diff --git a/Makefile b/Makefile index 87f1328..807c1a5 100644 --- a/Makefile +++ b/Makefile @@ -20,12 +20,12 @@ release: german english # Default target english: sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[english]{babel}/' $(MAIN_TEX) - -cd $(SRC_DIR) && latexmk -g + -cd $(SRC_DIR) && latexmk -lualatex -g main.tex mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_en_formula_collection.pdf german: sed -r -i 's/usepackage\[[^]]+\]\{babel\}/usepackage[german]{babel}/' $(MAIN_TEX) - -cd $(SRC_DIR) && latexmk -g + -cd $(SRC_DIR) && latexmk -lualatex -g main.tex mv $(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_formelsammlung.pdf # Clean auxiliary and output files diff --git a/src/.latexmkrc b/src/.latexmkrc index 594b57d..ad8b461 100644 --- a/src/.latexmkrc +++ b/src/.latexmkrc @@ -4,7 +4,8 @@ $out_dir = '../out'; # Set lualatex as the default engine $pdf_mode = 1; # Enable PDF generation mode -$pdflatex = 'lualatex -interaction=nonstopmode -shell-escape' +# $pdflatex = 'lualatex --interaction=nonstopmode --shell-escape' +$lualatex = 'lualatex %O --interaction=nonstopmode --shell-escape %S' # Additional options for compilation # '-verbose', diff --git a/src/ch/ch.tex b/src/ch/ch.tex index b710aa7..ccdb97a 100644 --- a/src/ch/ch.tex +++ b/src/ch/ch.tex @@ -21,9 +21,3 @@ } \end{formula} - \Section[ - \eng{List of elements} - \ger{Liste der Elemente} - ]{elements} - \printAllElements - diff --git a/src/cm/charge_transport.tex b/src/cm/charge_transport.tex index f519aa0..20059dd 100644 --- a/src/cm/charge_transport.tex +++ b/src/cm/charge_transport.tex @@ -26,6 +26,7 @@ \begin{formula}{scattering_time} \desc{Scattering time}{Momentum relaxation time}{} \desc[german]{Streuzeit}{}{} + \quantity{\tau}{\s}{s} \ttxt{ \eng{$\tau$\\ the average time between scattering events weighted by the characteristic momentum change cause by the scattering process.} } @@ -33,6 +34,7 @@ \begin{formula}{current_density} \desc{Current density}{Ohm's law}{$n$ charge particle density} \desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte} + \quantity{\vec{j}}{\ampere\per\m^2}{v} \eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{\E}} \end{formula} \begin{formula}{conductivity} @@ -50,8 +52,8 @@ \ger{Annahme eines freien Fermionengases, welches dem Pauli-Prinzip unterliegt. Nur Elektronen in einem Energiebereich von $\kB T$ um die Fermi Energe $\EFermi$ nehmen an Streuprozessen teil.} \end{ttext} \begin{formula}{current_density} - \desc{Current density}{}{} - \desc[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} diff --git a/src/cm/cm.tex b/src/cm/cm.tex index 2ae47e5..67b1589 100644 --- a/src/cm/cm.tex +++ b/src/cm/cm.tex @@ -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} diff --git a/src/cm/crystal.tex b/src/cm/crystal.tex new file mode 100644 index 0000000..283abfc --- /dev/null +++ b/src/cm/crystal.tex @@ -0,0 +1,199 @@ +\Section[ + \eng{Crystals} + \ger{Kristalle} +]{crystal} +\Subsection[ + \eng{Bravais lattice} + \ger{Bravais-Gitter} +]{bravais} + \eng[bravais_table2]{In 2D, there are 5 different Bravais lattices} + \ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter} + + \eng[bravais_table3]{In 3D, there are 14 different Bravais lattices} + \ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter} + + \Eng[lattice_system]{Lattice system} + \Ger[lattice_system]{Gittersystem} + \Eng[crystal_family]{Crystal system} + \Ger[crystal_family]{Kristall-system} + \Eng[point_group]{Point group} + \Ger[point_group]{Punktgruppe} + \eng[bravais_lattices]{Bravais lattices} + \ger[bravais_lattices]{Bravais Gitter} + + \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}} + \renewcommand\tabularxcolumn[1]{m{#1}} + \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X} + \begin{table}[H] + \centering + \expandafter\caption\expandafter{\gt{bravais_table2}} + \label{tab:bravais2} + + \begin{adjustbox}{width=\textwidth} + \begin{tabularx}{\textwidth}{||Z|c|Z|Z||} + \hline + \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4} + & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline + \GT{monoclinic} (m) & $\text{C}_\text{2}$ & \bvimg{mp} & \\ \hline + \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline + \GT{tetragonal} (t) & $\text{D}_\text{4}$ & \bvimg{tp} & \\ \hline + \GT{hexagonal} (h) & $\text{D}_\text{6}$ & \bvimg{hp} & \\ \hline + \end{tabularx} + \end{adjustbox} + \end{table} + + + + \begin{table}[H] + \centering + \caption{\gt{bravais_table3}} + \label{tab:bravais3} + + % \newcolumntype{g}{>{\columncolor[]{0.8}}} + \begin{adjustbox}{width=\textwidth} + % \begin{tabularx}{\textwidth}{|c|} + % asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\ + % asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\ + % \end{tabularx} + % \begin{tabular}{|c|} + % asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\ + % asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\ + % \end{tabular} + % \\ + \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||} + \hline + \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7} + & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline + \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP} & & & \\ \hline + \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS} & & \\ \hline + \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline + \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} & & \bvimg{tI} & \\ \hline + \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} & & & \\ \cline{2-7} + & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} & & & \\ \hline + \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} & & \bvimg{cI} & \bvimg{cF} \\ \hline + \end{tabularx} + \end{adjustbox} + \end{table} + + \begin{formula}{lattice_constant} + \desc{Lattice constant}{Parameter (length or angle) describing the smallest unit cell}{} + \desc[german]{Gitterkonstante}{Parameter (Länge oder Winkel) der die Einheitszelle beschreibt}{} + \quantity{a}{}{s} + \end{formula} + + \begin{formula}{lattice_vector} + \desc{Lattice vector}{}{$n_i \in \Z$} + \desc[german]{Gittervektor}{}{} + \quantity{\vec{R}}{}{\angstrom} + \eq{\vec{R} = n_1 \vec{a_1} + n_2 \vec{a_2} + n_3 \vec{a_3}} + \end{formula} + + \TODO{primitive unit cell: contains one lattice point}\\ + \begin{formula}{miller} + \desc{Miller index}{}{Miller family: planes that are equivalent due to crystal symmetry} + \desc[german]{Millersche Indizes}{}{} + \eq{ + (hkl) & \text{\GT{plane}}\\ + [hkl] & \text{\GT{direction}}\\ + \{hkl\} & \text{\GT{millerFamily}} + } + \end{formula} + + +\Subsection[ + \eng{Reciprocal lattice} + \ger{Reziprokes Gitter} +]{reci} + \begin{ttext} + \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.} + \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.} + \end{ttext} + + \begin{formula}{vectors} + \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell} + \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle} + \eq{ + \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\ + \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\ + \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2} + } + \end{formula} + \begin{formula}{reciprocal_lattice_vector} + \desc{Reciprokal attice vector}{}{$n_i \in \Z$} + \desc[german]{Reziproker Gittervektor}{}{} + \quantity{\vec{G}}{}{\angstrom} + \eq{\vec{G}_{{hkl}} = h \vec{b_1} + k \vec{b_2} + l \vec{b_3}} + \end{formula} + + \Subsection[ + \eng{Scattering processes} + \ger{Streuprozesse} + ]{scatter} + \begin{formula}{matthiessen} + \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{\QtyRef{mobility}, \QtyRef{scattering_time}} + \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{} + \eq{ + \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\ + \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i} + } + \end{formula} + +\Subsection[ + \eng{Lattices} + \ger{Gitter} +]{lat} + \begin{formula}{sc} + \desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}} + \desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{} + \eq{ + \vec{a}_{1}=a \begin{pmatrix} 1\\0\\0 \end{pmatrix},\, + \vec{a}_{2}=a \begin{pmatrix} 0\\1\\0 \end{pmatrix},\, + \vec{a}_{3}=a \begin{pmatrix} 0\\0\\1 \end{pmatrix} + } + \end{formula} + \begin{formula}{bcc} + \desc{Body centered cubic (BCC)}{Reciprocal: \fqEqRef{cm:bravais:fcc}}{\QtyRef{lattice_constant}} + \desc[german]{Kubisch raumzentriert (BCC)}{Reziprok: \fqEqRef{cm:bravais:fcc}}{} + \eq{ + \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} -1\\1\\1 \end{pmatrix},\, + \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\-1\\1 \end{pmatrix},\, + \vec{a}_{3}=\frac{a}{2} \begin{pmatrix} 1\\1\\-1 \end{pmatrix} + } + \end{formula} + + \begin{formula}{fcc} + \desc{Face centered cubic (FCC)}{Reciprocal: \fqEqRef{cm:bravais:bcc}}{\QtyRef{lattice_constant}} + \desc[german]{Kubisch flächenzentriert (FCC)}{Reziprok: \fqEqRef{cm:bravais:bcc}}{} + \eq{ + \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} 0\\1\\1 \end{pmatrix},\, + \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\0\\1 \end{pmatrix},\, + \vec{a}_{3}=\frac{a}{2} \begin{pmatrix} 1\\1\\0 \end{pmatrix} + } + \end{formula} + + \begin{formula}{diamond} + \desc{Diamond lattice}{}{} + \desc[german]{Diamantstruktur}{}{} + \ttxt{ + \eng{\fqEqRef{cm:bravais:fcc} with basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ and $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$} + \ger{\fqEqRef{cm:bravais:fcc} mit Basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ und $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$} + } + \end{formula} + \begin{formula}{zincblende} + \desc{Zincblende lattice}{}{} + \desc[german]{Zinkblende-Struktur}{}{} + \ttxt{ + \includegraphics[width=0.5\textwidth]{img/cm_zincblende.png} + \eng{Like \fqEqRef{cm:bravais:diamond} but with different species on each basis} + \ger{Wie \fqEqRef{cm:bravais:diamond} aber mit unterschiedlichen Spezies auf den Basen} + } + \end{formula} + \begin{formula}{wurtzite} + \desc{Wurtzite structure}{hP4}{} + \desc[german]{Wurtzite-Struktur}{hP4}{} + \ttxt{ + \includegraphics[width=0.5\textwidth]{img/cm_wurtzite.png} + Placeholder + } + \end{formula} + diff --git a/src/cm/egas.tex b/src/cm/egas.tex new file mode 100644 index 0000000..893c0eb --- /dev/null +++ b/src/cm/egas.tex @@ -0,0 +1,72 @@ +\Section[ + \eng{Free electron gas} + \ger{Freies Elektronengase} +]{egas} +\begin{ttext} + \eng{Assumptions: electrons can move freely and independent of each other.} + \ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.} +\end{ttext} + +\begin{formula}{drift_velocity} + \desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity} + \desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit} + \eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}} +\end{formula} + +\begin{formula}{mean_free_path} + \desc{Mean free path}{}{} + \desc[german]{Mittlere freie Weglänge}{}{} + \eq{\ell = \braket{v} \tau} +\end{formula} + +\begin{formula}{mobility} + \desc{Electrical mobility}{How quickly a particle moves through a material when moved by an electric field}{$q$ \qtyRef{charge}, $m$ \qtyRef{mass}, $\tau$ \qtyRef{scattering_time}} + \desc[german]{Elektrische Mobilität / Beweglichkeit}{Leichtigkeit mit der sich durch ein Elektrisches Feld beeinflusstes Teilchen im Material bewegt}{} + \quantity{\mu}{\centi\m^2\per\volt\s}{s} + \eq{\mu = \frac{q \tau}{m}} +\end{formula} + +\Subsection[ + \eng{2D electron gas} + \ger{2D Elektronengas} +]{2deg} + + \begin{ttext} + \eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.