Refactor formula

Makefile

@@ -20,12 +20,12 @@ release: german english
 # Default target
 english: 
 	sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[english]{babel}/' $(MAIN_TEX)
-	-cd $(SRC_DIR) && latexmk -g
+	-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
 	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
+	-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
 	mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_formelsammlung.pdf
 
 # Clean auxiliary and output files

src/.latexmkrc

@@ -4,7 +4,8 @@ $out_dir = '../out';
 
 # Set lualatex as the default engine
 $pdf_mode = 1; # Enable PDF generation mode
-$pdflatex = 'lualatex  -interaction=nonstopmode -shell-escape'
+# $pdflatex = 'lualatex --interaction=nonstopmode --shell-escape'
+$lualatex = 'lualatex %O --interaction=nonstopmode --shell-escape %S'
 
 # Additional options for compilation
     # '-verbose',

src/ch/ch.tex

@@ -21,9 +21,3 @@
             }
         \end{formula}
 
-    \Section[
-        \eng{List of elements}
-        \ger{Liste der Elemente}
-    ]{elements}
-        \printAllElements
-

src/cm/charge_transport.tex

@@ -26,6 +26,7 @@
     \begin{formula}{scattering_time}
         \desc{Scattering time}{Momentum relaxation time}{}
         \desc[german]{Streuzeit}{}{}
+        \quantity{\tau}{\s}{s}
         \ttxt{
             \eng{$\tau$\\ the average time between scattering events weighted by the characteristic momentum change cause by the scattering process.}
         }
@@ -33,6 +34,7 @@
     \begin{formula}{current_density}
         \desc{Current density}{Ohm's law}{$n$ charge particle density}
         \desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte}
+        \quantity{\vec{j}}{\ampere\per\m^2}{v}
         \eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{\E}}
     \end{formula}
     \begin{formula}{conductivity}
@@ -50,8 +52,8 @@
         \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{Electrical current density}{}{}
-        \desc[german]{Stromdichte}{}{}
+        \desc[german]{Elektrische Stromdichte}{}{}
         \eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
     \end{formula}
     \TODO{The formula for the conductivity is the same as in the drude model?}
@@ -83,3 +85,11 @@
             I_\text{T} = \frac{2e}{h} \int_{U_\txL}^\infty \left(f(E, \mu_\txL) -f(E, \mu_\txR)\right) T(E) \d E
         }
     \end{formula}
+
+    \begin{formula}{continuity}
+        \desc{Charge continuity equation}{Electric charge can only change by the amount of electric current}{\QtyRef{charge_density}, \QtyRef{current_density}}
+        \desc[german]{Kontinuitätsgleichung der Ladung}{Elektrische Ladung kann sich nur durch die Stärke des Stromes ändern}{}
+        \eq{
+            \pdv{\rho}{t} = - \nabla \vec{j}
+        }
+    \end{formula}

src/cm/cm.tex

@@ -2,322 +2,4 @@
     \eng{Condensed matter physics}
     \ger{Festkörperphysik}
 ]{cm}
-    \TODO{Bonds, hybridized orbitals, tight binding}
+    \TODO{Bonds, hybridized orbitals}
-\Section[
-    \eng{Bravais lattice}
-    \ger{Bravais-Gitter}
-]{bravais}
-
-    % \begin{ttext}
-    %     \eng{
-
-    %     }
-    %     \ger{
-
-    %     }
-    % \end{ttext}
-
-    \eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
-    \ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}
-
-    \eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
-    \ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}
-
-    \Eng[lattice_system]{Lattice system}
-    \Ger[lattice_system]{Gittersystem}
-    \Eng[crystal_family]{Crystal system}
-    \Ger[crystal_family]{Kristall-system}
-    \Eng[point_group]{Point group}
-    \Ger[point_group]{Punktgruppe}
-    \eng[bravais_lattices]{Bravais lattices}
-    \ger[bravais_lattices]{Bravais Gitter}
-
-    \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
-    \renewcommand\tabularxcolumn[1]{m{#1}}
-    \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
-    \begin{table}[H]
-        \centering
-        \expandafter\caption\expandafter{\gt{bravais_table2}}
-        \label{tab:bravais2}
-    
-        \begin{adjustbox}{width=\textwidth}
-        \begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
-            \hline
-            \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
-                                                 & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
-            \GT{monoclinic} (m) & $\text{C}_\text{2}$   & \bvimg{mp} & \\ \hline
-            \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
-            \GT{tetragonal} (t) & $\text{D}_\text{4}$   & \bvimg{tp} & \\ \hline
-            \GT{hexagonal} (h) & $\text{D}_\text{6}$    & \bvimg{hp} & \\ \hline
-        \end{tabularx}
-        \end{adjustbox}
-    \end{table}
-    
-
-
-    \begin{table}[H]
-        \centering
-        \caption{\gt{bravais_table3}}
-        \label{tab:bravais3}
-    
-        % \newcolumntype{g}{>{\columncolor[]{0.8}}}
-        \begin{adjustbox}{width=\textwidth}
-            % \begin{tabularx}{\textwidth}{|c|}
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            % \end{tabularx}
-            % \begin{tabular}{|c|}
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
-            % \end{tabular}
-            % \\
-        \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
-            \hline
-            \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
-                                                 & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
-            \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP}  &  &  &  \\  \hline
-            \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS}  &  &  \\ \hline
-            \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
-            \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} &  & \bvimg{tI} & \\ \hline
-            \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} &  &  & \\ \cline{2-7}
-             & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} &  &  & \\ \hline
-            \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} &  & \bvimg{cI} & \bvimg{cF} \\ \hline
-        \end{tabularx}
-        \end{adjustbox}
-    \end{table}
-
-    \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}{}{Miller family: planes that are equivalent due to crystal symmetry}
-        \desc[german]{Millersche Indizes}{}{}
-        \eq{
-            (hkl) & \text{\GT{plane}}\\
-            [hkl] & \text{\GT{direction}}\\
-            \{hkl\} & \text{\GT{millerFamily}}
-        }
-    \end{formula}
-    
-
-\Section[
-    \eng{Reciprocal lattice}
-    \ger{Reziprokes Gitter}
-    ]{reci}
-    \begin{ttext}
-        \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
-        \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
-    \end{ttext}
-
-    \begin{formula}{vectors}
-        \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
-        \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
-        \eq{
-            \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
-            \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
-            \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
-        }
-    \end{formula}
-
-    \Subsection[
-        \eng{Scattering processes}
-        \ger{Streuprozesse}
-    ]{scatter}
-        \begin{formula}{matthiessen}
-            \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{$\mu$ mobility, $\tau$ scattering time}
-            \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{$\mu$ Moblitiät, $\tau$ Streuzeit}
-            \eq{
-                \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
-                \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
-            }
-        \end{formula}
-    
-
-\Section[
-    \eng{Free electron gas}
-    \ger{Freies Elektronengase}
-]{free_e_gas}
-    \begin{ttext}
-        \eng{Assumptions: electrons can move freely and independent of each other.}
-        \ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.}
-    \end{ttext}
-
-    \begin{formula}{drift_velocity}
-        \desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity}
-        \desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit}
-        \eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}}
-    \end{formula}
-
-    \begin{formula}{mean_free_time}
-        \desc{Mean free time}{}{}
-        \desc[german]{Streuzeit}{}{}
-        \eq{\tau}
-    \end{formula}
-
-    \begin{formula}{mean_free_path}
-        \desc{Mean free path}{}{}
-        \desc[german]{Mittlere freie Weglänge}{}{}
-        \eq{\ell = \braket{v} \tau}
-    \end{formula}
-
-    \begin{formula}{mobility}
-        \desc{Electrical mobility}{}{$q$ charge, $m$ mass}
-        \desc[german]{Beweglichkeit}{}{$q$ Ladung, $m$ Masse}
-        \eq{\mu = \frac{q \tau}{m}}
-    \end{formula}
-
-    \Subsection[
-        \eng{2D electron gas}
-        \ger{2D Elektronengas}
-    ]{2deg}
-
-        \begin{ttext}
-            \eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
-            \ger{
-                Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird.
-            }
-        \end{ttext}
-        \begin{formula}{confinement_energy}
-            \desc{Confinement energy}{Raises ground state energy}{}
-            \desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{}
-            \eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}}
-        \end{formula}
-
-        \Eng[plain_wave]{plain wave}
-        \Ger[plain_wave]{ebene Welle}
-        \begin{formula}{energy}
-            \desc{Energy}{}{}
-            \desc[german]{Energie}{}{}
-            \eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}}
-        \end{formula}
-
-    \Subsection[
-        \eng{1D electron gas / quantum wire}
-        \ger{1D Eleltronengas / Quantendraht}
-    ]{1deg}
-
-        \begin{formula}{energy}
-            \desc{Energy}{}{}
-            \desc[german]{Energie}{}{}
-            \eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2}
-        \end{formula}
-        \TODO{condunctance}
-        
-    \Subsection[
-        \eng{0D electron gas / quantum dot}
-        \ger{0D Elektronengase / Quantenpunkt}
-    ]{0deg}
-
-        \TODO{TODO}
-
-\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/crystal.tex

@@ -0,0 +1,199 @@
+\Section[
+    \eng{Crystals}
+    \ger{Kristalle}
+]{crystal}
+\Subsection[
+    \eng{Bravais lattice}
+    \ger{Bravais-Gitter}
+]{bravais}
+    \eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
+    \ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}
+
+    \eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
+    \ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}
+
+    \Eng[lattice_system]{Lattice system}
+    \Ger[lattice_system]{Gittersystem}
+    \Eng[crystal_family]{Crystal system}
+    \Ger[crystal_family]{Kristall-system}
+    \Eng[point_group]{Point group}
+    \Ger[point_group]{Punktgruppe}
+    \eng[bravais_lattices]{Bravais lattices}
+    \ger[bravais_lattices]{Bravais Gitter}
+
+    \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
+    \renewcommand\tabularxcolumn[1]{m{#1}}
+    \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
+    \begin{table}[H]
+        \centering
+        \expandafter\caption\expandafter{\gt{bravais_table2}}
+        \label{tab:bravais2}
+    
+        \begin{adjustbox}{width=\textwidth}
+        \begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
+            \hline
+            \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
+                                                 & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
+            \GT{monoclinic} (m) & $\text{C}_\text{2}$   & \bvimg{mp} & \\ \hline
+            \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
+            \GT{tetragonal} (t) & $\text{D}_\text{4}$   & \bvimg{tp} & \\ \hline
+            \GT{hexagonal} (h) & $\text{D}_\text{6}$    & \bvimg{hp} & \\ \hline
+        \end{tabularx}
+        \end{adjustbox}
+    \end{table}
+    
+
+
+    \begin{table}[H]
+        \centering
+        \caption{\gt{bravais_table3}}
+        \label{tab:bravais3}
+    
+        % \newcolumntype{g}{>{\columncolor[]{0.8}}}
+        \begin{adjustbox}{width=\textwidth}
+            % \begin{tabularx}{\textwidth}{|c|}
+            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
+            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
+            % \end{tabularx}
+            % \begin{tabular}{|c|}
+            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
+            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
+            % \end{tabular}
+            % \\
+        \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
+            \hline
+            \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
+                                                 & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
+            \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP}  &  &  &  \\  \hline
+            \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS}  &  &  \\ \hline
+            \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
+            \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} &  & \bvimg{tI} & \\ \hline
+            \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} &  &  & \\ \cline{2-7}
+             & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} &  &  & \\ \hline
+            \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} &  & \bvimg{cI} & \bvimg{cF} \\ \hline
+        \end{tabularx}
+        \end{adjustbox}
+    \end{table}
+
+    \begin{formula}{lattice_constant}
+        \desc{Lattice constant}{Parameter (length or angle) describing the smallest unit cell}{}
+        \desc[german]{Gitterkonstante}{Parameter (Länge oder Winkel) der die Einheitszelle beschreibt}{}
+        \quantity{a}{}{s}
+    \end{formula}
+
+    \begin{formula}{lattice_vector}
+        \desc{Lattice vector}{}{$n_i \in \Z$}
+        \desc[german]{Gittervektor}{}{}
+        \quantity{\vec{R}}{}{\angstrom}
+        \eq{\vec{R} = n_1 \vec{a_1} + n_2 \vec{a_2} + n_3 \vec{a_3}}
+    \end{formula}
+
+    \TODO{primitive unit cell: contains one lattice point}\\
+    \begin{formula}{miller}
+        \desc{Miller index}{}{Miller family: planes that are equivalent due to crystal symmetry}
+        \desc[german]{Millersche Indizes}{}{}
+        \eq{
+            (hkl) & \text{\GT{plane}}\\
+            [hkl] & \text{\GT{direction}}\\
+            \{hkl\} & \text{\GT{millerFamily}}
+        }
+    \end{formula}
+    
+
+\Subsection[
+    \eng{Reciprocal lattice}
+    \ger{Reziprokes Gitter}
+]{reci}
+    \begin{ttext}
+        \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
+        \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
+    \end{ttext}
+
+    \begin{formula}{vectors}
+        \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
+        \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
+        \eq{
+            \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
+            \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
+            \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
+        }
+    \end{formula}
+    \begin{formula}{reciprocal_lattice_vector}
+        \desc{Reciprokal attice vector}{}{$n_i \in \Z$}
+        \desc[german]{Reziproker Gittervektor}{}{}
+        \quantity{\vec{G}}{}{\angstrom}
+        \eq{\vec{G}_{{hkl}} = h \vec{b_1} + k \vec{b_2} + l \vec{b_3}}
+    \end{formula}
+
+    \Subsection[
+        \eng{Scattering processes}
+        \ger{Streuprozesse}
+    ]{scatter}
+        \begin{formula}{matthiessen}
+            \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{\QtyRef{mobility}, \QtyRef{scattering_time}}
+            \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{}
+            \eq{
+                \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
+                \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
+            }
+        \end{formula}
+
+\Subsection[
+    \eng{Lattices}
+    \ger{Gitter}
+]{lat}
+    \begin{formula}{sc}
+        \desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}}
+        \desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{}
+        \eq{
+            \vec{a}_{1}=a \begin{pmatrix} 1\\0\\0 \end{pmatrix},\, 
+            \vec{a}_{2}=a \begin{pmatrix} 0\\1\\0 \end{pmatrix},\, 
+            \vec{a}_{3}=a \begin{pmatrix} 0\\0\\1 \end{pmatrix} 
+        }
+    \end{formula}
+    \begin{formula}{bcc}
+        \desc{Body centered cubic (BCC)}{Reciprocal: \fqEqRef{cm:bravais:fcc}}{\QtyRef{lattice_constant}}
+        \desc[german]{Kubisch raumzentriert (BCC)}{Reziprok: \fqEqRef{cm:bravais:fcc}}{}
+        \eq{
+            \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} -1\\1\\1 \end{pmatrix},\, 
+            \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\-1\\1 \end{pmatrix},\, 
+            \vec{a}_{3}=\frac{a}{2} \begin{pmatrix} 1\\1\\-1 \end{pmatrix} 
+        }
+    \end{formula}
+
+    \begin{formula}{fcc}
+        \desc{Face centered cubic (FCC)}{Reciprocal: \fqEqRef{cm:bravais:bcc}}{\QtyRef{lattice_constant}}
+        \desc[german]{Kubisch flächenzentriert (FCC)}{Reziprok: \fqEqRef{cm:bravais:bcc}}{}
+        \eq{
+            \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} 0\\1\\1 \end{pmatrix},\,
+            \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\0\\1 \end{pmatrix},\, 
+            \vec{a}_{3}=\frac{a}{2} \begin{pmatrix} 1\\1\\0 \end{pmatrix}
+        }
+    \end{formula}
+
+    \begin{formula}{diamond}
+        \desc{Diamond lattice}{}{}
+        \desc[german]{Diamantstruktur}{}{}
+        \ttxt{
+            \eng{\fqEqRef{cm:bravais:fcc} with basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ and $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$}
+            \ger{\fqEqRef{cm:bravais:fcc} mit Basis  $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ und $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$}
+        }
+    \end{formula}
+    \begin{formula}{zincblende}
+        \desc{Zincblende lattice}{}{}
+        \desc[german]{Zinkblende-Struktur}{}{}
+        \ttxt{
+            \includegraphics[width=0.5\textwidth]{img/cm_zincblende.png}
+            \eng{Like \fqEqRef{cm:bravais:diamond} but with different species on each basis}
+            \ger{Wie  \fqEqRef{cm:bravais:diamond} aber mit unterschiedlichen Spezies auf den Basen}
+        }
+    \end{formula}
+    \begin{formula}{wurtzite}
+        \desc{Wurtzite structure}{hP4}{}
+        \desc[german]{Wurtzite-Struktur}{hP4}{}
+        \ttxt{
+            \includegraphics[width=0.5\textwidth]{img/cm_wurtzite.png}
+            Placeholder
+        }
+    \end{formula}
+

