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Refactor formula

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matthias@quintern.xyz 2025-01-10 09:59:07 +01:00
parent 7745922b1f
commit a333c7a5fb
35 changed files with 1870 additions and 1445 deletions
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4
Makefile
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@ -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

3
src/.latexmkrc
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@ -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',

6
src/ch/ch.tex
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@ -21,9 +21,3 @@
}
\end{formula}
\Section[
\eng{List of elements}
\ger{Liste der Elemente}
]{elements}
\printAllElements

14
src/cm/charge_transport.tex
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@ -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[german]{Stromdichte}{}{}
\desc{Electrical current density}{}{}
\desc[german]{Elektrische Stromdichte}{}{}
\eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
\end{formula}
\TODO{The formula for the conductivity is the same as in the drude model?}
@ -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}

320
src/cm/cm.tex
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@ -2,322 +2,4 @@
\eng{Condensed matter physics}
\ger{Festkörperphysik}
]{cm}
\TODO{Bonds, hybridized orbitals, tight binding}
\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}
\TODO{Bonds, hybridized orbitals}

199
src/cm/crystal.tex Normal file
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@ -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}

72
src/cm/egas.tex Normal file
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@ -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}

102
src/cm/other.tex Normal file
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@ -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}

15
src/cm/semiconductors.tex
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@ -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}

41
src/computational.tex
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@ -1,10 +1,10 @@
\Part[
\eng{Computational Physics}
\ger{Computergestützte Physik}
]{comp}
]{cmp}
\Section[
\eng{Many-body physics}
\ger{Vielteilchenphysik}
\eng{Quantum many-body physics}
\ger{Quanten-Vielteilchenphysik}
]{mb}
\TODO{TODO}
\Subsection[
@ -18,10 +18,22 @@
\ger{Matrix Produktzustände}
]{mps}
\Section[
\eng{Misc}
\ger{Verschiedenes}
]{misc}
\eng{Electronic structure theory}
% \ger{}
]{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}

46
src/constants.tex
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@ -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}
\val{4.135667969\dots\xE{-15}}{\eV\s}
\end{constant}
\constant{h}{def}{
\val{6.62607015\cdot 10^{-34}}{\joule\s}
\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}
\val{\NA \cdot \kB}{}
\end{constant}
\constant{R}{def}{
\val{8.31446261815324}{\joule\per\mol\kelvin}
\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}
\end{constant}
\constant{\NA}{def}{
\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}
\end{constant}
\constant{\kB}{def}{
\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}
\val{\NA\,e}{}
\end{constant}
\constant{F}{def}{
\val{9.64853321233100184}{\coulomb\per\mol}
\val{\NA\,e}{}
}
\end{formula}

139
src/ed/ed.tex Normal file
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@ -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}

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\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}

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\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}

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\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}

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\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}

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\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}