} + \ger{ + Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird. + } + \end{ttext} + \begin{formula}{confinement_energy} + \desc{Confinement energy}{Raises ground state energy}{} + \desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{} + \eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}} + \end{formula} + + \Eng[plain_wave]{plain wave} + \Ger[plain_wave]{ebene Welle} + \begin{formula}{energy} + \desc{Energy}{}{} + \desc[german]{Energie}{}{} + \eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}} + \end{formula} + +\Subsection[ + \eng{1D electron gas / quantum wire} + \ger{1D Eleltronengas / Quantendraht} +]{1deg} + + \begin{formula}{energy} + \desc{Energy}{}{} + \desc[german]{Energie}{}{} + \eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2} + \end{formula} + \TODO{condunctance} + +\Subsection[ + \eng{0D electron gas / quantum dot} + \ger{0D Elektronengase / Quantenpunkt} +]{0deg} + + \TODO{TODO} + diff --git a/src/cm/other.tex b/src/cm/other.tex new file mode 100644 index 0000000..64101d5 --- /dev/null +++ b/src/cm/other.tex @@ -0,0 +1,102 @@ +\Section[ + \eng{Band theory} + \ger{Bändermodell} +]{band} + \Subsection[ + \eng{Hybrid orbitals} + \ger{Hybridorbitale} + ]{hybrid_orbitals} + \begin{ttext} + \eng{Hybrid orbitals are linear combinations of other atomic orbitals.} + \ger{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.} + \end{ttext} + + % chemmacros package + \begin{formula}{sp3} + \desc{sp3 Orbital}{\GT{eg} \ce{CH4}}{} + \desc[german]{sp3 Orbital}{}{} + \eq{ + 1\text{s} + 3\text{p} = \text{sp3} + \orbital{sp3} + } + \end{formula} + \begin{formula}{sp2} + \desc{sp2 Orbital}{}{} + \desc[german]{sp2 Orbital}{}{} + \eq{ + 1\text{s} + 2\text{p} = \text{sp2} + \orbital{sp2} + } + \end{formula} + \begin{formula}{sp} + \desc{sp Orbital}{}{} + \desc[german]{sp Orbital}{}{} + \eq{ + 1\text{s} + 1\text{p} = \text{sp} + \orbital{sp} + } + \end{formula} + + + +\Section[ + \eng{Diffusion} + \ger{Diffusion} +]{diffusion} + \begin{formula}{diffusion_coefficient} + \desc{Diffusion coefficient}{}{} + \desc[german]{Diffusionskoeffizient}{}{} + \quantity{D}{\m^2\per\s}{s} + \end{formula} + + \begin{formula}{particle_current_density} + \desc{Particle current density}{Number of particles through an area}{} + \desc[german]{Teilchenstromdichte}{Anzahl der Teilchen durch eine Fläche}{} + \quantity{J}{1\per\s^2}{s} + \end{formula} + + \begin{formula}{einstein_relation} + \desc{Einstein relation}{Classical}{\QtyRef{diffusion_coefficient}, \mu \qtyRef{mobility}, \QtyRef{temperature}, $q$ \qtyRef{charge}} + \desc[german]{Einsteinrelation}{Klassisch}{} + \eq{D = \frac{\mu \kB T}{q}} + \end{formula} + + \begin{formula}{concentration} + \desc{Concentration}{A quantity per volume}{} + \desc[german]{Konzentration}{Eine Größe pro Volumen}{} + \quantity{c}{x\per\m^3}{s} + \end{formula} + + \begin{formula}{fick_law_1} + \desc{Fick's first law}{Particle movement is proportional to concentration gradient}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}} + \desc[german]{Erstes Ficksches Gesetz}{Teilchenbewegung ist proportional zum Konzentrationsgradienten}{} + \eq{J = -D\frac{c}{x}} + \end{formula} + + \begin{formula}{fick_law_2} + \desc{Fick's second law}{}{\QtyRef{particle_current_density}, \QtyRef{diffusion_coefficient}, \QtyRef{concentration}} + \desc[german]{Zweites Ficksches Gesetz}{}{} + \eq{\pdv{c}{t} = D \pdv[2]{c}{x}} + \end{formula} + +\Section[ + \eng{\GT{misc}} + \ger{\GT{misc}} +]{misc} + + \begin{formula}{exciton} + \desc{Exciton}{}{} + \desc[german]{Exziton}{}{} + \ttxt{ + \eng{Quasi particle, excitation in condensed matter as bound electron-hole pair.} + \ger{Quasiteilchen, Anregung im Festkörper als gebundenes Elektron-Loch-Paar} + } + \end{formula} + + \begin{formula}{work_function} + \desc{Work function}{Lowest energy required to remove an electron into the vacuum}{} + \desc[german]{Austrittsarbeit}{eng. "Work function"; minimale Energie um ein Elektron aus dem Festkörper zu lösen}{} + \quantity{W}{\eV}{s} + \eq{-e\phi - \EFermi} + \end{formula} + diff --git a/src/cm/semiconductors.tex b/src/cm/semiconductors.tex index e1a0bff..9e1f0c5 100644 --- a/src/cm/semiconductors.tex +++ b/src/cm/semiconductors.tex @@ -52,6 +52,21 @@ CdS & 2.58 & 2.42 & \GT{direct} \end{tabular} + \begin{formula}{min_maj} + \desc{Minority / Majority charge carriers}{}{} + \desc[german]{Minoritäts- / Majoritätsladungstraäger}{}{} + \ttxt{ + \eng{ + Majority carriers: higher number of particles ($e^-$ in n-type, $h^+$ in p-type)\\ + Minority carriers: lower number of particles ($h^+$ in n-type, $e^-$ in p-type) + } + \ger{ + Majoritätsladungstraäger: höhere Teilchenzahl ($e^-$ in n-Typ, $h^+$ in p-Typ)\\ + Minoritätsladungsträger: niedrigere Teilchenzahl ($h^+$ in n-Typ, $e^-$ in p-Typ) + } + } + \end{formula} + diff --git a/src/computational.tex b/src/computational.tex index 2cffdcd..40bea99 100644 --- a/src/computational.tex +++ b/src/computational.tex @@ -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} @@ -117,14 +133,15 @@ \eng{Statistical method} \end{ttext} - + + \TODO{ab-initio MD, force-field MD} \Section[ \eng{Gradient