src/cm/egas.tex

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

src/cm/other.tex

@@ -0,0 +1,102 @@
+\Section[
+    \eng{Band theory}
+    \ger{Bändermodell}
+]{band}
+    \Subsection[
+        \eng{Hybrid orbitals}
+        \ger{Hybridorbitale}
+    ]{hybrid_orbitals}  
+    \begin{ttext}
+        \eng{Hybrid orbitals are linear combinations of other atomic orbitals.}
+        \ger{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.}
+    \end{ttext}
+
+    % chemmacros package
+    \begin{formula}{sp3}
+        \desc{sp3 Orbital}{\GT{eg} \ce{CH4}}{}
+        \desc[german]{sp3 Orbital}{}{}
+        \eq{
+            1\text{s} + 3\text{p} = \text{sp3}
+            \orbital{sp3}
+        }
+    \end{formula}
+    \begin{formula}{sp2}
+        \desc{sp2 Orbital}{}{}
+        \desc[german]{sp2 Orbital}{}{}
+        \eq{
+            1\text{s} + 2\text{p} = \text{sp2}
+            \orbital{sp2}
+        }
+    \end{formula}
+    \begin{formula}{sp}
+        \desc{sp Orbital}{}{}
+        \desc[german]{sp Orbital}{}{}
+        \eq{
+            1\text{s} + 1\text{p} = \text{sp}
+            \orbital{sp}
+        }
+    \end{formula}
+
+
+
+\Section[
+    \eng{Diffusion}
+    \ger{Diffusion}
+]{diffusion}    
+    \begin{formula}{diffusion_coefficient}
+        \desc{Diffusion coefficient}{}{}
+        \desc[german]{Diffusionskoeffizient}{}{}
+        \quantity{D}{\m^2\per\s}{s}
+    \end{formula}
+
+    \begin{formula}{particle_current_density}
+        \desc{Particle current density}{Number of particles through an area}{}
+        \desc[german]{Teilchenstromdichte}{Anzahl der Teilchen durch eine Fläche}{}
+        \quantity{J}{1\per\s^2}{s}
+    \end{formula}
+
+    \begin{formula}{einstein_relation}
+        \desc{Einstein relation}{Classical}{\QtyRef{diffusion_coefficient}, \mu \qtyRef{mobility}, \QtyRef{temperature}, $q$ \qtyRef{charge}}
+        \desc[german]{Einsteinrelation}{Klassisch}{}
+        \eq{D = \frac{\mu \kB T}{q}}
+    \end{formula}   
+
+    \begin{formula}{concentration}
+        \desc{Concentration}{A quantity per volume}{}
+        \desc[german]{Konzentration}{Eine Größe pro Volumen}{}
+        \quantity{c}{x\per\m^3}{s}
+    \end{formula}
+
+    \begin{formula}{fick_law_1}
+        \desc{Fick's first law}{Particle movement is proportional to concentration gradient}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}}
+        \desc[german]{Erstes Ficksches Gesetz}{Teilchenbewegung ist proportional zum Konzentrationsgradienten}{}
+        \eq{J = -D\frac{c}{x}}
+    \end{formula}
+
+    \begin{formula}{fick_law_2}
+        \desc{Fick's second law}{}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}}
+        \desc[german]{Zweites Ficksches Gesetz}{}{}
+        \eq{\pdv{c}{t} = D \pdv[2]{c}{x}}
+    \end{formula}
+
+\Section[
+    \eng{\GT{misc}}
+    \ger{\GT{misc}}
+]{misc}
+
+    \begin{formula}{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}
+
+    \begin{formula}{work_function}
+        \desc{Work function}{Lowest energy required to remove an electron into the vacuum}{}
+        \desc[german]{Austrittsarbeit}{eng. "Work function"; minimale Energie um ein Elektron aus dem Festkörper zu lösen}{}
+        \quantity{W}{\eV}{s}
+        \eq{-e\phi - \EFermi}
+    \end{formula}
+

src/cm/semiconductors.tex

@@ -52,6 +52,21 @@
         CdS     & 2.58 & 2.42 & \GT{direct}
     \end{tabular}
 
+    \begin{formula}{min_maj}
+        \desc{Minority / Majority charge carriers}{}{}
+        \desc[german]{Minoritäts- / Majoritätsladungstraäger}{}{}
+        \ttxt{
+            \eng{
+                Majority carriers: higher number of particles ($e^-$ in n-type, $h^+$ in p-type)\\
+                Minority carriers: lower number of particles  ($h^+$ in n-type, $e^-$ in p-type)
+            }
+            \ger{
+                Majoritätsladungstraäger: höhere Teilchenzahl ($e^-$ in n-Typ, $h^+$ in p-Typ)\\
+                Minoritätsladungsträger: niedrigere Teilchenzahl  ($h^+$ in n-Typ, $e^-$ in p-Typ)
+            }
+        }
+    \end{formula}   
+
 
 
 

src/computational.tex

@@ -1,10 +1,10 @@
 \Part[
     \eng{Computational Physics}
     \ger{Computergestützte Physik}
-]{comp}
+]{cmp}
 \Section[
-    \eng{Many-body physics}
+    \eng{Quantum many-body physics}
-    \ger{Vielteilchenphysik}
+    \ger{Quanten-Vielteilchenphysik}
 ]{mb}
 \TODO{TODO}
     \Subsection[
@@ -18,10 +18,22 @@
         \ger{Matrix Produktzustände}
     ]{mps}
 
+
+
 \Section[
-    \eng{Misc}
+    \eng{Electronic structure theory}
-    \ger{Verschiedenes}
+    % \ger{}
-]{misc}
+]{elsth}
+    \begin{formula}{hamiltonian}
+        \desc{Electronic structure Hamiltonian}{}{$\hat{T}$ kinetic energy, $\hat{V}$ electrostatic potential, $\txe$ electrons, $\txn$ nucleons}
+        % \desc[german]{}{}{}
+        \eq{
+            \hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\e \leftrightarrow \e} + V_{\n \leftrightarrow \e} + V_{\n \leftrightarrow \n} \\
+            \shortintertext{with}
+            \hat{T}_i &= -\sum_{n=1}^{N_i} \frac{\hbar^2}{2 m_i} \vec{\nabla}^2_n \\
+            \hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j \e^2}{\abs{\vecr_k - \vecr_l}}
+        }
+    \end{formula}
     \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}
@@ -31,17 +43,17 @@
     \end{formula}
 
 
-\Section[
+\Subsection[
     \eng{Tight-binding}
     \ger{Tight-binding}
 ]{tb}
 
 
-\Section[
+\Subsection[
     \eng{Density functional theory (DFT)}
     \ger{Dichtefunktionaltheorie (DFT)}
 ]{dft}
-    \Subsection[
+    \Subsubsection[
         \eng{Hartree-Fock}
         \ger{Hartree-Fock}
     ]{hf}
@@ -84,7 +96,7 @@
             }
         \end{formula}
         \begin{formula}{scf}
-            \desc{Self-consistend field}{}{}
+            \desc{Self-consistend field cycle}{}{}
             % \desc[german]{}{}{}
             \ttxt{
                 \eng{
@@ -97,6 +109,10 @@
             }
         \end{formula}
 
+\Section[
+    \eng{Atomic dynamics}
+    % \ger{}
+]{ad}
     \Subsection[
         \eng{Kohn-Sham}
         \ger{Kohn-Sham}
@@ -107,7 +123,7 @@
         \eng{Born-Oppenheimer Approximation}
         \ger{Born-Oppenheimer Näherung}
     ]{bo}
-        \TODO{TODO}
+        \TODO{TODO, BO surface}
 
     \Subsection[
         \eng{Molecular Dynamics}
@@ -118,13 +134,14 @@
             
         \end{ttext}
 
+        \TODO{ab-initio MD, force-field MD}
 
 
 
 \Section[
     \eng{Gradient descent}
     \ger{Gradientenverfahren}
-    ]{gd}
+]{gd}
     \TODO{TODO}
 
 

src/constants.tex

@@ -2,35 +2,45 @@
     \eng{Constants}
     \ger{Konstanten}
 ]{constants}
-    \begin{constant}{planck}{h}{def}
+    \begin{formula}{planck}
         \desc{Planck Constant}{}{}
         \desc[german]{Plancksches Wirkumsquantum}{}{}
-        \val{6.62607015\cdot 10^{-34}}{\joule\s}
+        \constant{h}{def}{
-        \val{4.135667969\dots\xE{-15}}{\eV\s}
+            \val{6.62607015\cdot 10^{-34}}{\joule\s}
-    \end{constant}
+            \val{4.135667969\dots\xE{-15}}{\eV\s}
+        }
+    \end{formula}
 
-    \begin{constant}{universal_gas}{R}{def}
+    \begin{formula}{universal_gas}
         \desc{Universal gas constant}{Proportionality factor for ideal gases}{\ConstRef{avogadro}, \ConstRef{boltzmann}}
         \desc[german]{Universelle Gaskonstante}{Proportionalitätskonstante für ideale Gase}{}
-        \val{8.31446261815324}{\joule\per\mol\kelvin}
+        \constant{R}{def}{
-        \val{\NA \cdot \kB}{}
+            \val{8.31446261815324}{\joule\per\mol\kelvin}
-    \end{constant}
+            \val{\NA \cdot \kB}{}
+        }
+    \end{formula}
 
-    \begin{constant}{avogadro}{\NA}{def}
+    \begin{formula}{avogadro}
         \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}
+        \constant{\NA}{def}{
-    \end{constant}
+            \val{6.02214076 \xE{23}}{1\per\mole}
+        }
+    \end{formula}
 
-    \begin{constant}{boltzmann}{\kB}{def}
+    \begin{formula}{boltzmann}
         \desc{Boltzmann constant}{Temperature-Energy conversion factor}{}
         \desc[german]{Boltzmann-Konstante}{Temperatur-Energie Umrechnungsfaktor}{}
-        \val{1.380649 \xE{-23}}{\joule\per\kelvin}
+        \constant{\kB}{def}{
-    \end{constant}
+            \val{1.380649 \xE{-23}}{\joule\per\kelvin}
+        }
+    \end{formula}
 
-    \begin{constant}{faraday}{F}{def}
+    \begin{formula}{faraday}
         \desc{Faraday constant}{Electric charge of one mol of single-charged ions}{\ConstRef{avogadro}, \ConstRef{boltzmann}}
         \desc[german]{Faraday-Konstante}{Elektrische Ladungs von einem Mol einfach geladener Ionen}{}
-        \val{9.64853321233100184}{\coulomb\per\mol}
+        \constant{F}{def}{
-        \val{\NA\,e}{}
+            \val{9.64853321233100184}{\coulomb\per\mol}
-    \end{constant}
+            \val{\NA\,e}{}
+        }
+    \end{formula}

src/ed/ed.tex

@@ -0,0 +1,139 @@
+\Part[
+    \eng{Electrodynamics}
+    \ger{Elektrodynamik}
+]{ed}
+
+% pure electronic stuff in el
+% pure magnetic stuff in mag
+% electromagnetic stuff in em
+
+% TODO move
+\Section[
+    \eng{Hall-Effect}
+    \ger{Hall-Effekt}
+    ]{hall}
+
+    \begin{formula}{cyclotron}
+        \desc{Cyclontron frequency}{}{}
+        \desc[german]{Zyklotronfrequenz}{}{}
+        \eq{\omega_\text{c} = \frac{e B}{\masse}}
+    \end{formula}
+    \TODO{Move}
+
+
+    \Subsection[
+        \eng{Classical Hall-Effect}
+        \ger{Klassischer Hall-Effekt}
+        ]{classic}
+        \begin{ttext}
+            \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
+            \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
+        \end{ttext}
+        \begin{formula}{voltage}
+            \desc{Hall voltage}{}{$n$ charge carrier density}
+            \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
+            \eq{U_\text{H} = \frac{I B}{ne d}}
+        \end{formula}
+
+        \begin{formula}{coefficient}
+            \desc{Hall coefficient}{Sometimes $R_\txH$}{}
+            \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
+            \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
+        \end{formula}
+
+        \begin{formula}{resistivity}
+            \desc{Resistivity}{}{}
+            \desc[german]{Spezifischer Widerstand}{}{}
+            \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
+        \end{formula}
+
+
+    \Subsection[
+        \eng{Integer quantum hall effect}
+        \ger{Ganzahliger Quantenhalleffekt}
+    ]{quantum}  
+
+        \begin{formula}{conductivity}
+            \desc{Conductivity tensor}{}{}
+            \desc[german]{Leitfähigkeitstensor}{}{}
+            \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+        \end{formula}
+
+        \begin{formula}{resistivity_tensor}
+            \desc{Resistivity tensor}{}{}
+            \desc[german]{Spezifischer Widerstands-tensor}{}{}
+            \eq{
+                \rho = \sigma^{-1}
+                % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+            }
+        \end{formula}
+
+        \begin{formula}{resistivity}
+            \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
+            \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
+            \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
+        \end{formula}
+
+        % \begin{formula}{qhe}
+        %     \desc{Integer quantum hall effect}{}{}
+        %     \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
+        %     \fig{img/qhe-klitzing.jpeg}
+        % \end{formula}
+
+        \begin{formula}{fqhe}
+            \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
+            \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
+            \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
+        \end{formula}
+
+        \begin{ttext}
+            \eng{
+                \begin{itemize}
+                    \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
+                    \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
+                    \item \textbf{Spin} (QSHE): spin currents instead of charge currents
+                    \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
+                \end{itemize}
+            }
+            \ger{
+                \begin{itemize}
+                    \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
+                    \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
+                    \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
+                    \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
+                \end{itemize}
+            }
+        \end{ttext}
+    
+
+    \TODO{sort}
+    \begin{formula}{impedance_c}
+        \desc{Impedance of a capacitor}{}{}
+        \desc[german]{Impedanz eines Kondesnators}{}{}
+        \eq{Z_{C} = \frac{1}{i\omega C}}
+    \end{formula}
+
+    \begin{formula}{impedance_l}
+        \desc{Impedance of an inductor}{}{}
+        \desc[german]{Impedanz eines Induktors}{}{}
+        \eq{Z_{L} = i\omega L}
+    \end{formula}
+
+    \TODO{impedance addition for parallel / linear}
+
+\Section[
+    \eng{Dipole-stuff}
+    \ger{Dipol-zeug}
+]{dipole}
+
+    \begin{formula}{poynting}
+        \desc{Dipole radiation Poynting vector}{}{}
+        \desc[german]{Dipolsrahlung Poynting-Vektor}{}{}
+        \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}}
+    \end{formula}
+
+    \begin{formula}{power}
+        \desc{Time-average power}{}{}
+        \desc[german]{Zeitlich mittlere Leistung}{}{}
+        \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
+    \end{formula}

src/ed/el.tex

@@ -0,0 +1,51 @@
+
+\Section[
+    \eng{Electric field}
+    \ger{Elektrisches Feld}
+]{el}
+\begin{formula}{electric_field}
+        \desc{Electric field}{Surrounds charged particles}{}
+        \desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{}
+        \quantity{\vec{\E}}{\volt\per\m=\kg\m\per\s^3\ampere}{v}
+    \end{formula}
+    \begin{formula}{gauss_law}
+        \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface}
+        \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche}
+        \eq{\PhiE = \iint_S \vec{\E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}}
+    \end{formula}
+
+    \begin{formula}{permittivity}
+        \desc{Permittivity}{Electric polarizability of a dielectric material}{}
+        \desc[german]{Permitivität}{Dielektrische Konstante\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{}
+        \quantity{\epsilon}{\ampere\s\per\volt\m=\farad\per\m=\coulomb\per\volt\m=C^2\per\newton\m^2=\ampere^2\s^4\per\kg\m^3}{}
+    \end{formula}
+    \begin{formula}{relative_permittivity}
+        \desc{Relative permittivity / Dielectric constant}{}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}}
+        \desc[german]{Relative Permittivität / Dielectric constant}{}{}
+        \eq{
+            \epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0}
+        }
+    \end{formula}
+
+    \begin{formula}{vacuum_permittivity}
+        \desc{Vacuum permittivity}{Electric constant}{}
+        \desc[german]{Vakuum Permittivität}{Elektrische Feldkonstante}{}
+        \constant{\epsilon_0}{exp}{
+            \val{8.8541878188(14)\xE{-1}}{\ampere\s\per\volt\m}
+        }
+    \end{formula}
+
+    \begin{formula}{electric_susceptibility}
+        \desc{Electric susceptibility}{Describes how polarized a dielectric material becomes when an electric field is applied}{$\epsilon_\txr$ \fqEqRef{ed:el:relative_permittivity}}
+        \desc[german]{Elektrische Suszeptibilität}{Beschreibt wie stark ein dielektrisches Material polarisiert wird, wenn ein elektrisches Feld angelegt wird}{}
+        \quantity{\chi_\txe}{}{s}
+        \eq{
+            \epsilon_\txr = 1 + \chi_\txe
+        }
+    \end{formula}
+    \begin{formula}{dielectric_polarization_density}
+        \desc{Dielectric polarization density}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_susceptibility}, \QtyRef{electric_field}}
+        \desc[german]{Dielektrische Polarisationsdichte}{}{}
+        \eq{\vec{P} = \epsilon_0 \chi_\txe \vec{\E}}
+    \end{formula}
+