319
src/main.tex Executable file → Normal file
View File

@ -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{tabularx} % bravais table
\usepackage{multirow} % for superconducting qubit table
\usepackage{hhline} % for superconducting qubit table
\usepackage{colortbl} % color table
\usepackage{tabularx} % bravais table
\usepackage{multirow} % for superconducting qubit table
\usepackage{hhline} % for superconducting qubit table
% TOOLING
\usepackage{graphicx}
\usepackage{etoolbox}
\usepackage{luacode}
\usepackage{expl3} % switch case and other stuff
% \usepackage{luacode}
\usepackage{expl3} % switch case and other stuff
\usepackage{substr}
\usepackage{xcolor}
% FORMATING
\usepackage{float} % float barrier
\usepackage{subcaption} % subfigure
\usepackage[hidelinks]{hyperref}
\usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
\usepackage{titlesec} % colored titles
\usepackage{array}
\usepackage{float} % float barrier
\usepackage{subcaption} % subfigures
\usepackage[hidelinks]{hyperref} % hyperrefs for \fqEqRef, \qtyRef, etc
\usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
\usepackage{titlesec} % colored titles
\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
\usepackage{chemmacros} % for orbitals
% set display math skips
\AtBeginDocument{
\abovedisplayskip=0pt
\abovedisplayshortskip=0pt
\belowdisplayskip=0pt
\belowdisplayshortskip=0pt
}
\usepackage{MnSymbol} % for >>> \ggg sign
\usepackage[version=4,arrows=pgf-filled]{mhchem}
\usepackage{upgreek} % upright greek letters for chemmacros
\usepackage{chemmacros} % for orbitals images
% \usepackage{esdiff} % derivatives
% esdiff breaks when taking \dot{q} has argument
\usepackage{derivative}
\usepackage[version=4,arrows=pgf-filled]{mhchem}
\usepackage{bbold} % \mathbb font
\usepackage{braket}
\usepackage{siunitx}
\usepackage{derivative} % \odv, \pdv
\usepackage{bbold} % \mathbb font
\usepackage{braket} % <bra|ket>
\usepackage{siunitx} % \si \SI units
\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\sectionname{}
\def\subsectionname{}
\def\subsubsectionname{}
\edef\fqname{\partname}
\def\partName{#2}
\def\sectionName{}
\def\subsectionName{}
\def\subsubsectionName{}
\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\subsectionname{}
\def\subsubsectionname{}
\edef\fqname{\partname:\sectionname}
\def\sectionName{#2}
\def\subsectionName{}
\def\subsubsectionName{}
\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\subsubsectionname{}
\edef\fqname{\partname:\sectionname:\subsectionname}
\def\subsectionName{#2}
\def\subsubsectionName{}
\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}
\edef\fqname{\partname:\sectionname:\subsectionname:\subsubsectionname}
\def\subsubsectionName{#2}
\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}{
\input{#1}
}{
\ifstrequal{#1}{\inputOnlyFile}{
\input{#1}
}{}
% yes this could surely be done in tex
\directlua{
if '\luaescapestring{\inputOnlyFile}' == 'all' or string.startswith('\luaescapestring{#1}', '\luaescapestring{\inputOnlyFile}') then
tex.print("\\input{\luaescapestring{#1}}")
end
}
}
% \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}
\ger{Mathematik}
]{math}
% \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}}
\eng{Appendix}
\ger{Anhang}
]{appendix}
% \listofmyenv
\listofquantities
% \listofquantities
\listoffigures
\listoftables
\Section[
\eng{List of elements}
\ger{Liste der Elemente}
]{elements}
\printAllElements
% \bibliographystyle{plain}
% \bibliography{ref}

97
src/math/calculus.tex
View File

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

10
src/math/geometry.tex
View File

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

77
src/math/linalg.tex
View File

@ -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}

5
src/math/math.tex Normal file
View File

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

8
src/math/probability_theory.tex
View File

@ -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}}
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions::poisson]{Poissonverteilung}}
\end{ttext}
\eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \hyperref[sec:pb:distributions:poisson]{poisson distribution}}
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions:poisson]{Poissonverteilung}}
\end{ttext}\\
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\centering

110
src/quantities.tex
View File

@ -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}
\Ger[si_base_units]{SI Basisgrößen}
% Put quantites here that are referenced often, even if they are not exciting themselves.
% This could later allow making a list of all links to this quantity, creating a list of releveant formulas
\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}}
\begin{quantity}{volume}{V}{\m^d}{}
\desc{Volume}{$d$ dimensional Volume}{}
\desc[german]{Volumen}{$d$ dimensionales Volumen}{}
\end{quantity}
\Subsection[
\eng{Mechanics}
\ger{Mechanik}
]{mech}
\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}