descent} \ger{Gradientenverfahren} - ]{gd} +]{gd} \TODO{TODO} diff --git a/src/constants.tex b/src/constants.tex index fe035cd..fd03cf2 100644 --- a/src/constants.tex +++ b/src/constants.tex @@ -2,35 +2,45 @@ \eng{Constants} \ger{Konstanten} ]{constants} - \begin{constant}{planck}{h}{def} + \begin{formula}{planck} \desc{Planck Constant}{}{} \desc[german]{Plancksches Wirkumsquantum}{}{} - \val{6.62607015\cdot 10^{-34}}{\joule\s} - \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} diff --git a/src/ed/ed.tex b/src/ed/ed.tex new file mode 100644 index 0000000..28d6311 --- /dev/null +++ b/src/ed/ed.tex @@ -0,0 +1,139 @@ +\Part[ + \eng{Electrodynamics} + \ger{Elektrodynamik} +]{ed} + +% pure electronic stuff in el +% pure magnetic stuff in mag +% electromagnetic stuff in em + +% TODO move +\Section[ + \eng{Hall-Effect} + \ger{Hall-Effekt} + ]{hall} + + \begin{formula}{cyclotron} + \desc{Cyclontron frequency}{}{} + \desc[german]{Zyklotronfrequenz}{}{} + \eq{\omega_\text{c} = \frac{e B}{\masse}} + \end{formula} + \TODO{Move} + + + \Subsection[ + \eng{Classical Hall-Effect} + \ger{Klassischer Hall-Effekt} + ]{classic} + \begin{ttext} + \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.} + \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.} + \end{ttext} + \begin{formula}{voltage} + \desc{Hall voltage}{}{$n$ charge carrier density} + \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte} + \eq{U_\text{H} = \frac{I B}{ne d}} + \end{formula} + + \begin{formula}{coefficient} + \desc{Hall coefficient}{Sometimes $R_\txH$}{} + \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{} + \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}} + \end{formula} + + \begin{formula}{resistivity} + \desc{Resistivity}{}{} + \desc[german]{Spezifischer Widerstand}{}{} + \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}} + \end{formula} + + + \Subsection[ + \eng{Integer quantum hall effect} + \ger{Ganzahliger Quantenhalleffekt} + ]{quantum} + + \begin{formula}{conductivity} + \desc{Conductivity tensor}{}{} + \desc[german]{Leitfähigkeitstensor}{}{} + \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} } + \end{formula} + + \begin{formula}{resistivity_tensor} + \desc{Resistivity tensor}{}{} + \desc[german]{Spezifischer Widerstands-tensor}{}{} + \eq{ + \rho = \sigma^{-1} + % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} } + } + \end{formula} + + \begin{formula}{resistivity} + \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor} + \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor} + \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}} + \end{formula} + + % \begin{formula}{qhe} + % \desc{Integer quantum hall effect}{}{} + % \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{} + % \fig{img/qhe-klitzing.jpeg} + % \end{formula} + + \begin{formula}{fqhe} + \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors} + \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler} + \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...} + \end{formula} + + \begin{ttext} + \eng{ + \begin{itemize} + \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer + \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction + \item \textbf{Spin} (QSHE): spin currents instead of charge currents + \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields + \end{itemize} + } + \ger{ + \begin{itemize} + \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig + \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch + \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme + \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld + \end{itemize} + } + \end{ttext} + + + \TODO{sort} + \begin{formula}{impedance_c} + \desc{Impedance of a capacitor}{}{} + \desc[german]{Impedanz eines Kondesnators}{}{} + \eq{Z_{C} = \frac{1}{i\omega C}} + \end{formula} + + \begin{formula}{impedance_l} + \desc{Impedance of an inductor}{}{} + \desc[german]{Impedanz eines Induktors}{}{} + \eq{Z_{L} = i\omega L} + \end{formula} + + \TODO{impedance addition for parallel / linear} + +\Section[ + \eng{Dipole-stuff} + \ger{Dipol-zeug} +]{dipole} + + \begin{formula}{poynting} + \desc{Dipole radiation Poynting vector}{}{} + \desc[german]{Dipolsrahlung Poynting-Vektor}{}{} + \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}} + \end{formula} + + \begin{formula}{power} + \desc{Time-average power}{}{} + \desc[german]{Zeitlich mittlere Leistung}{}{} + \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}} + \end{formula} diff --git a/src/ed/el.tex b/src/ed/el.tex new file mode 100644 index 0000000..b915e7e --- /dev/null +++ b/src/ed/el.tex @@ -0,0 +1,51 @@ + +\Section[ + \eng{Electric field} + \ger{Elektrisches Feld} +]{el} +\begin{formula}{electric_field} + \desc{Electric field}{Surrounds charged particles}{} + \desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{} + \quantity{\vec{\E}}{\volt\per\m=\kg\m\per\s^3\ampere}{v} + \end{formula} + \begin{formula}{gauss_law} + \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface} + \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche} + \eq{\PhiE = \iint_S \vec{\E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}} + \end{formula} + + \begin{formula}{permittivity} + \desc{Permittivity}{Electric polarizability of a dielectric material}{} + \desc[german]{Permitivität}{Dielektrische Konstante\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{} + \quantity{\epsilon}{\ampere\s\per\volt\m=\farad\per\m=\coulomb\per\volt\m=C^2\per\newton\m^2=\ampere^2\s^4\per\kg\m^3}{} + \end{formula} + \begin{formula}{relative_permittivity} + \desc{Relative