src/ed/em.tex

@@ -0,0 +1,82 @@
+\Section[
+    \eng{Electromagnetism}
+    \ger{Elektromagnetismus}
+]{em}
+    \begin{formula}{speed_of_light}
+        \desc{Speed of light}{in the vacuum}{}
+        \desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
+        \constant{c}{exp}{
+            \val{299792458}{\m\per\s}
+        }
+    \end{formula}
+    \begin{formula}{vacuum_relations}
+        \desc{Vacuum permittivity - permeability relation}{\TODO{Does this have a name?}}{\ConstRef{vacuum_permittivity}, \ConstRef{magnetic_vacuum_permeability}, \ConstRef{speed_of_light}}
+        \desc[german]{Vakuum Permittivität - Permeabilität Beziehung}{}{}
+        \eq{
+            \epsilon_0 \mu_0 = \frac{1}{c^2}
+        }
+    \end{formula}
+
+    \begin{formula}{poisson_equation}
+        \desc{Poisson equation for electrostatics}{}{\QtyRef{charge_density}, \QtyRef{permittivity}, $\Phi$ Potential}
+        \desc[german]{Poisson Gleichung in der Elektrostatik}{}{}
+        \eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}}
+        \TODO{double check $\Phi$}
+    \end{formula}
+
+    \begin{formula}{poynting}
+        \desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field [$\si{\W\per\m^2}$]}{}
+        \desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes  [$\si{\W\per\m^2}$]}{}
+        \eq{\vec{S} = \vec{E} \times \vec{H}}
+    \end{formula}
+
+    \Subsection[
+        \eng{Maxwell-Equations}
+        \ger{Maxwell-Gleichungen}
+    ]{Maxwell}
+        \begin{formula}{vacuum}
+            \desc{Vacuum}{microscopic formulation}{}
+            \desc[german]{Vakuum}{Mikroskopische Formulierung}{}
+            \eq{
+                \Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\
+                \Div \vec{B} &= 0 \\
+                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
+                \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t}
+            }
+        \end{formula}
+
+        \begin{formula}{material}
+            \desc{Matter}{Macroscopic formulation}{}
+            \desc[german]{Materie}{Makroskopische Formulierung}{}
+            \eq{
+                \Div \vec{D} &= \rho_\text{el} \\
+                \Div \vec{B} &= 0 \\
+                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
+                \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
+            }
+        \end{formula}
+        \TODO{Polarization}
+
+    \Subsection[
+        \eng{Induction}
+        \ger{Induktion}
+    ]{induction}
+        \begin{formula}{farady_law}
+            \desc{Faraday's law of induction}{}{}
+            \desc[german]{Faradaysche Induktionsgesetz}{}{}
+            \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
+        \end{formula}
+
+        \begin{formula}{lenz}
+            \desc{Lenz's law}{}{}
+            \desc[german]{Lenzsche Regel}{}{}
+            \ttxt{
+                \eng{
+                    Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux.
+                }
+                \ger{
+                    Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt.
+                }
+            }
+        \end{formula}
+

src/ed/mag.te

@@ -0,0 +1,115 @@
+\Section[
+    \eng{Magnetic field}
+    \ger{Magnetfeld}
+]{mag}
+
+    \begin{formula}{magnetic_flux}
+        \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
+        \desc[german]{Magnetischer Fluss}{}{}
+        \quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
+        \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
+    \end{formula}
+
+    \begin{formula}{magnetic_flux_density}
+        \desc{Magnetic flux density}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}}
+        \desc[german]{Magnetische Flussdichte}{Definiert über \fqEqRef{ed:mag:lorentz}}{}
+        \quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{}
+        \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
+    \end{formula}
+
+    \begin{formula}{magnetic_field_intensity}
+        \desc{Magnetic field intensity}{}{}
+        \desc[german]{Magnetische Feldstärke}{}{}
+        \quantity{\vec{H}}{\ampere\per\m}{vector}
+        \eq{
+            \vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M}
+        }
+    \end{formula}
+
+    \begin{formula}{lorentz}
+        \desc{Lorentz force law}{Force on charged particle}{}
+        \desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{}
+        \eq{
+            \vec{F} = q \vec{\E} + q \vec{v}\times\vec{B}
+        }
+    \end{formula}
+
+    \begin{formula}{magnetic_permeability}
+        \desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
+        \desc[german]{Magnetisch Permeabilität}{}{}
+        \quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
+        \eq{\mu=\frac{B}{H}}
+    \end{formula}
+    \begin{formula}{magnetic_vacuum_permeability}
+        \desc{Magnetic vauum permeability}{}{}
+        \desc[german]{Magnetische Vakuumpermeabilität}{}{}
+        \constant{\mu_0}{exp}{
+            \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2}
+        }
+    \end{formula}
+    \begin{formula}{relative_permeability}
+        \desc{Relative permeability}{}{}
+        \desc[german]{Realtive Permeabilität}{}{}
+        \eq{
+            \mu_\txr = \frac{\mu}{\mu_0}
+        }
+    \end{formula}
+
+    \begin{formula}{gauss_law}
+        \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
+        \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
+        \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
+    \end{formula}
+
+    \begin{formula}{magnetization}
+        \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{}
+        \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{}
+        \quantity{\vec{M}}{\ampere\per\m}{vector}
+        \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}}
+    \end{formula}
+
+    \begin{formula}{magnetic_moment}
+        \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{}
+        \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{}
+        \quantity{\vec{m}}{\ampere\m^2}{vector}
+    \end{formula}
+
+    \begin{formula}{angular_torque}
+        \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}}
+        \desc[german]{Drehmoment}{}{}
+        \eq{\vec{\tau} = \vec{m} \times \vec{B}}
+    \end{formula}
+
+    \begin{formula}{magnetic_susceptibility}
+        \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}}
+        \desc[german]{Suszeptibilität}{}{}
+        \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
+    \end{formula}
+
+
+
+
+    \Subsection[
+        \eng{Magnetic materials}
+        \ger{Magnetische Materialien}
+    ]{materials}
+        \begin{formula}{paramagnetism}
+            \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
+            \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
+        \end{formula}
+
+        \begin{formula}{diamagnetism}
+            \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
+            \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
+        \end{formula}
+
+        \begin{formula}{ferromagnetism}
+            \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
+            \eq{
+                \mu_\txr \gg 1
+            }
+        \end{formula}
+

src/ed/mag.tex

@@ -0,0 +1,115 @@
+\Section[
+    \eng{Magnetic field}
+    \ger{Magnetfeld}
+]{mag}
+
+    \begin{formula}{magnetic_flux}
+        \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
+        \desc[german]{Magnetischer Fluss}{}{}
+        \quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
+        \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
+    \end{formula}
+
+    \begin{formula}{magnetic_flux_density}
+        \desc{Magnetic flux density}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}}
+        \desc[german]{Magnetische Flussdichte}{Definiert über \fqEqRef{ed:mag:lorentz}}{}
+        \quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{}
+        \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
+    \end{formula}
+
+    \begin{formula}{magnetic_field_intensity}
+        \desc{Magnetic field intensity}{}{}
+        \desc[german]{Magnetische Feldstärke}{}{}
+        \quantity{\vec{H}}{\ampere\per\m}{vector}
+        \eq{
+            \vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M}
+        }
+    \end{formula}
+
+    \begin{formula}{lorentz}
+        \desc{Lorentz force law}{Force on charged particle}{}
+        \desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{}
+        \eq{
+            \vec{F} = q \vec{\E} + q \vec{v}\times\vec{B}
+        }
+    \end{formula}
+
+    \begin{formula}{magnetic_permeability}
+        \desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
+        \desc[german]{Magnetisch Permeabilität}{}{}
+        \quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
+        \eq{\mu=\frac{B}{H}}
+    \end{formula}
+    \begin{formula}{magnetic_vacuum_permeability}
+        \desc{Magnetic vauum permeability}{}{}
+        \desc[german]{Magnetische Vakuumpermeabilität}{}{}
+        \constant{\mu_0}{exp}{
+            \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2}
+        }
+    \end{formula}
+    \begin{formula}{relative_permeability}
+        \desc{Relative permeability}{}{}
+        \desc[german]{Realtive Permeabilität}{}{}
+        \eq{
+            \mu_\txr = \frac{\mu}{\mu_0}
+        }
+    \end{formula}
+
+    \begin{formula}{gauss_law}
+        \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
+        \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
+        \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
+    \end{formula}
+
+    \begin{formula}{magnetization}
+        \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{}
+        \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{}
+        \quantity{\vec{M}}{\ampere\per\m}{vector}
+        \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}}
+    \end{formula}
+
+    \begin{formula}{magnetic_moment}
+        \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{}
+        \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{}
+        \quantity{\vec{m}}{\ampere\m^2}{vector}
+    \end{formula}
+
+    \begin{formula}{angular_torque}
+        \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}}
+        \desc[german]{Drehmoment}{}{}
+        \eq{\vec{\tau} = \vec{m} \times \vec{B}}
+    \end{formula}
+
+    \begin{formula}{magnetic_susceptibility}
+        \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}}
+        \desc[german]{Suszeptibilität}{}{}
+        \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
+    \end{formula}
+
+
+
+
+    \Subsection[
+        \eng{Magnetic materials}
+        \ger{Magnetische Materialien}
+    ]{materials}
+        \begin{formula}{paramagnetism}
+            \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
+            \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
+        \end{formula}
+
+        \begin{formula}{diamagnetism}
+            \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
+            \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
+        \end{formula}
+
+        \begin{formula}{ferromagnetism}
+            \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
+            \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
+            \eq{
+                \mu_\txr \gg 1
+            }
+        \end{formula}
+

src/electrodynamics.tex

@@ -1,394 +0,0 @@
-
-\Part[
-    \eng{Electrodynamics}
-    \ger{Elektrodynamik}
-]{ed}
-
-
-% pure electronic stuff in el
-% pure magnetic stuff in mag
-% electromagnetic stuff in em
-
-\Section[
-    \eng{Electric field}
-    \ger{Elektrisches Feld}
-]{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}
-
-    \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}
-
-    \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}{Test desc}{Test def}
-        \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[german]{Magnetische Flussdichte}{}{}
-    \end{quantity}
-    \begin{formula}{magnetic_flux_density}
-        \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]{}{Definiert über \fqEqRef{ed:mag:lorentz}}{}
-        \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
-    \end{formula}
-
-    \begin{quantity}{magnetic_field_intensity}{\vec{H}}{\ampere\per\m}{vector}
-        \desc{Magnetic field intensity}{}{}
-        \desc[german]{Magnetische Feldstärke}{}{}
-    \end{quantity}
-    \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}}
-        \desc[german]{Magnetischer Fluss}{}{}
-        \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
-    \end{formula}
-
-    \begin{formula}{gauss_law}
-        \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
-        \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
-        \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
-    \end{formula}
-
-    \begin{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{formula}{magnetization}
-        \desc{\qtyRef{magnetization}}{}{$m$ \qtyRef{magnetic_moment}, $V$ \qtyRef{volume}}
-        \desc[german]{}{}{}
-        \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}{magnetic_susceptibility}
-        \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}}
-        \desc[german]{Suszeptibilität}{}{}
-        \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
-    \end{formula}
-
-
-
-
-    \Subsection[
-        \eng{Magnetic materials}
-        \ger{Magnetische Materialien}
-    ]{materials}
-        \begin{formula}{paramagnetism}
-            \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
-            \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
-            \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
-        \end{formula}
-
-        \begin{formula}{diamagnetism}
-            \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
-            \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
-            \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
-        \end{formula}
-
-        \begin{formula}{ferromagnetism}
-            \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
-            \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
-            \eq{
-                \mu_\txr \gg 1
-            }
-        \end{formula}
-
-\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}
-
-    \Subsection[
-        \eng{Maxwell-Equations}
-        \ger{Maxwell-Gleichungen}
-    ]{Maxwell}
-        \begin{formula}{vacuum}
-            \desc{Vacuum}{microscopic formulation}{}
-            \desc[german]{Vakuum}{Mikroskopische Formulierung}{}
-            \eq{
-                \Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\
-                \Div \vec{B} &= 0 \\
-                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
-                \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t}
-            }
-        \end{formula}
-
-        \begin{formula}{material}
-            \desc{Matter}{Macroscopic formulation}{}
-            \desc[german]{Materie}{Makroskopische Formulierung}{}
-            \eq{
-                \Div \vec{D} &= \rho_\text{el} \\
-                \Div \vec{B} &= 0 \\
-                \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\
-                \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
-            }
-        \end{formula}
-        \TODO{Polarization}
-
-    \Subsection[
-        \eng{Induction}
-        \ger{Induktion}
-    ]{induction}
-        \begin{formula}{farady_law}
-            \desc{Faraday's law of induction}{}{}
-            \desc[german]{Faradaysche Induktionsgesetz}{}{}
-            \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
-        \end{formula}
-
-        \begin{formula}{lenz}
-            \desc{Lenz's law}{}{}
-            \desc[german]{Lenzsche Regel}{}{}
-            \ttxt{
-                \eng{
-                    Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux.
-                }
-                \ger{
-                    Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt.
-                }
-            }
-        \end{formula}
-
-
-
-
-\Section[
-    \eng{Hall-Effect}
-    \ger{Hall-Effekt}
-    ]{hall}
-
-    \begin{formula}{cyclotron}
-        \desc{Cyclontron frequency}{}{}
-        \desc[german]{Zyklotronfrequenz}{}{}
-        \eq{\omega_\text{c} = \frac{e B}{\masse}}
-    \end{formula}
-    \TODO{Move}
-
-
-    \Subsection[
-        \eng{Classical Hall-Effect}
-        \ger{Klassischer Hall-Effekt}
-        ]{classic}
-        \begin{ttext}
-            \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
-            \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
-        \end{ttext}
-        \begin{formula}{voltage}
-            \desc{Hall voltage}{}{$n$ charge carrier density}
-            \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
-            \eq{U_\text{H} = \frac{I B}{ne d}}
-        \end{formula}
-
-        \begin{formula}{coefficient}
-            \desc{Hall coefficient}{Sometimes $R_\txH$}{}
-            \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
-            \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity}{}{}
-            \desc[german]{Spezifischer Widerstand}{}{}
-            \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
-        \end{formula}
-
-
-    \Subsection[
-        \eng{Integer quantum hall effect}
-        \ger{Ganzahliger Quantenhalleffekt}
-    ]{quantum}  
-
-        \begin{formula}{conductivity}
-            \desc{Conductivity tensor}{}{}
-            \desc[german]{Leitfähigkeitstensor}{}{}
-            \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity tensor}{}{}
-            \desc[german]{Spezifischer Widerstands-tensor}{}{}
-            \eq{
-                \rho = \sigma^{-1}
-                % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
-            }
-        \end{formula}
-
-        \begin{formula}{resistivity}
-            \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
-            \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
-            \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
-        \end{formula}
-
-        % \begin{formula}{qhe}
-        %     \desc{Integer quantum hall effect}{}{}
-        %     \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
-        %     \fig{img/qhe-klitzing.jpeg}
-        % \end{formula}
-
-        \begin{formula}{fqhe}
-            \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
-            \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
-            \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
-        \end{formula}
-
-        \begin{ttext}
-            \eng{
-                \begin{itemize}
-                    \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
-                    \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
-                    \item \textbf{Spin} (QSHE): spin currents instead of charge currents
-                    \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
-                \end{itemize}
-            }
-            \ger{
-                \begin{itemize}
-                    \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
-                    \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
-                    \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
-                    \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
-                \end{itemize}
-            }
-        \end{ttext}
-    
-
-    \TODO{sort}
-    \begin{formula}{impedance_c}
-        \desc{Impedance of a capacitor}{}{}
-        \desc[german]{Impedanz eines Kondesnators}{}{}
-        \eq{Z_{C} = \frac{1}{i\omega C}}
-    \end{formula}
-
-    \begin{formula}{impedance_l}
-        \desc{Impedance of an inductor}{}{}
-        \desc[german]{Impedanz eines Induktors}{}{}
-        \eq{Z_{L} = i\omega L}
-    \end{formula}
-
-    \TODO{impedance addition for parallel / linear}
-
-\Section[
-    \eng{Dipole-stuff}
-    \ger{Dipol-zeug}
-]{dipole}
-
-    \begin{formula}{poynting}
-        \desc{Dipole radiation Poynting vector}{}{}
-        \desc[german]{Dipolsrahlung Poynting-Vektor}{}{}
-        \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}}
-    \end{formula}
-
-    \begin{formula}{power}
-        \desc{Time-average power}{}{}
-        \desc[german]{Zeitlich mittlere Leistung}{}{}
-        \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
-    \end{formula}