140
src/quantum_computing.tex
View File

@ -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
\begin{tikzpicture}
\draw (0, 0) \squidloop{loop}{};
\end{tikzpicture}
}
\centering
\begin{tikzpicture}
\draw (0, 0) \squidloop{loop}{};
\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
\begin{tikzpicture}
\draw (0,0) to[sV=$V_\text{g}$] (0,2);
% \draw (0,0) to (2,0);
\draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
\draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
\draw (0,0) to (2,0);
\end{tikzpicture}
}
\centering
\begin{tikzpicture}
\draw (0,0) to[sV=$V_\text{g}$] (0,2);
% \draw (0,0) to (2,0);
\draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
\draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
\draw (0,0) to (2,0);
\end{tikzpicture}
\end{formula}
@ -256,15 +252,13 @@
\baditem Geringe Anharmonizität $\alpha$
\end{itemize}
}{}
\content{
\centering
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% 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)
to[capacitor=$C_C$] ++(0,3);
\end{tikzpicture}
}
\centering
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% 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)
to[capacitor=$C_C$] ++(0,3);
\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
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to[capacitor=$C_\text{g}$] ++(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[capacitor=$C_C$] ++(0,3);
\end{tikzpicture}
}
\centering
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to[capacitor=$C_\text{g}$] ++(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[capacitor=$C_C$] ++(0,3);
\end{tikzpicture}
\end{formula}
\begin{formula}{energy}
@ -318,25 +310,23 @@
\begin{formula}{circuit}
\desc{Phase qubit}{}{}
\desc[german]{Phase Qubit}{}{}
\content{
\centering
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1)
% to ++(2,0) coordinate(top2)
% to ++(2,0) coordinate(top3);
% \draw (0,0)
% to ++(2,0) coordinate(bot1)
% to ++(2,0) coordinate(bot2)
% to ++(2,0) coordinate(bot3);
\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(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);
\node at (3,-1.5) {$\Phi_\text{ext}$};
\end{tikzpicture}
\\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
}
\centering
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1)
% to ++(2,0) coordinate(top2)
% to ++(2,0) coordinate(top3);
% \draw (0,0)
% to ++(2,0) coordinate(bot1)
% to ++(2,0) coordinate(bot2)
% to ++(2,0) coordinate(bot3);
\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(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);
\node at (3,-1.5) {$\Phi_\text{ext}$};
\end{tikzpicture}
\\\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
\begin{tikzpicture}
\draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
\draw (0,0) to ++(3,0)
to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
to ++(-3,0);
\node at (1.5,-1.5) {$\Phi_\text{ext}$};
\end{tikzpicture}
\centering
\begin{tikzpicture}
\draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
\draw (0,0) to ++(3,0)
to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
to ++(-3,0);
\node at (1.5,-1.5) {$\Phi_\text{ext}$};
\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
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1);
\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 ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
\node at (1,-0.5) {$\Phi_\text{ext}$};
\end{tikzpicture}
\\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
}
\centering
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1);
\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 ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
\node at (1,-0.5) {$\Phi_\text{ext}$};
\end{tikzpicture}
\\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
\end{formula}
\def\temp{$E_\text{C} = \frac{(2e)^2}{2C}, E_\text{L} = \frac{\varphi_0^2}{2L}, \delta_\text{s} = \frac{\varphi_\text{s}}{\varphi_0}$}