permittivity / Dielectric constant}{}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}} + \desc[german]{Relative Permittivität / Dielectric constant}{}{} + \eq{ + \epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0} + } + \end{formula} + + \begin{formula}{vacuum_permittivity} + \desc{Vacuum permittivity}{Electric constant}{} + \desc[german]{Vakuum Permittivität}{Elektrische Feldkonstante}{} + \constant{\epsilon_0}{exp}{ + \val{8.8541878188(14)\xE{-1}}{\ampere\s\per\volt\m} + } + \end{formula} + + \begin{formula}{electric_susceptibility} + \desc{Electric susceptibility}{Describes how polarized a dielectric material becomes when an electric field is applied}{$\epsilon_\txr$ \fqEqRef{ed:el:relative_permittivity}} + \desc[german]{Elektrische Suszeptibilität}{Beschreibt wie stark ein dielektrisches Material polarisiert wird, wenn ein elektrisches Feld angelegt wird}{} + \quantity{\chi_\txe}{}{s} + \eq{ + \epsilon_\txr = 1 + \chi_\txe + } + \end{formula} + \begin{formula}{dielectric_polarization_density} + \desc{Dielectric polarization density}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_susceptibility}, \QtyRef{electric_field}} + \desc[german]{Dielektrische Polarisationsdichte}{}{} + \eq{\vec{P} = \epsilon_0 \chi_\txe \vec{\E}} + \end{formula} + diff --git a/src/ed/em.tex b/src/ed/em.tex new file mode 100644 index 0000000..74c29b0 --- /dev/null +++ b/src/ed/em.tex @@ -0,0 +1,82 @@ +\Section[ + \eng{Electromagnetism} + \ger{Elektromagnetismus} +]{em} + \begin{formula}{speed_of_light} + \desc{Speed of light}{in the vacuum}{} + \desc[german]{Lightgeschwindigkeit}{in the vacuum}{} + \constant{c}{exp}{ + \val{299792458}{\m\per\s} + } + \end{formula} + \begin{formula}{vacuum_relations} + \desc{Vacuum permittivity - permeability relation}{\TODO{Does this have a name?}}{\ConstRef{vacuum_permittivity}, \ConstRef{magnetic_vacuum_permeability}, \ConstRef{speed_of_light}} + \desc[german]{Vakuum Permittivität - Permeabilität Beziehung}{}{} + \eq{ + \epsilon_0 \mu_0 = \frac{1}{c^2} + } + \end{formula} + + \begin{formula}{poisson_equation} + \desc{Poisson equation for electrostatics}{}{\QtyRef{charge_density}, \QtyRef{permittivity}, $\Phi$ Potential} + \desc[german]{Poisson Gleichung in der Elektrostatik}{}{} + \eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}} + \TODO{double check $\Phi$} + \end{formula} + + \begin{formula}{poynting} + \desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field [$\si{\W\per\m^2}$]}{} + \desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes [$\si{\W\per\m^2}$]}{} + \eq{\vec{S} = \vec{E} \times \vec{H}} + \end{formula} + + \Subsection[ + \eng{Maxwell-Equations} + \ger{Maxwell-Gleichungen} + ]{Maxwell} + \begin{formula}{vacuum} + \desc{Vacuum}{microscopic formulation}{} + \desc[german]{Vakuum}{Mikroskopische Formulierung}{} + \eq{ + \Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\ + \Div \vec{B} &= 0 \\ + \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\ + \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t} + } + \end{formula} + + \begin{formula}{material} + \desc{Matter}{Macroscopic formulation}{} + \desc[german]{Materie}{Makroskopische Formulierung}{} + \eq{ + \Div \vec{D} &= \rho_\text{el} \\ + \Div \vec{B} &= 0 \\ + \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\ + \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t} + } + \end{formula} + \TODO{Polarization} + + \Subsection[ + \eng{Induction} + \ger{Induktion} + ]{induction} + \begin{formula}{farady_law} + \desc{Faraday's law of induction}{}{} + \desc[german]{Faradaysche Induktionsgesetz}{}{} + \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}} + \end{formula} + + \begin{formula}{lenz} + \desc{Lenz's law}{}{} + \desc[german]{Lenzsche Regel}{}{} + \ttxt{ + \eng{ + Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux. + } + \ger{ + Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt. + } + } + \end{formula} + diff --git a/src/ed/mag.te b/src/ed/mag.te new file mode 100644 index 0000000..a656ff0 --- /dev/null +++ b/src/ed/mag.te @@ -0,0 +1,115 @@ +\Section[ + \eng{Magnetic field} + \ger{Magnetfeld} +]{mag} + + \begin{formula}{magnetic_flux} + \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}} + \desc[german]{Magnetischer Fluss}{}{} + \quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar} + \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}} + \end{formula} + + \begin{formula}{magnetic_flux_density} + \desc{Magnetic flux density}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}} + \desc[german]{Magnetische Flussdichte}{Definiert über \fqEqRef{ed:mag:lorentz}}{} + \quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{} + \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})} + \end{formula} + + \begin{formula}{magnetic_field_intensity} + \desc{Magnetic field intensity}{}{} + \desc[german]{Magnetische Feldstärke}{}{} + \quantity{\vec{H}}{\ampere\per\m}{vector} + \eq{ + \vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M} + } + \end{formula} + + \begin{formula}{lorentz} + \desc{Lorentz force law}{Force on charged particle}{} + \desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{} + \eq{ + \vec{F} = q \vec{\E} + q \vec{v}\times\vec{B} + } + \end{formula} + + \begin{formula}{magnetic_permeability} + \desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}} + \desc[german]{Magnetisch Permeabilität}{}{} + \quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar} + \eq{\mu=\frac{B}{H}} + \end{formula} + \begin{formula}{magnetic_vacuum_permeability} + \desc{Magnetic