src/main.tex

@@ -1,27 +1,29 @@
+%! TeX program = lualatex
+% (for vimtex)
 \documentclass[11pt, a4paper]{article}
 % \usepackage[utf8]{inputenc}
-\usepackage[german]{babel}
+\usepackage[english]{babel}
 \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
 % ENVIRONMENTS etc
 \usepackage{adjustbox}
-\usepackage{colortbl}  % color table
+\usepackage{colortbl}   % color table
-\usepackage{tabularx}  % bravais table
+\usepackage{tabularx}   % bravais table
-\usepackage{multirow}  % for superconducting qubit table
+\usepackage{multirow}   % for superconducting qubit table
-\usepackage{hhline}    % for superconducting qubit table
+\usepackage{hhline}     % for superconducting qubit table
 % TOOLING
 \usepackage{graphicx}
 \usepackage{etoolbox}
-\usepackage{luacode}
+% \usepackage{luacode}
-\usepackage{expl3} % switch case and other stuff
+\usepackage{expl3}      % switch case and other stuff
 \usepackage{substr}
 \usepackage{xcolor}
 % FORMATING
-\usepackage{float}  % float barrier
+\usepackage{float}                  % float barrier
-\usepackage{subcaption} % subfigure
+\usepackage{subcaption}             % subfigures
-\usepackage[hidelinks]{hyperref}
+\usepackage[hidelinks]{hyperref}    % hyperrefs for \fqEqRef, \qtyRef, etc
-\usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
+\usepackage[shortlabels]{enumitem}  % easily change enum symbols to i), a. etc
-\usepackage{titlesec}  % colored titles
+\usepackage{titlesec}   % colored titles
-\usepackage{array}
+\usepackage{array}      % more array options
 \newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type
 % \usepackage{sectsty}
 % TRANSLATION
@@ -29,29 +31,39 @@
 \input{util/translation.tex}
 \input{util/colorscheme.tex}
 % GRAPHICS
-\usepackage{tikz} % drawings
+\usepackage{tikz}       % drawings
 \usetikzlibrary{decorations.pathmorphing}
 \usetikzlibrary{calc}
 % speed up compilation by externalizing figures
 % \usetikzlibrary{external}
 % \tikzexternalize[prefix=tikz_figures]
 % \tikzexternalize
-\usepackage{circuitikz}
+\usepackage{circuitikz} % electrical circuits with tikz
 % SCIENCE PACKAGES
 \usepackage{mathtools}
-\usepackage{MnSymbol}  % for >>> \ggg sign
+% set display math skips
-\usepackage{chemmacros}  % for orbitals
+\AtBeginDocument{
+    \abovedisplayskip=0pt
+    \abovedisplayshortskip=0pt
+    \belowdisplayskip=0pt   
+    \belowdisplayshortskip=0pt
+}
+\usepackage{MnSymbol}   % for >>> \ggg sign
+\usepackage[version=4,arrows=pgf-filled]{mhchem}
+\usepackage{upgreek}    % upright greek letters for chemmacros
+\usepackage{chemmacros} % for orbitals images
 % \usepackage{esdiff} % derivatives
 % esdiff breaks when taking \dot{q} has argument
-\usepackage{derivative}
+\usepackage{derivative} % \odv, \pdv
-\usepackage[version=4,arrows=pgf-filled]{mhchem}
+\usepackage{bbold}      % \mathbb font
-\usepackage{bbold}  % \mathbb font
+\usepackage{braket}     % <bra|ket>
-\usepackage{braket}
+\usepackage{siunitx}    % \si \SI units
-\usepackage{siunitx}
 \sisetup{output-decimal-marker = {,}}
 \sisetup{separate-uncertainty}
 \sisetup{per-mode = power}
 \sisetup{exponent-product=\ensuremath{\cdot}}
+% DEBUG
+% \usepackage{lua-visual-debug}
 % DUMB STUFF
 % \usepackage{emoji}
 % \newcommand\temoji[1]{\text{\emoji{#1}}}
@@ -64,6 +76,8 @@
 % \def\nu{\temoji{unicorn}}
 % \def\mu{\temoji{mouse}}
 
+
+
 \newcommand{\TODO}[1]{{\color{bright_red}TODO:#1}}
 \newcommand{\ts}{\textsuperscript}
 
@@ -74,41 +88,57 @@
 % 2: key
 \newcommand{\Part}[2][desc]{
     \newpage
-    \def\partname{#2}
+    \def\partName{#2}
-    \def\sectionname{}
+    \def\sectionName{}
-    \def\subsectionname{}
+    \def\subsectionName{}
-    \def\subsubsectionname{}
+    \def\subsubsectionName{}
-    \edef\fqname{\partname}
+    \edef\fqname{\partName}
     #1
-    \part{\GT{\fqname}} 
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \part{\fqnameText} 
     \label{sec:\fqname}
 }
 \newcommand{\Section}[2][]{
-    \def\sectionname{#2}
+    \def\sectionName{#2}
-    \def\subsectionname{}
+    \def\subsectionName{}
-    \def\subsubsectionname{}
+    \def\subsubsectionName{}
-    \edef\fqname{\partname:\sectionname}
+    \edef\fqname{\partName:\sectionName}
     #1
-    \section{\GT{\fqname}} 
+    % this is necessary so that \section takes the fully expanded string. Otherwise the pdf toc will have just the fqname
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \section{\fqnameText}
     \label{sec:\fqname}
 }
 % \newcommand{\Subsection}[1]{\Subsection{#1}{}}
 \newcommand{\Subsection}[2][]{
-    \def\subsectionname{#2}
+    \def\subsectionName{#2}
-    \def\subsubsectionname{}
+    \def\subsubsectionName{}
-    \edef\fqname{\partname:\sectionname:\subsectionname}
+    \edef\fqname{\partName:\sectionName:\subsectionName}
     #1
-    \subsection{\GT{\fqname}}
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \subsection{\fqnameText}
     \label{sec:\fqname}
 }
 \newcommand{\Subsubsection}[2][]{
-    \def\subsubsectionname{#2}
+    \def\subsubsectionName{#2}
-    \edef\fqname{\partname:\sectionname:\subsectionname:\subsubsectionname}
+    \edef\fqname{\partName:\sectionName:\subsectionName:\subsubsectionName}
     #1
-    \subsubsection{\GT{\fqname}}
+    \edef\fqnameText{\expandafter\GetTranslation\expandafter{\fqname}}
+    \subsubsection{\fqnameText}
     \label{sec:\fqname}
 }
+\edef\fqname{NULL}
 
+\newcommand\luaDoubleFieldValue[3]{%
+    \directlua{
+        if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
+            tex.sprint(#1[#2][#3])
+            return
+        end
+        luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
+        tex.sprint("???")
+    }%
+}
 % REFERENCES
 % All xyzRef commands link to the key using the translated name
 % Uppercase (XyzRef) commands have different link texts, but the same link target
@@ -118,7 +148,7 @@
 \newrobustcmd{\fqEqRef}[1]{%
     % \edef\fqeqrefname{\GT{#1}}
     % \hyperref[eq:#1]{\fqeqrefname}
-    \hyperref[eq:#1]{\GT{#1}}%
+    \hyperref[f:#1]{\GT{#1}}%
 }
 % Section
 % <name>
@@ -128,20 +158,22 @@
 % Quantities
 % <symbol>
 \newrobustcmd{\qtyRef}[1]{%
-    \hyperref[qty:#1]{\GT{qty:#1}}%
+    \edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"fqname"}}%
+    \hyperref[qty:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
 }
 % <symbol> <name>
 \newrobustcmd{\QtyRef}[1]{%
-    ${\luavar{quantities["#1"]["symbol"]}}$ \hyperref[qty:#1]{\GT{qty:#1}}%
+    $\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
 }
 % Constants
 % <name>
 \newrobustcmd{\constRef}[1]{%
-    \hyperref[const:#1]{\GT{const:#1}}%
+    \edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"fqname"}}%
+    \hyperref[const:#1]{\expandafter\GT\expandafter{\tempname:#1}}%
 }
 % <symbol> <name>
 \newrobustcmd{\ConstRef}[1]{%
-    $\luavar{constants["#1"]["symbol"]}$ \hyperref[const:#1]{\GT{const:#1}}%
+    $\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
 }
 % Element from periodic table
 % <symbol>
@@ -157,37 +189,55 @@
 
 % LUA sutff
 \newcommand\luavar[1]{\directlua{tex.sprint(#1)}}
+\directlua{
+    function string.startswith(s, start)
+        return string.sub(s,1,string.len(start)) == start
+    end
+}
 % Write directlua command to aux and run it as well
+% This one expands the argument in the aux file:
+\newcommand\directLuaAuxExpand[1]{
+    \immediate\write\luaauxfile{\noexpand\directlua{#1}}
+    \directlua{#1}
+}
+% This one does not:
 \newcommand\directLuaAux[1]{
     \immediate\write\luaauxfile{\noexpand\directlua{\detokenize{#1}}}
     \directlua{#1}
 }
+% read
+\IfFileExists{\jobname.lua.aux}{%
+  \input{\jobname.lua.aux}%
+}{%
+    % \@latex@warning@no@line{"Lua aux not loaded!"}
+}
+\def\luaAuxLoaded{False}
+% write
 \newwrite\luaauxfile
 \immediate\openout\luaauxfile=\jobname.lua.aux
-\immediate\write\luaauxfile{\noexpand\def\noexpand\luaAuxLoaded{lua aux loaded}}%
+\immediate\write\luaauxfile{\noexpand\def\noexpand\luaAuxLoaded{True}}%
 \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}
+
+
+% INPUT
+% 1: starting pattern of files to input using the Input command. All other files are ignored 
+\newcommand\InputOnly[1]{\edef\inputOnlyFile{#1}}
+\edef\inputOnlyFile{all}
 \newcommand\Input[1]{
-    \ifstrequal{\relax}{\inputOnlyFile}{
+    % yes this could surely be done in tex
-        \input{#1}
+    \directlua{
-    }{
+        if '\luaescapestring{\inputOnlyFile}' == 'all' or string.startswith('\luaescapestring{#1}', '\luaescapestring{\inputOnlyFile}') then
-        \ifstrequal{#1}{\inputOnlyFile}{
+            tex.print("\\input{\luaescapestring{#1}}")
-            \input{#1}
+        end
-        }{}
     }
 }
 
-% \includeonly{mechanics}
-% \includeonly{low_temp}
 
 \title{Formelsammlung}
 \author{Matthias Quintern}
@@ -197,10 +247,10 @@
   \input{\jobname.translations.aux}
 }{}
 
-
+\def\translationsAuxLoaded{False}
 \newwrite\translationsaux
 \immediate\openout\translationsaux=\jobname.translations.aux
-\immediate\write\translationsaux{\noexpand\def\noexpand\translationsAuxLoaded{translations aux loaded}}%
+\immediate\write\translationsaux{\noexpand\def\noexpand\translationsAuxLoaded{True}}%
 \AtEndDocument{\immediate\closeout\translationsaux}
 
 \makeatletter\let\percentchar\@percentchar\makeatother
@@ -212,104 +262,65 @@
 
 \input{util/translations.tex}
 
+% \InputOnly{math}
+
+\Input{math/math}
+\Input{math/linalg}
+\Input{math/geometry}
+\Input{math/calculus}
+\Input{math/probability_theory}
+
+\Input{mechanics}
+\Input{statistical_mechanics}
+
+\Input{ed/ed}
+\Input{ed/el}
+\Input{ed/mag}
+\Input{ed/em}
+
+\Input{quantum_mechanics}
+\Input{atom}
+
+\Input{cm/cm}
+\Input{cm/crystal}
+\Input{cm/egas}
+\Input{cm/charge_transport}
+\Input{cm/low_temp}
+\Input{cm/semiconductors}
+\Input{cm/other}
+\Input{cm/techniques}
+
+\Input{topo}
+
+\Input{quantum_computing}
+
+\Input{computational}
+
+\Input{quantities}
+\Input{constants}
+
+\Input{ch/periodic_table}  % only definitions
+\Input{ch/ch}
+
+
+% \newpage
+% \Input{test}
+
+\newpage
 \Part[
-    \eng{Mathematics}
+    \eng{Appendix}
-    \ger{Mathematik}
+    \ger{Anhang}
-]{math}
+]{appendix}
-% \include{math/linalg}
-% \include{math/geometry}
-% \input{math/calculus.tex}
-% \include{math/probability_theory}
-
-\include{mechanics}
-
-\include{statistical_mechanics}
-
-\include{electrodynamics}
-    
-% \include{quantum_mechanics}
-% \include{atom}
-
-\input{cm/cm.tex}
-\input{cm/charge_transport.tex}
-\input{cm/low_temp.tex}
-\input{cm/semiconductors.tex}
-% \include{cm/techniques}
-
-\include{topo}
-
-% \include{quantum_computing}
-
-\include{computational}
-
-\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}
-
-\paragraph{Testing GT, GetTranslation, IfTranslationExists, IfTranslation}
-\addtranslation{english}{ttest}{This is the english translation of \texttt{ttest}}
-\noindent
-GT: ttest = \GT{ttest}\\
-GetTranslation: ttest = \GetTranslation{ttest}\\
-Is english? = \IfTranslation{english}{ttest}{yes}{no} \\
-Is german? = \IfTranslation{german}{ttest}{yes}{no} \\
-Is defined = \IfTranslationExists{ttest}{yes}{no} \\
-
-\paragraph{Testing translation keys containing macros}
-\def\ttest{NAME}
-% \addtranslation{english}{\ttest:name}{With variable}
-% \addtranslation{german}{\ttest:name}{Mit Variable}
-% \addtranslation{english}{NAME:name}{Without variable}
-% \addtranslation{german}{NAME:name}{Without Variable}
-\DT[\ttest:name]{english}{DT With variable}
-\DT[\ttest:name]{german}{DT Mit Variable}
-\noindent
-GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\
-GetTranslation: {\textbackslash}ttest:name = \GetTranslation{\ttest:name}\\
-Is english? = \IfTranslation{english}{\ttest:name}{yes}{no} \\
-Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\
-Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\
-Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
-
-% \DT[qty:test]{english}{HAHA}
-
-\paragraph{Testing hyperrefs}
-\noindent{This text is labeled with "test" \label{test}}\\
-\hyperref[test]{This should refer to the line above}\\
-Link to quantity which is defined after the reference: \qtyRef{test}\\
-\DT[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
-\end{equation}
-
-\paragraph{Testing translation keys with token symbols like undescores}
-\noindent
-\GT{absolute_undefined_translation_with_underscors}\\
-\gt{relative_undefined_translation_with_underscors}\\
-\GT{absolute_undefined_translation_with_&ampersand}
-
-\paragraph{Aux files}
-\noindent Lua Aux loaded? \luaAuxLoaded\\
-Translations Aux loaded? \translationsAuxLoaded\\
-
-
-\newpage
-\Eng[appendix]{Appendix}
-\Ger[appendix]{Anhang}
-\part*{\GT{appendix}}
 % \listofmyenv
-\listofquantities
+% \listofquantities
 \listoffigures
 \listoftables
+\Section[
+    \eng{List of elements}
+    \ger{Liste der Elemente}
+]{elements}
+    \printAllElements
+
 % \bibliographystyle{plain}
 % \bibliography{ref}
 

src/math/calculus.tex

@@ -172,35 +172,88 @@
             }
         \end{formula}
 
-    \Subection[
+    \Subsection[
-        \eng{List of common integrals}
+        \eng{Integrals}
-        \ger{Liste nützlicher Integrale}
+        \ger{Integralrechnung}
-    ]{integrals}
+    ]{integral}
-
+        \begin{formula}{partial}
-        % Put links to other integrals here
+            \desc{Partial integration}{}{}
-        \fqEqRef{cal:log:integral}
+            \desc[german]{Partielle integration}{}{}
-
-        \begin{formula}{spherical-coordinates}
-            \desc{Spherical coordinates}{}{}
-            \desc[german]{Kugelkoordinaten}{}{}
             \eq{
-                x &= r \sin\phi,\cos\theta \\
+                \int_a^b f'(x)\cdot g(x) \d x= \left[f(x)\cdot g(x)\right]_a^b - \int_a^b f(x)\cdot g'(x) \d x
-                y &= r \cos\phi,\cos\theta \\
-                z &= r \sin\theta
             }
         \end{formula}
-        \begin{formula}{spheical-coordinates-int}
+
-            \desc{Integration in spherical coordinates}{}{}
+        \begin{formula}{substitution}
-            \desc[german]{Integration in Kugelkoordinaten}{}{}
+            \desc{Integration by substitution}{}{}
-            \eq{\iiint\d x \d y \d z= \int_0^{\infty} \!\! \int_0^{2\pi} \!\! \int_0^\pi \d r \d\phi\d\theta \, r^2\sin\theta}
+            \desc[german]{Integration durch Substitution}{}{}
+            \eq{
+                \int_a^b f(g(x))\,g'(x) \d x = \int_{g(a)}^{g(b)} f(z) \d z
+            }
         \end{formula}
 
