EFermi{E_\text{F}}
-
+\def\Evalence{E_\text{v}}
+\def\Econd{E_\text{c}}
+\def\Egap{E_\text{gap}}
 \def\masse{m_\textrm{e}}
+\def\Four{\mathcal{F}}  % Fourier transform
+\def\Lebesgue{\mathcal{L}}  % Lebesgue
+\def\O{\mathcal{O}} 
+\def\PhiB{\Phi_\text{B}}
+\def\PhiE{\Phi_\text{E}}
 
+
+% SYMBOLS
 \def\R{\mathbb{R}}
 \def\C{\mathbb{C}}
 \def\Z{\mathbb{Z}}
 \def\N{\mathbb{N}}
+% caligraphic
+\def\calE{\mathcal{E}}
+% upright
+\def\txA{\text{A}}
+\def\txB{\text{B}}
+\def\txC{\text{C}}
+\def\txD{\text{D}}
+\def\txE{\text{E}}
+\def\txF{\text{F}}
+\def\txG{\text{G}}
+\def\txH{\text{H}}
+\def\txI{\text{I}}
+\def\txJ{\text{J}}
+\def\txK{\text{K}}
+\def\txL{\text{L}}
+\def\txM{\text{M}}
+\def\txN{\text{N}}
+\def\txO{\text{O}}
+\def\txP{\text{P}}
+\def\txQ{\text{Q}}
+\def\txR{\text{R}}
+\def\txS{\text{S}}
+\def\txT{\text{T}}
+\def\txU{\text{U}}
+\def\txV{\text{V}}
+\def\txW{\text{W}}
+\def\txX{\text{X}}
+\def\txY{\text{Y}}
+\def\txZ{\text{Z}}
 
-\def\Four{\mathcal{F}}  % Fourier transform
+\def\txa{\text{a}}
-\def\Lebesgue{\mathcal{L}}  % Lebesgue
+\def\txb{\text{b}}
-\def\Order{\mathcal{O}} 
+\def\txc{\text{c}}
-
+\def\txd{\text{d}}
+\def\txe{\text{e}}
+\def\txf{\text{f}}
+\def\txg{\text{g}}
+\def\txh{\text{h}}
+\def\txi{\text{i}}
+\def\txj{\text{j}}
+\def\txk{\text{k}}
+\def\txl{\text{l}}
+\def\txm{\text{m}}
+\def\txn{\text{n}}
+\def\txo{\text{o}}
+\def\txp{\text{p}}
+\def\txq{\text{q}}
+\def\txr{\text{r}}
+\def\txs{\text{s}}
+\def\txt{\text{t}}
+\def\txu{\text{u}}
+\def\txv{\text{v}}
+\def\txw{\text{w}}
+\def\txx{\text{x}}
+\def\txy{\text{y}}
+\def\txz{\text{z}}
 % complex, may be changed later to idot or upright...
 \def\I{i}
 
+% SPACES
 \def\sdots{\,\dots\,}
 \def\qdots{\quad\dots\quad}
 \def\qRarrow{\quad\Rightarrow\quad}
 
+% DELIMITERS
 \DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
 \DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
 \DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
 
+% OPERATORS
 \DeclareMathOperator{\e}{e}
 \DeclareMathOperator{\T}{T}  % transposed
 \DeclareMathOperator{\sgn}{sgn}
@@ -44,7 +114,6 @@
 % diff, for integrals and stuff
 % \DeclareMathOperator{\dd}{d}
 \renewcommand*\d{\mathop{}\!\mathrm{d}}
-
 % functions with paranthesis
 \newcommand\CmdWithParenthesis[2]{
     #1\left(#2\right)
@@ -52,3 +121,4 @@
 \newcommand\Exp[1]{\CmdWithParenthesis{\exp}{#1}}
 \newcommand\Sin[1]{\CmdWithParenthesis{\sin}{#1}}
 \newcommand\Cos[1]{\CmdWithParenthesis{\cos}{#1}}
+\newcommand\Order[1]{\CmdWithParenthesis{\mathcal{O}}{#1}}

src/util/translation.tex

@@ -15,19 +15,29 @@
 % expandafter required because the translation commands dont expand anything
 % shortcuts for translations
 % 1: key
-\newcommand{\gt}[1]{\expandafter\GetTranslation\expandafter{\fqname:#1}}
-\newcommand{\GT}[1]{\expandafter\GetTranslation\expandafter{#1}}
 