vauum permeability}{}{} + \desc[german]{Magnetische Vakuumpermeabilität}{}{} + \constant{\mu_0}{exp}{ + \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2} + } + \end{formula} + \begin{formula}{relative_permeability} + \desc{Relative permeability}{}{} + \desc[german]{Realtive Permeabilität}{}{} + \eq{ + \mu_\txr = \frac{\mu}{\mu_0} + } + \end{formula} + + \begin{formula}{gauss_law} + \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface} + \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche} + \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0} + \end{formula} + + \begin{formula}{magnetization} + \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{} + \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{} + \quantity{\vec{M}}{\ampere\per\m}{vector} + \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}} + \end{formula} + + \begin{formula}{magnetic_moment} + \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{} + \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{} + \quantity{\vec{m}}{\ampere\m^2}{vector} + \end{formula} + + \begin{formula}{angular_torque} + \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}} + \desc[german]{Drehmoment}{}{} + \eq{\vec{\tau} = \vec{m} \times \vec{B}} + \end{formula} + + \begin{formula}{magnetic_susceptibility} + \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}} + \desc[german]{Suszeptibilität}{}{} + \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1} + \end{formula} + + + + + \Subsection[ + \eng{Magnetic materials} + \ger{Magnetische Materialien} + ]{materials} + \begin{formula}{paramagnetism} + \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} + \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{} + \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0} + \end{formula} + + \begin{formula}{diamagnetism} + \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} + \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{} + \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0} + \end{formula} + + \begin{formula}{ferromagnetism} + \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} + \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{} + \eq{ + \mu_\txr \gg 1 + } + \end{formula} + diff --git a/src/ed/mag.tex b/src/ed/mag.tex new file mode 100644 index 0000000..a656ff0 --- /dev/null +++ b/src/ed/mag.tex @@ -0,0 +1,115 @@ +\Section[ + \eng{Magnetic field} + \ger{Magnetfeld} +]{mag} + + \begin{formula}{magnetic_flux} + \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}} + \desc[german]{Magnetischer Fluss}{}{} + \quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar} + \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}} + \end{formula} + + \begin{formula}{magnetic_flux_density} + \desc{Magnetic flux density}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}} + \desc[german]{Magnetische Flussdichte}{Definiert über \fqEqRef{ed:mag:lorentz}}{} + \quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{} + \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})} + \end{formula} + + \begin{formula}{magnetic_field_intensity} + \desc{Magnetic field intensity}{}{} + \desc[german]{Magnetische Feldstärke}{}{} + \quantity{\vec{H}}{\ampere\per\m}{vector} + \eq{ + \vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M} + } + \end{formula} + + \begin{formula}{lorentz} + \desc{Lorentz force law}{Force on charged particle}{} + \desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{} + \eq{ + \vec{F} = q \vec{\E} + q \vec{v}\times\vec{B} + } + \end{formula} + + \begin{formula}{magnetic_permeability} + \desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}} + \desc[german]{Magnetisch Permeabilität}{}{} + \quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar} + \eq{\mu=\frac{B}{H}} + \end{formula} + \begin{formula}{magnetic_vacuum_permeability} + \desc{Magnetic vauum permeability}{}{} + \desc[german]{Magnetische Vakuumpermeabilität}{}{} + \constant{\mu_0}{exp}{ + \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2} + } + \end{formula} + \begin{formula}{relative_permeability} + \desc{Relative permeability}{}{} + \desc[german]{Realtive Permeabilität}{}{} + \eq{ + \mu_\txr = \frac{\mu}{\mu_0} + } + \end{formula} + + \begin{formula}{gauss_law} + \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface} + \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche} + \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0} + \end{formula} + + \begin{formula}{magnetization} + \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{} + \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{} + \quantity{\vec{M}}{\ampere\per\m}{vector} + \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}} + \end{formula} + + \begin{formula}{magnetic_moment} + \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{} + \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{} + \quantity{\vec{m}}{\ampere\m^2}{vector} + \end{formula} + + \begin{formula}{angular_torque} + \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}} + \desc[german]{Drehmoment}{}{} + \eq{\vec{\tau} = \vec{m} \times \vec{B}} + \end{formula} + + \begin{formula}{magnetic_susceptibility} + \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}} + \desc[german]{Suszeptibilität}{}{} + \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1} + \end{formula} + + + + + \Subsection[ + \eng{Magnetic materials} + \ger{Magnetische