-        \begin{formula}{riemann_zeta}
+        \begin{formula}{gauss}
-            \desc{Riemann Zeta Function}{}{}
+            \desc{Gauss's theorem / Divergence theorem}{Divergence in a volume equals the flux through the surface}{$A = \partial V$}
-            \desc[german]{Riemannsche Zeta-Funktion}{}{}
+            \desc[german]{Satz von Gauss}{Divergenz in einem Volumen ist gleich dem Fluss durch die Oberfläche}{}
-            \eq{\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \frac{1}{(1-2^{(1-s)})\Gamma(s)} \int_0^\infty \d\eta \frac{\eta^{(s-1)}}{\e^\eta + 1}}
+            \eq{
+                \iiint_V (\Div{\vec{F}}) \d V = \oiint_A \vec{F} \cdot \d\vec{A}
+            }
         \end{formula}
 
+        \begin{formula}{stokes}
+            \desc{Stokes's theorem}{}{$S = \partial A$}
+            \desc[german]{Klassischer Satz von Stokes}{}{}
+            \eq{\int_A (\Rot{\vec{F}}) \cdot \d\vec{S} = \oint_{S} \vec{F} \cdot \d \vec{r}}
+        \end{formula}
+        \Subsubsection[
+            \eng{List of common integrals}
+            \ger{Liste nützlicher Integrale}
+        ]{list}
+            % Put links to other integrals here
+            \fqEqRef{cal:log:integral}
+
+            \begin{formula}{arcfunctions}
+                \desc{Arcsine, arccosine, arctangent}{}{}
+                \desc[german]{Arkussinus, Arkuskosinus, Arkustangens}{}{}
+                \eq{
+                    \int \frac{1}{\sqrt{1-x^2}} \d x  = \arcsin x \\
+                    \int -\frac{1}{\sqrt{1-x^2}} \d x = \arccos x \\
+                    \int \frac{1}{x^2+1} \d x         = \arctan x
+                }
+            \end{formula}
+            \begin{formula}{archyperbolicfunctions}
+                \desc{Arcsinh, arccosh, arctanh}{}{}
+                % \desc[german]{Arkussinus, Arkuskosinus, Arkustangens}{}{}
+                \eq{
+                    \int \frac{1}{\sqrt{x^2+1}} \d x &= \arsinh x \\
+                    \int \frac{1}{\sqrt{x^2-1}} \d x &= \arcosh x \quad\eqnote{\GT{for} $(x > 1)$}\\
+                    \int \frac{1}{1-x^2} \d x        &= \artanh x \quad\eqnote{\GT{for} $(\abs{x} < 1)$}\\
+                    \int \frac{1}{1-x^2} \d x        &= \arcoth x \quad\eqnote{\GT{for} $(\abs{x} > 1)$}
+                }
+            \end{formula}
+
+            \begin{formula}{spherical-coordinates}
+                \desc{Spherical coordinates}{}{}
+                \desc[german]{Kugelkoordinaten}{}{}
+                \eq{
+                    x &= r \sin\phi,\cos\theta \\
+                    y &= r \cos\phi,\cos\theta \\
+                    z &= r \sin\theta
+                }
+            \end{formula}
+            \begin{formula}{spheical-coordinates-int}
+                \desc{Integration in spherical coordinates}{}{}
+                \desc[german]{Integration in Kugelkoordinaten}{}{}
+                \eq{\iiint\d x \d y \d z= \int_0^{\infty} \!\! \int_0^{2\pi} \!\! \int_0^\pi \d r \d\phi\d\theta \, r^2\sin\theta}
+            \end{formula}
+
+            \begin{formula}{riemann_zeta}
+                \desc{Riemann Zeta Function}{}{}
+                \desc[german]{Riemannsche Zeta-Funktion}{}{}
+                \eq{\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \frac{1}{(1-2^{(1-s)})\Gamma(s)} \int_0^\infty \d\eta \frac{\eta^{(s-1)}}{\e^\eta + 1}}
+            \end{formula}
 
 
+            \TODO{differential equation solutions}
+
 

src/math/geometry.tex

@@ -46,8 +46,8 @@
     \ger{Verschiedene Theoreme}
 ]{theorems}
     \begin{formula}{sum}
-        \desc{}{}{}
+        \desc{Hypthenuse in the unit circle}{}{}
-        \desc[german]{}{}{}
+        \desc[german]{Hypothenuse im Einheitskreis}{}{}
         \eq{1 &= \sin^2 x + \cos^2 x}
     \end{formula}
 
@@ -71,9 +71,9 @@
         }
     \end{formula}
 
-    \begin{formula}{name}
+    \begin{formula}{other}
-        \desc{}{}{$\tan\theta = b$}
+        \desc{Other}{}{$\tan\theta = b$}
-        \desc[german]{}{}{$\tan\theta = b$}
+        \desc[german]{Sonstige}{}{$\tan\theta = b$}
         \eq{\cos x + b\sin x = \sqrt{1 + b^2}\cos(x-\theta)}
     \end{formula}
 

src/math/linalg.tex

@@ -1,12 +1,66 @@
 \Section[
     \eng{Linear algebra}
     \ger{Lineare Algebra}
-    ]{linalg}
+]{linalg}
+
+    \Subsection[
+        \eng{Matrix basics}
+        \ger{Matrizen Basics}
+    ]{matrix}
+
+        \begin{formula}{matrix_matrix_product}
+            \desc{Matrix-matrix product as sum}{}{}
+            \desc[german]{Matrix-Matrix Produkt als Summe}{}{}
+            \eq{C_{ij} = \sum_{k} A_{ik} B_{kj}}
+        \end{formula}
+        \begin{formula}{matrix_vector_product}
+            \desc{Matrix-vector product as sum}{}{}
+            \desc[german]{Matrix-Vektor Produkt als Summe}{}{}
+            \eq{\vec{c}_{i} = \sum_{j} A_{ij} \vec{b}_{j}}
+        \end{formula}
+
+        \begin{formula}{symmetric}
+            \desc{Symmetric matrix}{}{$A$ $n\times n$ \GT{matrix}}
+            \desc[german]{Symmetrische matrix}{}{}
+            \eq{A^\T = A}
+        \end{formula}
+
+        \begin{formula}{unitary}
+            \desc{Unitary matrix}{}{}
+            \desc[german]{Unitäre Matrix}{}{}
+            \eq{U ^\dagger U = \id}
+        \end{formula}
+
+        \Subsubsection[
+            \eng{Transposed matrix}
+            \ger{Transponierte Matrix}
+        ]{transposed}
+            \begin{formula}{sum}
+                \desc{Sum}{}{}
+                \desc[german]{Summe}{}{}
+                \eq{(A+B)^\T = A^\T + B^\T}
+            \end{formula}
+            \begin{formula}{product}
+                \desc{Product}{}{}
+                \desc[german]{Produkt}{}{}
+                \eq{(AB)^\T = B^\T A^\T}
+            \end{formula}
+            \begin{formula}{inverse}
+                \desc{Inverse}{}{}
+                \desc[german]{Inverse}{}{}
+                \eq{(A^{-1})^\T = (A^\T)^{-1}}
+            \end{formula}
+            \begin{formula}{exponential}
+                \desc{Exponential}{}{}
+                \desc[german]{Exponential}{}{}
+                \eq{\exp(A^\T) = (\exp A)^\T \\ \ln(A^\T)=(\ln A)^\T}
+            \end{formula}
+        
 
     \Subsection[
         \eng{Determinant}
         \ger{Determinante}
-        ]{determinant}
+    ]{determinant}
         \begin{formula}{2x2}
             \desc{2x2 matrix}{}{}
             \desc[german]{2x2 Matrix}{}{}
@@ -43,7 +97,16 @@
 
     \Subsection[
         
-    ]{zeug}
+    ]{misc}
+
+        \begin{formula}{normal_equation}
+            \desc{Normal equation}{Solves a linear regression problem}{\mat{\theta} hypothesis / weight matrix, \mat{X} design matrix, \vec{y} output vector}
+            % \desc[german]{}{}{}
+            \eq{
+                \mat{\theta} = (\mat{X}^\T \mat{X})^{-1} \mat{X}^\T \vec{y}
+            }
+        \end{formula}   
+        
 
         \begin{formula}{inverse_2x2}
             \desc{Inverse $2\times 2$ matrix}{}{}
@@ -54,12 +117,6 @@
             }
         \end{formula}
 
-        \begin{formula}{unitary}
-            \desc{Unitary matrix}{}{}
-            \desc[german]{Unitäre Matrix}{}{}
-            \eq{U ^\dagger U = \id}
-        \end{formula}
-
         \begin{formula}{svd}
             \desc{Singular value decomposition}{Factorization of complex matrices through rotating \rightarrow rescaling \rightarrow rotation.}{$A$: $m\times n$ matrix, $U$: $m\times m$ unitary matrix, $\Lambda$: $m\times n$ rectangular diagonal matrix with non-negative numbers on the diagonal, $V$: $n\times n$ unitary matrix}
             \desc[german]{Singulärwertzerlegung}{Faktorisierung einer reellen oder komplexen Matrix durch Rotation \rightarrow Skalierung \rightarrow Rotation.}{}
@@ -93,7 +150,7 @@
         \end{formula}
 
 
-    \Subection[
+    \Subsection[
         \eng{Eigenvalues}
         \ger{Eigenwerte}
     ]{eigen}

src/math/math.tex

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

src/math/probability_theory.tex

@@ -102,7 +102,7 @@
                 \disteq{median}{x_0}
                 \disteq{variance}{\text{\GT{undefined}}}
             \end{distribution}
-
+            \noindent
             \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}.}
@@ -114,9 +114,9 @@
             \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}}
+                \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}}
+                \ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions:poisson]{Poissonverteilung}}
-            \end{ttext}
+            \end{ttext}\\
             \begin{minipage}{\distleftwidth}
                 \begin{figure}[H]
                     \centering

src/quantities.tex

@@ -1,77 +1,119 @@
 % if this causes a compilation error, check that none of the units have been redefined
 
-\Eng[si_base_units]{SI base units}
+% Put quantites here that are referenced often, even if they are not exciting themselves.
-\Ger[si_base_units]{SI Basisgrößen}
+% This could later allow making a list of all links to this quantity, creating a list of releveant formulas
 
-\paragraph{\GT{si_base_units}}
+\Section[
+    \eng{Physical quantities}
+    \ger{Physikalische Größen}
+]{quantities}
 
-    \begin{quantity}{time}{t}{\second}{}
+\Subsection[
+    \eng{SI quantities}
+    \ger{SI-Basisgrößen}
+]{si}
+    \begin{formula}{time}
         \desc{Time}{}{}
         \desc[german]{Zeit}{}{}
-    \end{quantity}
+        \quantity{t}{\second}{}
+    \end{formula}
 
-    \begin{quantity}{Length}{l}{\m}{e}
+    \begin{formula}{Length}
         \desc{Length}{}{}
         \desc[german]{Länge}{}{}
-    \end{quantity}
+        \quantity{l}{\m}{e}
+    \end{formula}
 
-    \begin{quantity}{mass}{m}{\kg}{es}
+    \begin{formula}{mass}
         \desc{Mass}{}{}
         \desc[german]{Masse}{}{}
-    \end{quantity}
+        \quantity{m}{\kg}{es}
+    \end{formula}
 
-    \begin{quantity}{temperature}{T}{\kelvin}{is}
+    \begin{formula}{temperature}
         \desc{Temperature}{}{}
         \desc[german]{Temperatur}{}{}
-    \end{quantity}
+        \quantity{T}{\kelvin}{is}
+    \end{formula}
 
-    \begin{quantity}{current}{I}{\ampere}{es}
+    \begin{formula}{current}
         \desc{Electric current}{}{}
         \desc[german]{Elektrischer Strom}{}{}
-    \end{quantity}
+        \quantity{I}{\ampere}{es}
+    \end{formula}
 
-    \begin{quantity}{amount}{n}{\mol}{es}
+    \begin{formula}{amount}
         \desc{Amount of substance}{}{}
         \desc[german]{Stoffmenge}{}{}
-    \end{quantity}
+        \quantity{n}{\mol}{es}
+    \end{formula}
 
-    \begin{quantity}{luminous_intensity}{I_\text{V}}{\candela}{s}
+    \begin{formula}{luminous_intensity}
         \desc{Luminous intensity}{}{}
         \desc[german]{Lichtstärke}{}{}
-    \end{quantity}
+        \quantity{I_\text{V}}{\candela}{s}
+    \end{formula}
 
-\paragraph{\GT{other}}
+\Subsection[
-    \begin{quantity}{volume}{V}{\m^d}{}
+    \eng{Mechanics}
-        \desc{Volume}{$d$ dimensional Volume}{}
+    \ger{Mechanik}
-        \desc[german]{Volumen}{$d$ dimensionales Volumen}{}
+]{mech}
-    \end{quantity}
 
-    \begin{quantity}{force}{\vec{F}}{\newton=\kg\m\per\second^2}{ev}
+    \begin{formula}{force}
         \desc{Force}{}{}
         \desc[german]{Kraft}{}{}
-    \end{quantity}
+        \quantity{\vec{F}}{\newton=\kg\m\per\second^2}{ev}
+    \end{formula}
 
-    \begin{quantity}{spring_constant}{k}{\newton\per\m=\kg\per\second^2}{s}
+    \begin{formula}{spring_constant}
         \desc{Spring constant}{}{}
         \desc[german]{Federkonstante}{}{}
-    \end{quantity}
+        \quantity{k}{\newton\per\m=\kg\per\second^2}{s}
+    \end{formula}
 
-    \begin{quantity}{velocity}{\vec{v}}{\m\per\s}{v}
+    \begin{formula}{velocity}
         \desc{Velocity}{}{}
         \desc[german]{Geschwindigkeit}{}{}
-    \end{quantity}
+        \quantity{\vec{v}}{\m\per\s}{v}
+    \end{formula}
 
-    \begin{quantity}{torque}{\tau}{\newton\m=\kg\m^2\per\s^2}{v}
+    \begin{formula}{torque}
         \desc{Torque}{}{}
         \desc[german]{Drehmoment}{}{}
-    \end{quantity}
+        \quantity{\tau}{\newton\m=\kg\m^2\per\s^2}{v}
+    \end{formula}
 
-    \begin{quantity}{heat_capacity}{C}{\joule\per\kelvin}{}
+\Subsection[
+    \eng{Thermodynamics}
+    \ger{Thermodynamik}
+]{td}
+    \begin{formula}{volume}
+        \desc{Volume}{$d$ dimensional Volume}{}
+        \desc[german]{Volumen}{$d$ dimensionales Volumen}{}
+        \quantity{V}{\m^d}{}
+    \end{formula}
+    \begin{formula}{heat_capacity}
         \desc{Heat capacity}{}{}
         \desc[german]{Wärmekapazität}{}{}
-    \end{quantity}
+        \quantity{C}{\joule\per\kelvin}{}
+    \end{formula}
 