-\newcommand{\IfTranslationExists}[1]{
+\newcommand{\IfTranslationExists}[1]{%
-    % \IfTranslation{english}{#1}%{#2}{#3}  % only check english. All translations must be defined for english
+    % only check english. All translations must be defined for english
-    % \edef\arg{#1}
+    \def\tempiftranslation{\IfTranslation{english}}%
-    \def\tempiftranslation{\IfTranslation{english}}
+    \expandafter\tempiftranslation\expandafter{#1}%
-    \expandafter\tempiftranslation\expandafter{#1}  % only check english. All translations must be defined for english
-    % {S\color{red}\arg END}
-    % \IfTranslation{english}{\arg}  % only check english. All translations must be defined for english
 }
-\newcommand{\iftranslation}[3]{
+\newcommand{\iftranslation}[3]{%
-    \IfTranslationExists{\fqname:#1}{#2}{#3}
+    \IfTranslationExists{\fqname:#1}{#2}{#3}%
+}
+
+\newcommand{\gt}[1]{%
+    \iftranslation{#1}{%
+        \expandafter\GetTranslation\expandafter{\fqname:#1}%
+    }{%
+        \fqname:\detokenize{#1}%
+    }%
+}
+\newrobustcmd{\GT}[1]{%\expandafter\GetTranslation\expandafter{#1}}
+    \IfTranslationExists{#1}{%
+        \expandafter\GetTranslation\expandafter{#1}%
+    }{%
+        \detokenize{#1}%
+    }%
 }
 
 % Define a translation and also make the fallback if it is the english translation
@@ -35,7 +45,10 @@
 \newcommand{\addtranslationcustom}[3]{
     \ifstrequal{#1}{english}{
         \addtranslationfallback{#2}{#3}
+        \immediate\write\translationsaux{\noexpand\addtranslationfallback{#2}{\detokenize{#3}}}
+        % \immediate\write\translationsaux{\noexpand\addtranslationfallback{#2}{{#3}}}%
     }{}
+    \immediate\write\translationsaux{\noexpand\addtranslation{#1}{#2}{\detokenize{#3}}}
     \addtranslation{#1}{#2}{#3}
 }
 
@@ -46,9 +59,11 @@
         % hack because using expandafter on the second arg didnt work
         \def\tempaddtranslation{\addtranslationcustom{#2}}
         \ifstrequal{#1}{\fqname}{
-            \expandafter\tempaddtranslation\expandafter{\fqname}{#3}
+            % \expandafter\tempaddtranslation\expandafter{\fqname}{#3}
+            \addtranslationcustom{#2}{#1}{#3}
         }{
-            \expandafter\tempaddtranslation\expandafter{\fqname:#1}{#3}
+            \addtranslationcustom{#2}{\fqname:#1}{#3}
+            % \expandafter\tempaddtranslation\expandafter{\fqname:#1}{#3}
         }
     }
 }
@@ -59,9 +74,11 @@
         % hack because using expandafter on the second arg didnt work
         \def\tempaddtranslation{\addtranslationcustom{#2}}
         \ifstrequal{#1}{dummy}{
-            \expandafter\tempaddtranslation\expandafter{\fqname}{#3}
+            % \expandafter\tempaddtranslation\expandafter{\fqname}{#3}
+            \addtranslationcustom{#2}{\fqname}{#3}
         }{
-            \expandafter\tempaddtranslation\expandafter{#1}{#3}
+            % \expandafter\tempaddtranslation\expandafter{#1}{#3}
+            \addtranslationcustom{#2}{#1}{#3}
         }
     }
 }

src/util/translations.tex

@@ -1,9 +1,37 @@
+% WORDS
+\Eng[even]{even}
+\Ger[even]{gerade}
+
+\Eng[odd]{odd}
+\Ger[odd]{ungerade}
+
+% SCIENTIFIC
 \Eng[angle_deg]{Degree}
 \Ger[angle_deg]{Grad}
 
 \Eng[angle_rad]{Radian}
 \Ger[angle_rad]{Rad}
 
+\Eng[time]{Time}
+\Ger[time]{Zeit}
+
+\Eng[ensemble]{Ensemble}
+\Ger[ensemble]{Ensemble}
+
+\Eng[area]{area}
+\Ger[area]{Fläche}
+
+% SPECIFIC
+\Eng[diamond]{Diamond}
+\Ger[diamond]{Diamant}
+
+% FORMATING
+\Eng[list_of_quantitites]{List of quantitites}
+\Ger[list_of_quantitites]{Liste von Größen}
+
+\Eng[other]{Others}
+\Ger[other]{Sonstige}
+
 \Eng[see_also]{See also}
 \Ger[see_also]{Siehe auch}
 
@@ -13,15 +41,8 @@
 \Eng[and_therefore_also]{and therefore also}
 \Ger[and_therefore_also]{und damit auch}
 
-\Eng[time]{Time}
+\Eng[const:exp]{Experimental value}
-\Ger[time]{Zeit}
+\Ger[const:exp]{Experimenteller Wert}
-
+\Eng[const:def]{Defined value}
-\Eng[ensemble]{Ensemble}
+\Ger[const:def]{Definierter Wert}
-\Ger[ensemble]{Ensemble}
-
-\Eng[even]{even}
-\Ger[even]{gerade}
-
-\Eng[odd]{odd}
-\Ger[odd]{ungerade}