Materialien} + ]{materials} + \begin{formula}{paramagnetism} + \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} + \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{} + \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0} + \end{formula} + + \begin{formula}{diamagnetism} + \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} + \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{} + \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0} + \end{formula} + + \begin{formula}{ferromagnetism} + \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} + \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{} + \eq{ + \mu_\txr \gg 1 + } + \end{formula} + diff --git a/src/electrodynamics.tex b/src/electrodynamics.tex deleted file mode 100644 index 7ebbf40..0000000 --- a/src/electrodynamics.tex +++ /dev/null @@ -1,394 +0,0 @@ - -\Part[ - \eng{Electrodynamics} - \ger{Elektrodynamik} -]{ed} - - -% pure electronic stuff in el -% pure magnetic stuff in mag -% electromagnetic stuff in em - -\Section[ - \eng{Electric field} - \ger{Elektrisches Feld} -]{el} - \begin{formula}{gauss_law} - \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface} - \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche} - \eq{\PhiE = \iint_S \vec{\E}\cdot\d\vec{S} = \frac{Q}{\varepsilon_0}} - \end{formula} - - \begin{quantity}{permittivity}{\epsilon}{\ampere\s\per\volt\m=\farad\per\m=\coulomb\per\volt\m=C^2\per\newton\m^2=\ampere^2\s^4\per\kg\m^3}{} - \desc{Permittivity}{Electric polarizability of a dielectric material}{} - \desc[german]{Permitivität}{Dielektrische Konstante\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{} - \end{quantity} - \begin{formula}{relative_permittivity} - \desc{Relative permittivity / Dielectric constant}{}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}} - \desc[german]{Relative Permittivität / Dielectric constant}{}{} - \eq{ - \epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0} - } - \end{formula} - - \begin{constant}{vacuum_permittivity}{\epsilon_0}{exp} - \desc{Vacuum permittivity}{Electric constant}{} - \desc[german]{Vakuum Permittivität}{Elektrische Feldkonstante}{} - \val{8.8541878188(14)\E{-1}}{\ampere\s\per\volt\m} - \end{constant} - - \begin{formula}{electric_susceptibility} - \desc{Electric susceptibility}{Describes how polarized a dielectric material becomes when an electric field is applied}{$\epsilon_\txr$ \fqEqRef{ed:el:relative_permittivity}} - \desc[german]{Elektrische Suszeptibilität}{Beschreibt wie stark ein dielektrisches Material polarisiert wird, wenn ein elektrisches Feld angelegt wird}{} - \eq{ - \epsilon_\txr = 1 + \chi_\txe - } - \end{formula} - \begin{formula}{dielectric_polarization_density} - \desc{Dielectric polarization density}{}{\ConstRef{vacuum_permittivity}, $\fqEqRef{ed:el:electric_susceptibility}$, \QtyRef{electric_field}} - \desc[german]{Dielektrische Polarisationsdichte}{}{} - \eq{\vec{P} = \epsilon_0 \chi_\txe \vec{\E}} - \end{formula} - -\Section[ - \eng{Magnetic field} - \ger{Magnetfeld} -]{mag} - - \Eng[magnetic_flux]{Magnetix flux density} - \Ger[magnetic_flux]{Magnetische Flussdichte} - - \begin{quantity}{magnetic_flux}{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar} - \desc{Magnetic flux}{Test desc}{Test def} - \desc[german]{Magnetischer Fluss}{Test desc}{Test def} - \end{quantity} - - \begin{quantity}{magnetic_flux_density}{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{} - \desc{Magnetic flux density}{}{} - \desc[german]{Magnetische Flussdichte}{}{} - \end{quantity} - \begin{formula}{magnetic_flux_density} - \desc{\qtyRef{magnetic_flux_density}}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}} - \desc[german]{}{Definiert über \fqEqRef{ed:mag:lorentz}}{} - \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})} - \end{formula} - - \begin{quantity}{magnetic_field_intensity}{\vec{H}}{\ampere\per\m}{vector} - \desc{Magnetic field intensity}{}{} - \desc[german]{Magnetische Feldstärke}{}{} - \end{quantity} - \begin{formula}{magnetic_field_intensity} - \desc{\qtyRef{magnetic_field_intensity}}{}{} - \desc[german]{}{}{} - \eq{ - \vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M} - } - \end{formula} - - \begin{formula}{lorentz} - \desc{Lorentz force law}{Force on charged particle}{} - \desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{} - \eq{ - \vec{F} = q \vec{\E} + q \vec{v}\times\vec{B} - } - \end{formula} - - \begin{quantity}{magnetic_permeability}{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar} - \desc{Magnetic permeability}{}{} - \desc[german]{Magnetisch Permeabilität}{}{} - \end{quantity} - \begin{formula}{magnetic_permeability} - \desc{\qtyRef{magnetic_permeability}}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}} - \desc[german]{}{}{} - \eq{\mu=\frac{B}{H}} - \end{formula} - \begin{constant}{magnetic_vacuum_permeability}{\mu_0}{exp} - \desc{Magnetic vauum permeability}{}{} - \desc[german]{Magnetische Vakuumpermeabilität}{}{} - \val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2} - \end{constant} - \begin{formula}{relative_permeability} - \desc{Relative permeability}{}{} - \desc[german]{Realtive Permeabilität}{}{} - \eq{ - \mu_\txr = \frac{\mu}{\mu_0} - } - \end{formula} - - \begin{formula}{magnetic_flux} - \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}} - \desc[german]{Magnetischer Fluss}{}{} - \eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}} - \end{formula} - - \begin{formula}{gauss_law} - \desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface} - \desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche} - \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0} - \end{formula} - - \begin{quantity}{magnetization}{\vec{M}}{\ampere\per\m}{vector} - \desc{Magnetization}{Vector