-    \begin{quantity}{charge}{q}{\coulomb=\ampere\s}{}
+\Subsection[
+    \eng{Electrodynamics}
+    \ger{Elektrodynamik}
+]{el}
+    \begin{formula}{charge}
         \desc{Charge}{}{}
         \desc[german]{Ladung}{}{}
-    \end{quantity}
+        \quantity{q}{\coulomb=\ampere\s}{}
+    \end{formula}
+    \begin{formula}{charge_density}
+        \desc{Charge density}{}{}
+        \desc[german]{Ladungsdichte}{}{}
+        \quantity{\rho}{\coulomb\per\m^3}{s}
+    \end{formula}
+
+\Subsection[
+    \eng{Others}
+    \ger{Sonstige}
+]{other}

src/quantum_computing.tex

@@ -92,12 +92,10 @@
             \begin{formula}{circuit}
                 \desc{SQUID}{Superconducting quantum interference device, consists of parallel \hyperref{sec:qc:scq:josephson_junction}{josephson junctions}, can be used to measure extremely weak magnetic fields}{}
                 \desc[german]{SQUID}{Superconducting quantum interference device, besteht aus parralelen \hyperref{sec:qc:scq:josephson_junction}{Josephson Junctions} und kann zur Messung extrem schwacher Magnetfelder genutzt werden}{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{tikzpicture}
+                    \draw (0, 0) \squidloop{loop}{};
-                        \draw (0, 0) \squidloop{loop}{};
+                \end{tikzpicture}
-                    \end{tikzpicture}
-                }
             \end{formula}
             \begin{formula}{hamiltonian}
                 \desc{Hamiltonian}{}{$\hat{\phi}$ phase difference across the junction}
@@ -217,16 +215,14 @@
                         \baditem Sensibel für charge noise
                     \end{itemize}
                 }{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{tikzpicture}
+                  \draw (0,0) to[sV=$V_\text{g}$] (0,2);
-                      \draw (0,0) to[sV=$V_\text{g}$] (0,2);
+                  % \draw (0,0) to (2,0);
-                      % \draw (0,0) to (2,0);
+                  \draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
-                      \draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
+                  \draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
-                      \draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
+                  \draw (0,0) to (2,0);
-                      \draw (0,0) to (2,0);
+                \end{tikzpicture}
-                    \end{tikzpicture}
-                }
             \end{formula}
 
 
@@ -256,15 +252,13 @@
                         \baditem Geringe Anharmonizität $\alpha$
                     \end{itemize}
                 }{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{tikzpicture}
+                    % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                    % to[capacitor=$C_\text{g}$] ++(2,0)
-                        % to[capacitor=$C_\text{g}$] ++(2,0)
+                    \draw (0,0) to ++(2,0) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to ++(0,-0.5) to ++(-2,0)
-                        \draw (0,0) to ++(2,0) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to ++(0,-0.5) to ++(-2,0)
+                     to[capacitor=$C_C$] ++(0,3);
-                         to[capacitor=$C_C$] ++(0,3);
+                \end{tikzpicture}
-                    \end{tikzpicture}
-                }
             \end{formula}
 
             \begin{formula}{hamiltonian}
@@ -280,16 +274,14 @@
                 \begin{formula}{circuit}
                     \desc{Frequency tunable transmon}{By using a \fqSecRef{qc:scq:elements:squid} instead of a \fqSecRef{qc:scq:elements:josephson_junction}, the qubit is frequency tunable through an external field}{}
                     \desc[german]{}{Durch Nutzung eines \fqSecRef{qc:scq:elements:squid} anstatt eines \fqSecRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{}
-                    \content{
+                    \centering
-                        \centering
+                    \begin{tikzpicture}
-                        \begin{tikzpicture}
+                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                            % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                        % to[capacitor=$C_\text{g}$] ++(2,0)
-                            % to[capacitor=$C_\text{g}$] ++(2,0)
+                        \draw (0,0) to ++(-2,0)
-                            \draw (0,0) to ++(-2,0)
+                        to ++(3,0) to ++(0,-0.5) \squidloop{loop}{SQUID} to ++(0,-0.5) to ++(-3,0)
-                            to ++(3,0) to ++(0,-0.5) \squidloop{loop}{SQUID} to ++(0,-0.5) to ++(-3,0)
+                        to[capacitor=$C_C$] ++(0,3);
-                            to[capacitor=$C_C$] ++(0,3);
+                    \end{tikzpicture}
-                        \end{tikzpicture}
-                    }
                 \end{formula}
 
                 \begin{formula}{energy}
@@ -318,25 +310,23 @@
             \begin{formula}{circuit}
                 \desc{Phase qubit}{}{}
                 \desc[german]{Phase Qubit}{}{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{tikzpicture}
+                    % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                    % to ++(2,0) coordinate(top1)
-                        % to ++(2,0) coordinate(top1)
+                    % to ++(2,0) coordinate(top2)
-                        % to ++(2,0) coordinate(top2)
+                    % to ++(2,0) coordinate(top3);
-                        % to ++(2,0) coordinate(top3);
+                    % \draw (0,0)
-                        % \draw (0,0)
+                    % to ++(2,0) coordinate(bot1)
-                        % to ++(2,0) coordinate(bot1)
+                    % to ++(2,0) coordinate(bot2)
-                        % to ++(2,0) coordinate(bot2)
+                    % to ++(2,0) coordinate(bot3);
-                        % to ++(2,0) coordinate(bot3);
+                    \draw[color=gray] (0,0) to[capacitor=$C_C$] (0,-2);
-                        \draw[color=gray] (0,0) to[capacitor=$C_C$] (0,-2);
+                    % \draw (top1) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to (bot2);
-                        % \draw (top1) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to (bot2);
+                    \draw(0,0) to ++(2,0) to[josephsoncap=$C_\text{J}$] ++(0,-2) to ++(-2,0);
-                        \draw(0,0) to ++(2,0) to[josephsoncap=$C_\text{J}$] ++(0,-2) to ++(-2,0);
+                    \draw (2,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-2) to ++(-2,0);
-                        \draw (2,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-2) to ++(-2,0);
+                    \node at (3,-1.5) {$\Phi_\text{ext}$};
-                        \node at (3,-1.5) {$\Phi_\text{ext}$};
+                \end{tikzpicture}
-                    \end{tikzpicture}
+                \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                    \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                }
             \end{formula}
             \begin{formula}{hamiltonian}
                 \desc{Hamiltonian}{}{$\delta = \frac{\phi}{\phi_0}$}
@@ -358,16 +348,15 @@
             \begin{formula}{circuit}
                 \desc{Flux qubit / Persistent current qubit}{}{}
                 \desc[german]{Flux Qubit / Persistent current qubit}{}{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{tikzpicture}
+                    \draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
-                        \draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
+                    \draw (0,0) to ++(3,0) 
-                        \draw (0,0) to ++(3,0) 
+                    to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
-                        to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
+                    to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
-                        to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
+                    to ++(-3,0);
-                        to ++(-3,0);
+                    \node at (1.5,-1.5) {$\Phi_\text{ext}$};
-                        \node at (1.5,-1.5) {$\Phi_\text{ext}$};
+                \end{tikzpicture}
-                    \end{tikzpicture}
                     % \begin{tikzpicture}
                     %     \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
                     %     to ++(2,0) coordinate(top1)
@@ -385,7 +374,6 @@
                     %     to[josephsoncap=$E_\text{J}$] (bot3);
                     %     \node at (5,0.5) {$\Phi_\text{ext}$};
                     % \end{tikzpicture}
-                }
             \end{formula}
 
 
@@ -403,18 +391,16 @@
                     Anstatt zu tunneln, können die Cooper-Paare über das induktive Element auf die Insel gelangen.
                     Das induktive Element besteht aus sehr vielen parallelen Josephson-Kontakten um parisitische Kapazitäten zu vermeiden.
                 }{}
-                \content{
+                \centering
-                    \centering
+                \begin{tikzpicture}
-                    \begin{tikzpicture}
+                    % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
-                        % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
+                    % to ++(2,0) coordinate(top1);
-                        % to ++(2,0) coordinate(top1);
+                    \draw[color=gray] (0,0) to ++(-2,0) to[capacitor=$C_C$] ++(0,-3) to ++(2,0);
-                        \draw[color=gray] (0,0) to ++(-2,0) to[capacitor=$C_C$] ++(0,-3) to ++(2,0);
+                    \draw (0,0) to[josephsoncap=$C_\text{J}$] ++(-0,-3);
-                        \draw (0,0) to[josephsoncap=$C_\text{J}$] ++(-0,-3);
+                    \draw (0,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
-                        \draw (0,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
+                    \node at (1,-0.5) {$\Phi_\text{ext}$};
-                        \node at (1,-0.5) {$\Phi_\text{ext}$};
+                \end{tikzpicture}
-                    \end{tikzpicture}
+                \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                    \\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
-                }
             \end{formula}
 
             \def\temp{$E_\text{C} = \frac{(2e)^2}{2C}, E_\text{L} = \frac{\varphi_0^2}{2L}, \delta_\text{s} = \frac{\varphi_\text{s}}{\varphi_0}$}

src/quantum_mechanics.tex

@@ -497,6 +497,15 @@
             \eq{\psi_k(\vec{r}) = e^{i \vec{k}\cdot \vec{r}} \cdot u_{\vec{k}}(\vec{r})}
         \end{formula}
 
+        \begin{formula}{periodicity}
+            \desc{Periodicity}{}{\QtyRef{lattice_vector}, \QtyRef{reciprocal_lattice_vector}}
+            \desc[german]{Periodizität}{}{}
+            \eq{
+                u_\vec{k}(\vec{r} + \vec{R}) = u_\vec{k}(\vec{r}) \\
+                \psi_{\vec{k}+\vec{G}}(\vec{r}) = \psi_\vec{k}(\vec{r})
+            }
+        \end{formula}
+
 
     \Section[
         \eng{Symmetries}

src/spv.tex

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

src/statistical_mechanics.tex

@@ -1,84 +1,84 @@
 \Part[
     \eng{Statistichal Mechanics}
     \ger{Statistische Mechanik}
-    ]{stat}
+]{stat}
 
-    \begin{ttext}
+\begin{ttext}
-        \eng{
+    \eng{
-            \textbf{Extensive 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{Intensive quantities:} Independent of system size, ratio of two extensive quantities
+        \textbf{Intensive quantities:} Independent of system size, ratio of two extensive quantities
-        }
+    }
-        \ger{
+    \ger{
-            \textbf{Extensive 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{Intensive Größen:} Unabhängig der Systemgröße, Verhältnis zweier extensiver Größen
+        \textbf{Intensive Größen:} Unabhängig der Systemgröße, Verhältnis zweier extensiver Größen
-        }
+    }
-    \end{ttext}
+\end{ttext}
 
-    \begin{formula}{liouville}
+\begin{formula}{liouville}
-        \desc{Liouville equation}{}{$\{\}$ poisson bracket}
+    \desc{Liouville equation}{}{$\{\}$ poisson bracket}
-        \desc[german]{Liouville-Gleichung}{}{$\{\}$ Poisson-Klammer}
+    \desc[german]{Liouville-Gleichung}{}{$\{\}$ Poisson-Klammer}
-        \eq{\pdv{\rho}{t} = - \sum_{i=1}^{N} \left(\pdv{\rho}{q_i} \pdv{H}{p_i} - \pdv{\rho}{p_i} \pdv{H}{q_i} \right) = \{H, \rho\}}
+    \eq{\pdv{\rho}{t} = - \sum_{i=1}^{N} \left(\pdv{\rho}{q_i} \pdv{H}{p_i} - \pdv{\rho}{p_i} \pdv{H}{q_i} \right) = \{H, \rho\}}
+\end{formula}
+
+\Section[
+    \eng{Entropy}
+    \ger{Entropie}
+]{entropy}
+
+    \begin{formula}{properties}
+        \desc{Positive-definite and additive}{}{}
+        \desc[german]{Positiv Definit und Additiv}{}{}
+        \eq{
+            S &\ge 0 \\
+            S(E_1, E_2) &= S_1 + S_2
+        }
     \end{formula}
 
-    \Section[
+    \begin{formula}{von_neumann}
-        \eng{Entropy}
+        \desc{Von-Neumann}{}{$\rho$ density matrix}
-        \ger{Entropie}
+        \desc[german]{Von-Neumann}{}{$\rho$ Dichtematrix}
-        ]{entropy}
+        \eq{S = - \kB \braket{\log \rho} = - \kB \tr(\rho \log\rho)}
+    \end{formula}
 
-        \begin{formula}{properties}
+    \begin{formula}{gibbs}
-            \desc{Positive-definite and additive}{}{}
+        \desc{Gibbs}{}{$p_n$ probability for micro state $n$}
-            \desc[german]{Positiv Definit und Additiv}{}{}
+        \desc[german]{Gibbs}{}{$p_n$ Wahrscheinlichkeit für Mikrozustand $n$}
-            \eq{
+        \eq{S = - \kB \sum_n p_n \log p_n}
-                S &\ge 0 \\
+    \end{formula}
-                S(E_1, E_2) &= S_1 + S_2
-            }
-        \end{formula}
 
-        \begin{formula}{von_neumann}
+    \begin{formula}{boltzmann}
-            \desc{Von-Neumann}{}{$\rho$ density matrix}
+        \desc{Boltzmann}{}{$\Omega$ \#micro states}
-            \desc[german]{Von-Neumann}{}{$\rho$ Dichtematrix}
+        \desc[german]{Boltzmann}{}{$\Omega$ \#Mikrozustände}
-            \eq{S = - \kB \braket{\log \rho} = - \kB \tr(\rho \log\rho)}
+        \eq{S = \kB \log\Omega}
-        \end{formula}
+    \end{formula}
 
-        \begin{formula}{gibbs}
+    \begin{formula}{temp}
-            \desc{Gibbs}{}{$p_n$ probability for micro state $n$}
+        \desc{Temperature}{}{}
-            \desc[german]{Gibbs}{}{$p_n$ Wahrscheinlichkeit für Mikrozustand $n$}
+        \desc[german]{Temperatur}{}{}
-            \eq{S = - \kB \sum_n p_n \log p_n}
+        \eq{\frac{1}{T} \coloneq \pdv{S}{E}_V}
-        \end{formula}
+    \end{formula}
 
-        \begin{formula}{boltzmann}
+    \begin{formula}{pressure}
-            \desc{Boltzmann}{}{$\Omega$ \#micro states}
+        \desc{Pressure}{}{}
-            \desc[german]{Boltzmann}{}{$\Omega$ \#Mikrozustände}
+        \desc[german]{Druck}{}{}
-            \eq{S = \kB \log\Omega}
+        \eq{p = T \pdv{S}{V}_E}
-        \end{formula}
+    \end{formula}
-
-        \begin{formula}{temp}
-            \desc{Temperature}{}{}
-            \desc[german]{Temperatur}{}{}
-            \eq{\frac{1}{T} \coloneq \pdv{S}{E}_V}
-        \end{formula}
-
-        \begin{formula}{pressure}
-            \desc{Pressure}{}{}
-            \desc[german]{Druck}{}{}
-            \eq{p = T \pdv{S}{V}_E}
-        \end{formula}
 
 \Part[
     \eng{Thermodynamics}
     \ger{Thermodynamik}
-    ]{td}
+]{td}
 
-    \begin{formula}{therm_wavelength}
+\begin{formula}{therm_wavelength}
-        \desc{Thermal wavelength}{}{}
+    \desc{Thermal wavelength}{}{}
-        \desc[german]{Thermische Wellenlänge}{}{}
+    \desc[german]{Thermische Wellenlänge}{}{}
-        \eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
+    \eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
-    \end{formula}
+\end{formula}
 
-    \Section[
+\Section[
-        \eng{Processes}
+    \eng{Processes}
-        \ger{Prozesse}
+    \ger{Prozesse}
-    ]{process}
+]{process}
     \begin{ttext}
         \eng{
             \begin{itemize}
@@ -149,7 +149,7 @@
     \Section[
         \eng{Phase transitions}
         \ger{Phasenübergänge}
-        ]{phases}
+    ]{phases}
 
         \begin{ttext}
             \eng{
@@ -187,7 +187,7 @@
         \Subsubsection[
             \eng{Osmosis}
             \ger{Osmose}
-            ]{osmosis}
+        ]{osmosis}
             \begin{ttext}
                 \eng{
                     Osmosis is the spontaneous net movement or diffusion of solvent molecules 
@@ -213,7 +213,7 @@
     \Subsection[
         \eng{Material properties}
         \ger{Materialeigenschaften}
-        ]{}
+    ]{props}
         \begin{formula}{heat_cap}
             \desc{Heat capacity}{}{$Q$ heat}
             \desc[german]{Wärmekapazität}{}{$Q$ Wärme}
@@ -266,12 +266,12 @@
 \Section[
     \eng{Laws of thermodynamics}
     \ger{Hauptsätze der Thermodynamik}
-    ]{laws}
+]{laws}
 