9
src/quantum_mechanics.tex
View File

@ -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}

41
src/spv.tex Normal file
View File

@ -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}

206
src/statistical_mechanics.tex
View File

@ -1,84 +1,84 @@
\Part[
\eng{Statistichal Mechanics}
\ger{Statistische Mechanik}
]{stat}
]{stat}
\begin{ttext}
\eng{
\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
}
\ger{
\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
}
\end{ttext}
\begin{ttext}
\eng{
\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
}
\ger{
\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
}
\end{ttext}
\begin{formula}{liouville}
\desc{Liouville equation}{}{$\{\}$ poisson bracket}
\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\}}
\begin{formula}{liouville}
\desc{Liouville equation}{}{$\{\}$ poisson bracket}
\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\}}
\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[
\eng{Entropy}
\ger{Entropie}
]{entropy}
\begin{formula}{von_neumann}
\desc{Von-Neumann}{}{$\rho$ density matrix}
\desc[german]{Von-Neumann}{}{$\rho$ Dichtematrix}
\eq{S = - \kB \braket{\log \rho} = - \kB \tr(\rho \log\rho)}
\end{formula}
\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}
\begin{formula}{gibbs}
\desc{Gibbs}{}{$p_n$ probability for micro state $n$}
\desc[german]{Gibbs}{}{$p_n$ Wahrscheinlichkeit für Mikrozustand $n$}
\eq{S = - \kB \sum_n p_n \log p_n}
\end{formula}
\begin{formula}{von_neumann}
\desc{Von-Neumann}{}{$\rho$ density matrix}
\desc[german]{Von-Neumann}{}{$\rho$ Dichtematrix}
\eq{S = - \kB \braket{\log \rho} = - \kB \tr(\rho \log\rho)}
\end{formula}
\begin{formula}{boltzmann}
\desc{Boltzmann}{}{$\Omega$ \#micro states}
\desc[german]{Boltzmann}{}{$\Omega$ \#Mikrozustände}
\eq{S = \kB \log\Omega}
\end{formula}
\begin{formula}{gibbs}
\desc{Gibbs}{}{$p_n$ probability for micro state $n$}
\desc[german]{Gibbs}{}{$p_n$ Wahrscheinlichkeit für Mikrozustand $n$}
\eq{S = - \kB \sum_n p_n \log p_n}
\end{formula}
\begin{formula}{temp}
\desc{Temperature}{}{}
\desc[german]{Temperatur}{}{}
\eq{\frac{1}{T} \coloneq \pdv{S}{E}_V}
\end{formula}
\begin{formula}{boltzmann}
\desc{Boltzmann}{}{$\Omega$ \#micro states}
\desc[german]{Boltzmann}{}{$\Omega$ \#Mikrozustände}
\eq{S = \kB \log\Omega}
\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}
\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}
\desc{Thermal wavelength}{}{}
\desc[german]{Thermische Wellenlänge}{}{}
\eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
\end{formula}
\begin{formula}{therm_wavelength}
\desc{Thermal wavelength}{}{}
\desc[german]{Thermische Wellenlänge}{}{}
\eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
\end{formula}
\Section[
\eng{Processes}
\ger{Prozesse}
]{process}
\Section[
\eng{Processes}
\ger{Prozesse}
]{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}
\eng{The corners opposite from the potential are the coefficients and each coefficients differential is opposite to it.}
\ger{Die Ecken gegenüber des Potentials sind die Koeffizienten, das Differential eines Koeffizienten ist in der Ecke gegenüber.}
\end{ttext}
}
\end{minipage}
\begin{ttext}
\eng{The corners opposite from the potential are the coefficients and each coefficients differential is opposite to it.}
\ger{Die Ecken gegenüber des Potentials sind die Koeffizienten, das Differential eines Koeffizienten ist in der Ecke gegenüber.}
\end{ttext}
\end{formula}
\Section[
\eng{Ideal gas}
\ger{Ideales Gas}
]{id_gas}
]{id_gas}
\begin{ttext}
\eng{The ideal gas consists of non-interacting, undifferentiable particles.}
\ger{Das ideale Gas besteht aus nicht-wechselwirkenden, ununterscheidbaren Teilchen.}
@ -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]
\centering
\tikzstyle{spring}=[thick,decorate,decoration={coil,aspect=0.8,amplitude=5,pre length=0.1cm,post length=0.1cm,segment length=10}]
\begin{tikzpicture}
\def\radius{0.5}
\coordinate (left) at (-3, 0);
\coordinate (right) at (3, 0);
\draw (left) circle (\radius);
\draw[spring] ($(left) + (\radius,0)$) -- ($(right) - (\radius,0)$);
\draw (right) circle (\radius);
\end{tikzpicture}
% \begin{figure}[h]
\centering
\tikzstyle{spring}=[thick,decorate,decoration={coil,aspect=0.8,amplitude=5,pre length=0.1cm,post length=0.1cm,segment length=10}]
\begin{tikzpicture}
\def\radius{0.5}
\coordinate (left) at (-3, 0);
\coordinate (right) at (3, 0);
\draw (left) circle (\radius);
\draw[spring] ($(left) + (\radius,0)$) -- ($(right) - (\radius,0)$);
\draw (right) circle (\radius);
\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.}{}
\figeq{img/potential_lennard_jones.pdf}{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
\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.}{}
\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}