     \Subsection[
         \eng{Zeroeth law}
         \ger{Nullter Hauptsatz}
-        ]{law0}
+    ]{law0}
         \begin{ttext}
             \eng{If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.}
             \ger{Wenn sich zwei Siesteme jeweils im thermischen Gleichgewicht mit einem dritten befinden, befinden sie sich auch untereinander im thermischen Gleichgewicht.}
@@ -307,7 +307,7 @@
     \Subsection[
         \eng{Second law}
         \ger{Zweiter Hauptsatz}
-        ]{law2}
+    ]{law2}
         \begin{ttext}
             \eng{
                 \textbf{Clausius}: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.\\
@@ -321,7 +321,7 @@
     \Subsection[
         \eng{Third law}
         \ger{Dritter Hauptsatz}
-        ]{law3}
+    ]{law3}
         \begin{ttext}
             \eng{It is impussible to cool a system to absolute zero.}
             \ger{Es ist unmöglich, ein System bis zum absoluten Nullpunkt abzukühlen.}
@@ -340,7 +340,7 @@
 \Section[
     \eng{Ensembles}
     \ger{Ensembles}
-    ]{ensembles}
+]{ensembles}
 
 
 
@@ -370,7 +370,7 @@
     \Subsection[
         \eng{Potentials}
         \ger{Potentiale}
-        ]{pots}
+    ]{pots}
         \begin{formula}{internal_energy}
             \desc{Internal energy}{}{}
             \desc[german]{Innere Energie}{}{}
@@ -401,7 +401,7 @@
         \begin{formula}{td-square}
             \desc{Thermodynamic squre}{}{}
             \desc[german]{Themodynamisches Quadrat}{Guggenheim Quadrat}{}
-            \content{
+            \begin{minipage}{0.3\textwidth}
                 \begin{tikzpicture}
                     \draw[thick] (0,0) grid (3,3);
                     \node at (0.5, 2.5) {$-S$};
@@ -413,17 +413,17 @@
                     \node at (1.5, 0.5) {\color{blue}$G$};
                     \node at (2.5, 0.5) {$T$};
                 \end{tikzpicture}
-                \begin{ttext}
+            \end{minipage}
-                    \eng{The corners opposite from the potential are the coefficients and each coefficients differential is opposite to it.}
+            \begin{ttext}
-                    \ger{Die Ecken gegenüber des Potentials sind die Koeffizienten, das Differential eines Koeffizienten ist in der Ecke gegenüber.}
+                \eng{The corners opposite from the potential are the coefficients and each coefficients differential is opposite to it.}
-                \end{ttext}
+                \ger{Die Ecken gegenüber des Potentials sind die Koeffizienten, das Differential eines Koeffizienten ist in der Ecke gegenüber.}
-            }
+            \end{ttext}
         \end{formula}
 
 \Section[
     \eng{Ideal gas}
     \ger{Ideales Gas}
-    ]{id_gas}
+]{id_gas}
     \begin{ttext}
         \eng{The ideal gas consists of non-interacting, undifferentiable particles.}
         \ger{Das ideale Gas besteht aus nicht-wechselwirkenden, ununterscheidbaren Teilchen.}
@@ -488,20 +488,18 @@
         \begin{formula}{desc}
             \desc{Molecule gas}{2 particles of mass $M$ connected by a ``spring'' with distance $L$}{}
             \desc[german]{Molekülgas}{2 Teilchen der Masse $M$ sind verbunden durch eine ``Feder'' mit Länge $L$}{}
-            \content{
+            % \begin{figure}[h]
-                % \begin{figure}[h]
+            \centering
-                \centering
+            \tikzstyle{spring}=[thick,decorate,decoration={coil,aspect=0.8,amplitude=5,pre length=0.1cm,post length=0.1cm,segment length=10}]
-                \tikzstyle{spring}=[thick,decorate,decoration={coil,aspect=0.8,amplitude=5,pre length=0.1cm,post length=0.1cm,segment length=10}]
+            \begin{tikzpicture}
-                \begin{tikzpicture}
+                \def\radius{0.5}
-                    \def\radius{0.5}
+                \coordinate (left) at (-3, 0);
-                    \coordinate (left) at (-3, 0);
+                \coordinate (right) at (3, 0);
-                    \coordinate (right) at (3, 0);
+                \draw (left) circle (\radius);
-                    \draw (left) circle (\radius);
+                \draw[spring] ($(left) + (\radius,0)$)  -- ($(right) - (\radius,0)$);
-                    \draw[spring] ($(left) + (\radius,0)$)  -- ($(right) - (\radius,0)$);
+                \draw (right) circle (\radius);
-                    \draw (right) circle (\radius);
+            \end{tikzpicture}
-                \end{tikzpicture}
                 % \end{figure}
-            }
         \end{formula}
 
         \begin{formula}{translation}
@@ -527,7 +525,7 @@
 \Section[
     \eng{Real gas}
     \ger{Reales Gas}
-    ]{real_gas}
+]{real_gas}
 
     \Subsection[
         \eng{Virial expansion}
@@ -559,8 +557,9 @@
 
         \begin{formula}{lennard_jones}
             \desc{Lennard-Jones potential}{Potential between two molecules. Attractive for $r > \sigma$, repulsive for $r < \sigma$.\\ In condensed matter: Attraction due to Landau Dispersion \TODO{verify} and repulsion due to Pauli exclusion principle.}{}
-            \desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$.\\ In Festkörpern: Anziehung durch Landau Dispesion und Abstoßung durch Pauli-Prinzip.}{}
+            \desc[german]{Lennard-Jones-Potential}{Potential zwischen zwei Molekülen. Attraktiv für $r > \sigma$, repulsiv für $r < \sigma$.\\ In Festkörpern: Anziehung durch Landau-Dispersion und Abstoßung durch Pauli-Prinzip.}{}
-            \figeq{img/potential_lennard_jones.pdf}{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
+            \fig[0.7]{img/potential_lennard_jones.pdf}
+            \eq{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
         \end{formula}
 
     \Subsection[
@@ -587,7 +586,7 @@
 \Section[
     \eng{Ideal quantum gas}
     \ger{Ideales Quantengas}
-    ]{id_qgas}
+]{id_qgas}
     \def\bosfer{$\pm$: {$\text{bos} \atop \text{fer}$}}
 
     \begin{formula}{fugacity}
@@ -632,7 +631,8 @@
     \begin{formula}{occupation_number}
         \desc{Occupation number}{}{\bosfer}
         \desc[german]{Besetzungszahl}{}{\bosfer}
-        \figeq{img/td_id_qgas_distributions.pdf}{%
+        \fig[0.7]{img/td_id_qgas_distributions.pdf}
+        \eq{
             \braket{n(\epsilon)} &= \frac{1}{\e^{\beta(\epsilon - \mu)} \mp 1} \\
             \shortintertext{\GT{for} $\epsilon - \mu \gg \kB T$}
                         &= \frac{1}{\e^{\beta(\epsilon - \mu)}}
@@ -678,7 +678,7 @@
     \Subsection[
         \eng{Bosons}
         \ger{Bosonen}
-        ]{bos}
+    ]{bos}
         \begin{formula}{partition-sum}
             \desc{Partition sum}{}{$p \in\N_0$}
             \desc[german]{Zustandssumme}{}{$p \in\N_0$}
@@ -694,7 +694,7 @@
     \Subsection[
         \eng{Fermions}
         \ger{Fermionen}
-        ]{fer}
+    ]{fer}
         \begin{formula}{partition_sum}
             \desc{Partition sum}{}{$p = 0,\,1$}
             \desc[german]{Zustandssumme}{}{$p = 0,\,1$}
@@ -703,7 +703,8 @@
         \begin{formula}{occupation}
             \desc{Occupation number}{Fermi-Dirac distribution. At $T=0$ \textit{Fermi edge} at $\epsilon=\mu$}{}
             \desc[german]{Besetzungszahl}{Fermi-Dirac Verteilung}{Bei $T=0$ \textit{Fermi-Kante} bei $\epsilon=\mu$}
-            \figeq{img/td_fermi_occupation.pdf}{\braket{n_p} = \frac{1}{\e^{\beta(\epsilon-\mu)}+1}}
+            \fig[0.7]{img/td_fermi_occupation.pdf}
+            \eq{\braket{n_p} = \frac{1}{\e^{\beta(\epsilon-\mu)}+1}}
         \end{formula}
 
         \begin{formula}{slater_determinant}
@@ -769,7 +770,8 @@
             \begin{formula}{heat_cap}
                 \desc{Heat capacity}{\gt{low_temps}}{differs from \fqEqRef{td:TODO:petit_dulong}}
                 \desc[german]{Wärmecapacity}{\gt{low_temps}}{weicht ab vom \fqEqRef{td:TODO:petit_dulong}}
-                \figeq{img/td_fermi_heat_capacity.pdf}{C_V = \pdv{E}{T}_V = N\kB \frac{\pi}{2} \left(\frac{T}{T_\text{F}}\right)}
+                \fig[0.7]{img/td_fermi_heat_capacity.pdf}
+                \eq{C_V = \pdv{E}{T}_V = N\kB \frac{\pi}{2} \left(\frac{T}{T_\text{F}}\right)}
             \end{formula}
 
             

src/test.tex

@@ -0,0 +1,84 @@
+\part{Testing}
+
+\paragraph{File loading}
+\noindent Lua Aux loaded? \luaAuxLoaded\\
+Translations Aux loaded? \translationsAuxLoaded\\
+Input only: \inputOnlyFile
+
+\paragraph{Testing GT, GetTranslation, IfTranslationExists, IfTranslation}
+\addtranslation{english}{ttest}{This is the english translation of \texttt{ttest}}
+\noindent
+GT: ttest = \GT{ttest}\\
+GetTranslation: ttest = \GetTranslation{ttest}\\
+Is english? = \IfTranslation{english}{ttest}{yes}{no} \\
+Is german? = \IfTranslation{german}{ttest}{yes}{no} \\
+Is defined = \IfTranslationExists{ttest}{yes}{no} \\
+
+\paragraph{Testing translation keys containing macros}
+\def\ttest{NAME}
+% \addtranslation{english}{\ttest:name}{With variable}
+% \addtranslation{german}{\ttest:name}{Mit Variable}
+% \addtranslation{english}{NAME:name}{Without variable}
+% \addtranslation{german}{NAME:name}{Without Variable}
+\DT[\ttest:name]{english}{DT With variable}
+\DT[\ttest:name]{german}{DT Mit Variable}
+\noindent
+GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\
+GetTranslation: {\textbackslash}ttest:name = \GetTranslation{\ttest:name}\\
+Is english? = \IfTranslation{english}{\ttest:name}{yes}{no} \\
+Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\
+Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\
+Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
+
+% \DT[qty:test]{english}{HAHA}
+
+\paragraph{Testing hyperrefs}
+\noindent{This text is labeled with "test" \label{test}}\\
+\hyperref[test]{This should refer to the line above}\\
+Link to quantity which is defined after the reference: \qtyRef{test}\\
+\DT[eq:test]{english}{If you read this, then the translation for eq:test was expandend!}
+Link to defined quantity: \qtyRef{mass}
+\\ Link to element with name: \ElRef{H}
+\begin{equation}
+    \label{eq:test}
+    E = mc^2
+\end{equation}
+
+\paragraph{Testing translation keys with token symbols like undescores}
+\noindent
+\GT{absolute_undefined_translation_with_underscors}\\
+\gt{relative_undefined_translation_with_underscors}\\
+\GT{absolute_undefined_translation_with_&ampersand}
+
+
+\paragraph{Testing formula2}
+\begin{formula}{test}
+    \desc{Test}{Test Description}{Defs}
+    \desc[german]{Test (DE)}{Beschreibung}{Defs (DE)}
+    \eq{
+        \text{equationwith}_{\alpha} \delta \E \left[yo\right]
+    }
+    \quantity{\tau}{\m\per\s}{iv}
+\end{formula}
+\begin{formula}{test2}
+    \desc{Test2}{Test Description}{Defs}
+    \desc[german]{Test2 (DE)}{Beschreibung}{Defs (DE)}
+    \ttxt{
+        \eng{This text is english}
+        \ger{Dieser Text ist deutsch}
+    }
+    \ttxt[moretext]{
+        \eng{This text is english, again}
+        \ger{Dieser Text ist wieder deutsch}
+    }
+    \begin{equation}
+        M\omega\rho\epsilon
+    \end{equation}
+\end{formula}
+\begin{formula}{test3}
+    \desc{Test2}{Test Description}{Defs}
+    \desc[german]{Test2 (DE)}{Beschreibung}{Defs (DE)}
+    Formula  with just plain text.
+\end{formula}
+
+

src/util/environments.tex

@@ -1,5 +1,5 @@
 % use this to define text in different languages for the key <env arg>
-% the translation for <env arg> when the environment ends.
+% the translation for <env arg> is printed when the environment ends.
 % (temporarily change fqname to the \fqname:<env arg> to allow
 % the use of \eng and \ger without the key parameter)
 % [1]: key
@@ -30,117 +30,41 @@
         \IfTranslationExists{#2}{
             \raggedright
             \GT{#2}
-        }{NO NAME} 
+        }{\detokenize{#2}}
         \IfTranslationExists{#3}{
            \\ {\color{dark1} \GT{#3}}
         }{}
     \end{minipage}
 }
 
+
+% TODO: rename
+\newsavebox{\contentBoxBox}
 % [1]: minipage width
-% 2: content
+% 2: fqname of a translation that holds the explanation
-% 3: fqname of a translation that holds the explanation
+\newenvironment{ContentBoxWithExplanation}[2][\eqwidth]{
-\newcommand{\ContentBoxWithExplanation}[3][\eqwidth]{
+    \def\ContentFqName{#2}
-    \fbox{
+    \begin{lrbox}{\contentBoxBox}
     \begin{minipage}{#1}
-        % \vspace{-\baselineskip}  % remove the space that comes from starting a new paragraph
+}{
-        #2
+        \IfTranslationExists{\ContentFqName}{%
-        \smartnewline
+            \smartnewline
-        \noindent\IfTranslationExists{#3}{
+            \noindent
             \begingroup
                 \color{dark1} 
-                \GT{#3}
+                \GT{\ContentFqName}
                 % \edef\temp{\GT{#1_defs}}
                 % \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
             \endgroup
         }{}
-        % \vspace{-\baselineskip}  % remove the space that comes from starting a new paragraph
     \end{minipage}
-    }
+    \end{lrbox}
-
+    \fbox{\usebox{\contentBoxBox}}
 }
 
-% 1: fqname, optional with #1_defs and #1_desc defined
-% 2: content
-\newcommand{\NameLeftContentRight}[2]{
-    \par\noindent\ignorespaces
-    % \textcolor{gray}{\hrule}
-    \vspace{0.5\baselineskip}
-    \NameWithDescription[\descwidth]{#1}{#1_desc}
-    \hfill
-    \ContentBoxWithExplanation[\eqwidth]{#2}{#1_defs}
-    \textcolor{dark3}{\hrule}
-    \vspace{0.5\baselineskip}
-    % \par
-    % \hrule
-}
 
-\newcommand{\insertEquation}[2]{
-    \NameLeftContentRight{\fqname:#1}{
-        \begin{align}
-            \label{eq:\fqname:#1}
-            #2
-        \end{align}
-    }
-}
 
-\newcommand{\insertFLAlign}[2]{  % eq name, #cols, eq
-    \NameLeftContentRight{\fqname:#1}{%
-        \begin{flalign}%
-            % dont place label when one is provided
-            % \IfSubStringInString{label}\unexpanded{#3}{}{
-            %     \label{eq:#1}
-            % }
-            #2%
-        \end{flalign}
-    }
-}
 