0
src/svgs/convertToPdf.sh Normal file → Executable file
View File

84
src/test.tex Normal file
View File

@ -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}

412
src/util/environments.tex
View File

@ -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
% 3: fqname of a translation that holds the explanation
\newcommand{\ContentBoxWithExplanation}[3][\eqwidth]{
\fbox{
% 2: fqname of a translation that holds the explanation
\newenvironment{ContentBoxWithExplanation}[2][\eqwidth]{
\def\ContentFqName{#2}
\begin{lrbox}{\contentBoxBox}
\begin{minipage}{#1}
% \vspace{-\baselineskip} % remove the space that comes from starting a new paragraph
#2
\smartnewline
\noindent\IfTranslationExists{#3}{
}{
\IfTranslationExists{\ContentFqName}{%
\smartnewline
\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]{
\insertFLAlign{#1}{##1}
\newcommand{\eqFLAlign}[2]{
\newFormulaEntry
\begin{alignat}{##1}%
% dont place label when one is provided
% \IfSubStringInString{label}\unexpanded{#3}{}{
% \label{eq:#1}
% }
##2%
\end{alignat}
}
% 1: file path
% 2: equation
\newcommand{\figeq}[2]{
\insertEquationWithFigure{#1}{##1}{##2}
}
% 1: any content
\newcommand{\content}[1]{
\NameLeftContentRight{\fqname:#1}{##1}
\newcommand{\fig}[2][1.0]{
\newFormulaEntry
\centering
\includegraphics[width=##1\textwidth]{##2}
}
% 1: content for the ttext environment
\newcommand{\ttxt}[1]{
\NameLeftContentRight{\fqname:#1}{
\begin{ttext}[#1:desc]
##1
\end{ttext}
\newcommand{\ttxt}[2][#1:desc]{
\newFormulaEntry
\begin{ttext}[##1]
##2
\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}
\NameLeftContentRight{\constName}{
\begingroup % for label
Symbol: $\luavar{constants["#1"]["symbol"]}$
% \\Unit: $\directlua{split_and_print_units(constants["#1"]["units"])}$
\directlua{
tex.print("\\\\\\GT{const:"..constants["#1"]["exp_or_def"].."}")
}
\directlua{
%--tex.sprint("Hier steht Luatext" .. ":", #constVals)
for i, pair in ipairs(constants["#1"]["values"]) do
tex.sprint("\\\\\\hspace*{1cm}${", pair["value"], "}\\,\\si{", pair["unit"], "}$")
%--tex.sprint("VALUE ", i, v)
end
}
% label it only once
\directlua{
if constants["#1"]["labeled"] == nil then
constants["#1"]["labeled"] = true
tex.print("\\label{const:#1}")
end
}
\endgroup
}
\begingroup % for label
Symbol: $\luavar{constants["#1"]["symbol"]}$
% \\Unit: $\directlua{split_and_print_units(constants["#1"]["units"])}$
\directlua{
tex.print("\\\\\\GT{const:"..constants["#1"]["exp_or_def"].."}")
}
\directlua{
%--tex.sprint("Hier steht Luatext" .. ":", #constVals)
for i, pair in ipairs(constants["#1"]["values"]) do
tex.sprint("\\\\\\hspace*{1cm}${", pair["value"], "}\\,\\si{", pair["unit"], "}$")
%--tex.sprint("VALUE ", i, v)
end
}
% label it only once
\directlua{
if constants["#1"]["labeled"] == nil then
constants["#1"]["labeled"] = true
tex.print("\\label{const:#1}")
end
}
\endgroup
}
\newcounter{constant}
% 1: key - must expand to a valid lua string!
% 2: symbol
% 3: either exp or def; experimentally or defined constant
\newenvironment{constant}[3]{
% [1]: language
% 2: name
% 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}
\NameLeftContentRight{\qtyName}{
\begingroup % for label
Symbol: $\luavar{quantities["#1"]["symbol"]}$
\\Unit: $\directlua{split_and_print_units(quantities["#1"]["units"])}$
% label it only once
\directlua{
if quantities["#1"]["labeled"] == nil then
quantities["#1"]["labeled"] = true
tex.print("\\label{qty:#1}")
end
}
\endgroup
}
\begingroup % for label
Symbol: $\luavar{quantities["#1"]["symbol"]}$
\\Unit: $\directlua{split_and_print_units(quantities["#1"]["units"])}$
% label it only once
\directlua{
if quantities["#1"]["labeled"] == nil then
quantities["#1"]["labeled"] = true
tex.print("\\label{qty:#1}")
end
}
\endgroup
}
% 1: key - must expand to a valid lua string!
% 2: symbol
% 3: units
% 4: comment key to translation
\newenvironment{quantity}[4]{
% language, name, description, 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",
pmf = "eq:pt:distributions:pmf",
cdf = "eq:pt:distributions:cdf",
mean = "eq:pt:mean",
variance = "eq:pt:variance"
pdf = "f:math:pt:pdf",
pmf = "f:math:pt:pmf",
cdf = "f:math:pt:cdf",
mean = "f:math:pt:mean",
variance = "f:math:pt:variance"
}
if cases["\luaescapestring{##1}"] \string~= nil then
tex.sprint("\\hyperref["..cases["\luaescapestring{##1}"].."]{\\GT{##1}}")

41
src/util/macros.tex
View File

@ -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}}}}

31
src/util/periodic_table.tex
View File

@ -50,8 +50,19 @@
% LIST
\newcommand\printElement[1]{
\edef\elementName{el:#1}
\NameLeftContentRight{\elementName}{
\begingroup % for label
\par\noindent\ignorespaces
\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
\directlua{
if elements["#1"]["labeled"] == nil then
elements["#1"]["labeled"] = true
tex.print("\\label{el:#1}")
end
}
\endgroup
}
\end{ContentBoxWithExplanation}
\endgroup
\textcolor{dark3}{\hrule}
\vspace{0.5\baselineskip}
\ignorespacesafterend
}
\newcommand{\printAllElements}{
\directlua{
%-- tex.sprint("\\printElement{"..val.."}")
for key, val in ipairs(elementsOrder) do
%-- tex.sprint(key, val);
tex.sprint("\\printElement{"..val.."}")
tex.print("\\printElement{"..val.."}")
end
}
}

2
src/util/translation.tex
View File

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

3
src/util/translations.tex
View File

@ -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}