-\newcommand{\insertAlignedAt}[3]{  % eq name, #cols, eq
-    \NameLeftContentRight{\fqname:#1}{%
-        \begin{alignat}{#2}%
-            % dont place label when one is provided
-            % \IfSubStringInString{label}\unexpanded{#3}{}{
-            %     \label{eq:#1}
-            % }
-            #3%
-        \end{alignat}
-    }
-}
-
-% [1]: width
-% 2: fqname
-% 3: file path
-% 4: equation
-\newcommand{\insertEquationWithFigure}[4][0.55]{
-    \par\noindent\ignorespaces
-    % \textcolor{gray}{\hrule}
-    \vspace{0.5\baselineskip}
-    \begin{minipage}{#1\textwidth}
-        \NameWithDescription[\textwidth]{\fqname:#2}{#2_desc}
-        % TODO: why is this ignored
-        \vspace{1.0cm}
-        % TODO: fix box is too large without 0.9
-        \ContentBoxWithExplanation[0.90\textwidth]{
-            \begin{align}
-                \label{eq:\fqname:#2}
-                #4
-            \end{align}
-        }{#2_defs}
-    \end{minipage}
-    \hfill
-    \begin{minipage}{\luavar{1.0-#1}\textwidth}
-        \begin{figure}[H]
-            \centering
-            \includegraphics[width=\textwidth]{#3}
-            \label{fig:\fqname:#2}
-        \end{figure}
-    \end{minipage}
-    \textcolor{dark3}{\hrule}
-    \vspace{0.5\baselineskip}
-}
-
-% 1: key
 \newenvironment{formula}[1]{
     % [1]: language
     % 2: name
@@ -152,39 +76,118 @@
         \ifblank{##3}{}{\dt[#1_desc]{##1}{##3}}
         \ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
     }
+    \directlua{n_formulaEntries = 0}
+    \newcommand{\newFormulaEntry}{
+        \directlua{
+            if n_formulaEntries > 0 then
+            tex.print("\\vspace{0.3\\baselineskip}\\hrule\\vspace{0.3\\baselineskip}")
+            end
+            n_formulaEntries = n_formulaEntries + 1
+        }
+        % \par\noindent\ignorespaces
+    }
     % 1: equation for align environment
     \newcommand{\eq}[1]{
-        \insertEquation{#1}{##1}
+        \newFormulaEntry
+        \begin{align}
+            \label{eq:\fqname:#1}
+            ##1
+        \end{align}
     }
     % 1: equation for alignat environment
     \newcommand{\eqAlignedAt}[2]{
-        \insertAlignedAt{#1}{##1}{##2}
+        \newFormulaEntry
+        \begin{flalign}%
+            \TODO{\text{remove macro}}
+            % dont place label when one is provided
+            % \IfSubStringInString{label}\unexpanded{#3}{}{
+            %     \label{eq:#1}
+            % }
+            ##1%
+        \end{flalign}
     }
     % 1: equation for flalign environment
-    \newcommand{\eqFLAlign}[1]{
+    \newcommand{\eqFLAlign}[2]{
-        \insertFLAlign{#1}{##1}
+        \newFormulaEntry
+        \begin{alignat}{##1}%
+            % dont place label when one is provided
+            % \IfSubStringInString{label}\unexpanded{#3}{}{
+            %     \label{eq:#1}
+            % }
+            ##2%
+        \end{alignat}
     }
-    % 1: file path
+    \newcommand{\fig}[2][1.0]{
-    % 2: equation
+        \newFormulaEntry
-    \newcommand{\figeq}[2]{
+        \centering
-        \insertEquationWithFigure{#1}{##1}{##2}
+        \includegraphics[width=##1\textwidth]{##2}
-    }
-    % 1: any content
-    \newcommand{\content}[1]{
-        \NameLeftContentRight{\fqname:#1}{##1}
     }
     % 1: content for the ttext environment
-    \newcommand{\ttxt}[1]{
+    \newcommand{\ttxt}[2][#1:desc]{
-        \NameLeftContentRight{\fqname:#1}{
+        \newFormulaEntry
-            \begin{ttext}[#1:desc]
+        \begin{ttext}[##1]
-                ##1
+            ##2
-            \end{ttext}
+        \end{ttext}
+    }
+    % 1: key - must expand to a valid lua string!
+    % 2: symbol
+    % 3: units
+    % 4: comment key to translation
+    \newcommand{\quantity}[3]{%
+        \directLuaAux{
+            quantities["#1"] = {} 
+            quantities["#1"]["symbol"]  = [[\detokenize{##1}]]
+            quantities["#1"]["units"]   = [[\detokenize{##2}]]
+            quantities["#1"]["comment"] = [[\detokenize{##3}]]
+        }\directLuaAuxExpand{
+            quantities["#1"]["fqname"]  = [[\fqname]] %-- fqname required for getting the translation key
         }
+        \newFormulaEntry
+        \printQuantity{#1}
     }
 
-}{\ignorespacesafterend}
+    % must be used only in third argument of "constant" command
-
+    % 1: value
+    % 2: unit
+    \newcommand{\val}[2]{
+        \directLuaAux{
+            table.insert(constants["#1"]["values"], { value = [[\detokenize{##1}]], unit = [[\detokenize{##2}]] })
+        }
+    }
+    % 1: symbol
+    % 2: either exp or def; experimentally or defined constant
+    % 3: one or more \val{value}{unit} commands
+    \newcommand{\constant}[3]{
+        \directLuaAux{
+            constants["#1"] = {}
+            constants["#1"]["symbol"]  = [[\detokenize{##1}]]
+            constants["#1"]["exp_or_def"]   = [[\detokenize{##2}]]
+            constants["#1"]["values"] = {} %-- array of {value, unit}
+        }\directLuaAuxExpand{
+            constants["#1"]["fqname"]  = [[\fqname]] %-- fqname required for getting the translation key
+        }
+        \begingroup
+            ##3
+        \endgroup
+        \newFormulaEntry
+        \printConstant{#1}
+    }
 
+    \begingroup
+        \label{f:\fqname:#1}
+        \par\noindent\ignorespaces
+        % \textcolor{gray}{\hrule}
+        \vspace{0.5\baselineskip}
+        \NameWithDescription[\descwidth]{\fqname:#1}{\fqname:#1_desc}
+        \hfill
+        \begin{ContentBoxWithExplanation}{\fqname:#1_defs}
+}{
+        \end{ContentBoxWithExplanation}
+    \endgroup
+    \textcolor{dark3}{\hrule}
+    \vspace{0.5\baselineskip}
+    \ignorespacesafterend
+}
 %
 % QUANTITY
 %
@@ -211,43 +214,6 @@
     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}%
@@ -260,67 +226,30 @@
     end
 }
 \newcommand\printConstant[1]{
-    \edef\constName{const:#1}
+    \begingroup % for label
-    \NameLeftContentRight{\constName}{
+        Symbol: $\luavar{constants["#1"]["symbol"]}$
-        \begingroup % for label
+        % \\Unit: $\directlua{split_and_print_units(constants["#1"]["units"])}$
-            Symbol: $\luavar{constants["#1"]["symbol"]}$
+        \directlua{
-            % \\Unit: $\directlua{split_and_print_units(constants["#1"]["units"])}$
+            tex.print("\\\\\\GT{const:"..constants["#1"]["exp_or_def"].."}")
-            \directlua{
+        }
-                tex.print("\\\\\\GT{const:"..constants["#1"]["exp_or_def"].."}")
+        \directlua{
-            }
+            %--tex.sprint("Hier steht Luatext" .. ":", #constVals)
-            \directlua{
+            for i, pair in ipairs(constants["#1"]["values"]) do
-                %--tex.sprint("Hier steht Luatext" .. ":", #constVals)
+            tex.sprint("\\\\\\hspace*{1cm}${", pair["value"], "}\\,\\si{", pair["unit"], "}$")
-                for i, pair in ipairs(constants["#1"]["values"]) do
+                %--tex.sprint("VALUE ", i, v)
-                tex.sprint("\\\\\\hspace*{1cm}${", pair["value"], "}\\,\\si{", pair["unit"], "}$")
+            end
-                    %--tex.sprint("VALUE ", i, v)
+        }
-                end
+        % label it only once
-            }
+        \directlua{ 
-            % label it only once
+            if constants["#1"]["labeled"] == nil then
-            \directlua{ 
+                constants["#1"]["labeled"] = true
-                if constants["#1"]["labeled"] == nil then
+                tex.print("\\label{const:#1}")
-                    constants["#1"]["labeled"] = true
+            end
-                    tex.print("\\label{const:#1}")
+        }
-                end
+    \endgroup
-            }
-        \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
-    % 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}}
-    }
-    \directLuaAux{
-        constants["#1"] = {};
-        constants["#1"]["symbol"]  = [[\detokenize{#2}]];
-        constants["#1"]["exp_or_def"]   = [[\detokenize{#3}]];
-        constants["#1"]["values"] = {} -- array of {value, unit};
-    }
-    % 1: value
-    % 2: unit
-    \newcommand{\val}[2]{
-        \directLuaAux{
-            table.insert(constants["#1"]["values"], { value = [[\detokenize{##1}]], unit = [[\detokenize{##2}]] })
-        }
-    }
-    \edef\lastConstName{#1}
-}{
-    \expandafter\printConstant{\lastConstName}
-    \ignorespacesafterend
-}
-
-
 
 \directLuaAux{
     if quantities == nil then
@@ -328,57 +257,18 @@
     end
 }
 \newcommand\printQuantity[1]{
-    \edef\qtyName{qty:#1}
+    \begingroup % for label
-    \NameLeftContentRight{\qtyName}{
+        Symbol: $\luavar{quantities["#1"]["symbol"]}$
-        \begingroup % for label
+        \\Unit: $\directlua{split_and_print_units(quantities["#1"]["units"])}$
-            Symbol: $\luavar{quantities["#1"]["symbol"]}$
+        % label it only once
-            \\Unit: $\directlua{split_and_print_units(quantities["#1"]["units"])}$
+        \directlua{ 
-            % label it only once
+            if quantities["#1"]["labeled"] == nil then
-            \directlua{ 
+                quantities["#1"]["labeled"] = true
-                if quantities["#1"]["labeled"] == nil then
+                tex.print("\\label{qty:#1}")
-                    quantities["#1"]["labeled"] = true
+            end
-                    tex.print("\\label{qty:#1}")
+        }
-                end
+    \endgroup
-            }
-        \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, definitions
-    \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
-    \directLuaAux{
-        quantities["#1"] = {} 
-        quantities["#1"]["symbol"]  = [[\detokenize{#2}]]
-        quantities["#1"]["units"]   = [[\detokenize{#3}]]
-        quantities["#1"]["comment"] = [[\detokenize{#4}]]
-    }
-    \def\lastQtyName{#1}
-}
-{
-    \expandafter\printQuantity{\lastQtyName}
-    \ignorespacesafterend
-    % for TOC
-    \refstepcounter{quantity}%
-    % \addquantity{\expandafter\gt\expandafter{\qtyname}}%
-}
-\newcounter{quantity}
-\newcommand{\listofquantities}{%
-    \section*{\GT{list_of_quantitites}}%
-    \addcontentsline{toc}{section}{\GT{list_of_quantitites}}%
-    \par\noindent\hrule\par\vspace{0.5\baselineskip}\@starttoc{myenv}%
-}
-\newcommand{\addquantity}[1]{\addcontentsline{quantity}{subsection}{\protect\numberline{\themyenv}#1}}
 
 % Custon environment with table of contents, requires etoolbox?
 % Define a custom list
@@ -414,11 +304,11 @@
         % add links to some names
         \directlua{
             local cases = {
-                pdf         = "eq:pt:distributions:pdf",
+                pdf         = "f:math:pt:pdf",
-                pmf         = "eq:pt:distributions:pmf",
+                pmf         = "f:math:pt:pmf",
-                cdf         = "eq:pt:distributions:cdf",
+                cdf         = "f:math:pt:cdf",
-                mean        = "eq:pt:mean",
+                mean        = "f:math:pt:mean",
-                variance    = "eq:pt:variance"
+                variance    = "f:math:pt:variance"
             }
             if cases["\luaescapestring{##1}"] \string~= nil then
                 tex.sprint("\\hyperref["..cases["\luaescapestring{##1}"].."]{\\GT{##1}}")

src/util/macros.tex

@@ -2,13 +2,6 @@
 \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\laplace{\Delta} % Laplace operator
@@ -102,6 +95,19 @@
 \def\qdots{\quad\dots\quad}
 \def\qRarrow{\quad\Rightarrow\quad}
 
+% ANNOTATIONS
+% 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}}
+\newcommand{\eqnote}[1]{
+    \text{\color{dark2}#1}
+}
+
+
 % DELIMITERS
 \DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
 \DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
@@ -109,13 +115,21 @@
 
 % OPERATORS
 \DeclareMathOperator{\e}{e}
-\DeclareMathOperator{\T}{T}  % transposed
+\def\T{\text{T}}  % transposed
 \DeclareMathOperator{\sgn}{sgn}
 \DeclareMathOperator{\tr}{tr}
 \DeclareMathOperator{\const}{const}
 \DeclareMathOperator{\erf}{erf}
 \DeclareMathOperator{\erfc}{erfc}
 \DeclareMathOperator{\cov}{cov}
+% \DeclareMathOperator{\arcsin}{arcsin}
+% \DeclareMathOperator{\arccos}{arccos}
+% \DeclareMathOperator{\arctan}{arctan}
+\DeclareMathOperator{\arccot}{arccot}
+\DeclareMathOperator{\arsinh}{arsinh}
+\DeclareMathOperator{\arcosh}{arcosh}
+\DeclareMathOperator{\artanh}{artanh}
+\DeclareMathOperator{\arcoth}{arcoth}
 % diff, for integrals and stuff
 % \DeclareMathOperator{\dd}{d}
 \renewcommand*\d{\mathop{}\!\mathrm{d}}
@@ -129,3 +143,14 @@
 \newcommand\Sin[1]{\CmdWithParenthesis{\sin}{#1}}
 \newcommand\Cos[1]{\CmdWithParenthesis{\cos}{#1}}
 \newcommand\Order[1]{\CmdWithParenthesis{\mathcal{O}}{#1}}
+
+% VECTOR AND MATRIX
+% use vecA to force an arrow
+\NewCommandCopy{\vecA}{\vec}
+% extra {} assure they can b directly used after _
+%% arrow/underline
+\newcommand\mat[1]{{\ensuremath{\underline{#1}}}}
+\renewcommand\vec[1]{{\ensuremath{\vecA{#1}}}}
+%% bold
+% \newcommand\mat[1]{{\ensuremath{\bm{#1}}}}
+% \renewcommand\vec[1]{{\ensuremath{\bm{#1}}}}

src/util/periodic_table.tex

@@ -50,8 +50,19 @@
 % LIST
 \newcommand\printElement[1]{
     \edef\elementName{el:#1}
-    \NameLeftContentRight{\elementName}{
+    \par\noindent\ignorespaces
-        \begingroup % for label
+    \vspace{0.5\baselineskip}
+    \begingroup
+        % label it only once
+        \directlua{ 
+            if elements["#1"]["labeled"] == nil then
+                elements["#1"]["labeled"] = true
+                tex.print("\\label{el:#1}")
+            end
+        }
+        \NameWithDescription[\descwidth]{\elementName}{\elementName_desc}
+        \hfill
+        \begin{ContentBoxWithExplanation}{\elementName_defs}
             \directlua{
                 tex.sprint("Symbol: \\ce{"..elements["#1"]["symbol"].."}")
                 tex.sprint("\\\\Number: "..elements["#1"]["atomic_number"])
@@ -63,22 +74,18 @@
                     %--tex.sprint("VALUE ", i, v)
                 end
             }
-            % label it only once
+        \end{ContentBoxWithExplanation}
-            \directlua{ 
+    \endgroup
-                if elements["#1"]["labeled"] == nil then
+    \textcolor{dark3}{\hrule}
-                    elements["#1"]["labeled"] = true
+    \vspace{0.5\baselineskip}
-                    tex.print("\\label{el:#1}")
+    \ignorespacesafterend
-                end
-            }
-        \endgroup
-    }
 }
 \newcommand{\printAllElements}{
     \directlua{
             %-- tex.sprint("\\printElement{"..val.."}")
         for key, val in ipairs(elementsOrder) do
             %-- tex.sprint(key, val);
-            tex.sprint("\\printElement{"..val.."}")
+            tex.print("\\printElement{"..val.."}")
         end
     }
 }

src/util/translation.tex

@@ -36,7 +36,7 @@
 \newrobustcmd{\GT}[1]{%\expandafter\GetTranslation\expandafter{#1}}
     \IfTranslationExists{#1}{%
         \expandafter\GetTranslation\expandafter{#1}%
-    }{%
+    }{% ??
         \detokenize{#1}%
     }%
 }

src/util/translations.tex

@@ -35,6 +35,9 @@
 \Eng[see_also]{See also}
 \Ger[see_also]{Siehe auch}
 
+\Eng[for]{for}
+\Ger[for]{für}
+
 \Eng[and_therefore]{and therefore}
 \Ger[and_therefore]{und damit}