field describing the density of magnetic dipoles}{} - \desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{} - \end{quantity} - \begin{formula}{magnetization} - \desc{\qtyRef{magnetization}}{}{$m$ \qtyRef{magnetic_moment}, $V$ \qtyRef{volume}} - \desc[german]{}{}{} - \eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}} - \end{formula} - - \begin{quantity}{magnetic_moment}{\vec{m}}{\ampere\m^2}{vector} - \desc{Magnetic moment}{Strength and direction of a magnetic dipole}{} - \desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{} - \end{quantity} - - \begin{formula}{angular_torque} - \desc{Torque}{}{$m$ \qtyRef{magnetic_moment}} - \desc[german]{Drehmoment}{}{} - \eq{\vec{\tau} = \vec{m} \times \vec{B}} - \end{formula} - - \begin{formula}{magnetic_susceptibility} - \desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}} - \desc[german]{Suszeptibilität}{}{} - \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1} - \end{formula} - - - - - \Subsection[ - \eng{Magnetic materials} - \ger{Magnetische Materialien} - ]{materials} - \begin{formula}{paramagnetism} - \desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} - \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{} - \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0} - \end{formula} - - \begin{formula}{diamagnetism} - \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} - \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{} - \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0} - \end{formula} - - \begin{formula}{ferromagnetism} - \desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} - \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{} - \eq{ - \mu_\txr \gg 1 - } - \end{formula} - -\Section[ - \eng{Electromagnetism} - \ger{Elektromagnetismus} -]{em} - \begin{constant}{speed_of_light}{c}{exp} - \desc{Speed of light}{in the vacuum}{} - \desc[german]{Lightgeschwindigkeit}{in the vacuum}{} - \val{299792458}{\m\per\s} - \end{constant} - \begin{formula}{vacuum_relations} - \desc{Vacuum permittivity - permeability relation}{\TODO{Does this have a name?}}{\ConstRef{vacuum_permittivity}, \ConstRef{magnetic_vacuum_permeability}, \ConstRef{speed_of_light}} - \desc[german]{Vakuum Permittivität - Permeabilität Beziehung}{}{} - \eq{ - \epsilon_0 \mu_0 = \frac{1}{c^2} - } - \end{formula} - - \begin{formula}{poisson_equation} - \desc{Poisson equation for electrostatics}{}{\QtyRef{charge_density}, \QtyRef{permittivity}, $\phi$} - \desc[german]{Poisson Gleichung in der Elektrostatik}{}{} - \eq{\laplace \Phi(\vecr) = -\frac{\rho(\vecr)}{\epsilon}} - \end{formula} - - \begin{formula}{poynting} - \desc{Poynting vector}{Directional energy flux or power flow of an electromagnetic field [$\si{\W\per\m^2}$]}{} - \desc[german]{Poynting-Vektor}{Gerichteter Energiefluss oder Leistungsfluss eines elektromgnetischen Feldes [$\si{\W\per\m^2}$]}{} - \eq{\vec{S} = \vec{E} \times \vec{H}} - \end{formula} - - \Subsection[ - \eng{Maxwell-Equations} - \ger{Maxwell-Gleichungen} - ]{Maxwell} - \begin{formula}{vacuum} - \desc{Vacuum}{microscopic formulation}{} - \desc[german]{Vakuum}{Mikroskopische Formulierung}{} - \eq{ - \Div \vec{\E} &= \frac{\rho_\text{el}}{\epsilon_0} \\ - \Div \vec{B} &= 0 \\ - \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\ - \Rot \vec{B} &= \mu_0 \vec{j} + \frac{1}{c^2} \odv{\vec{\E}}{t} - } - \end{formula} - - \begin{formula}{material} - \desc{Matter}{Macroscopic formulation}{} - \desc[german]{Materie}{Makroskopische Formulierung}{} - \eq{ - \Div \vec{D} &= \rho_\text{el} \\ - \Div \vec{B} &= 0 \\ - \Rot \vec{\E} &= - \odv{\vec{B}}{t} \\ - \Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t} - } - \end{formula} - \TODO{Polarization} - - \Subsection[ - \eng{Induction} - \ger{Induktion} - ]{induction} - \begin{formula}{farady_law} - \desc{Faraday's law of induction}{}{} - \desc[german]{Faradaysche Induktionsgesetz}{}{} - \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}} - \end{formula} - - \begin{formula}{lenz} - \desc{Lenz's law}{}{} - \desc[german]{Lenzsche Regel}{}{} - \ttxt{ - \eng{ - Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux. - } - \ger{ - Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt. - } - } - \end{formula} - - - - -\Section[ - \eng{Hall-Effect} - \ger{Hall-Effekt} - ]{hall} - - \begin{formula}{cyclotron} - \desc{Cyclontron frequency}{}{} - \desc[german]{Zyklotronfrequenz}{}{} - \eq{\omega_\text{c} = \frac{e B}{\masse}} - \end{formula} - \TODO{Move} - - - \Subsection[ - \eng{Classical Hall-Effect} - \ger{Klassischer Hall-Effekt} - ]{classic} - \begin{ttext} - \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.} - \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.} - \end{ttext} - \begin{formula}{voltage} - \desc{Hall voltage}{}{$n$ charge carrier density} - \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte} - \eq{U_\text{H} = \frac{I B}{ne d}} - \end{formula} - - \begin{formula}{coefficient} - \desc{Hall coefficient}{Sometimes $R_\txH$}{} - \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{} - \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}} - \end{formula} - - \begin{formula}{resistivity} - \desc{Resistivity}{}{} - \desc[german]{Spezifischer Widerstand}{}{} - \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}} - \end{formula} - - - \Subsection[ - \eng{Integer quantum hall effect} - \ger{Ganzahliger Quantenhalleffekt} - ]{quantum} - - \begin{formula}{conductivity} - \desc{Conductivity tensor}{}{} - \desc[german]{Leitfähigkeitstensor}{}{} - \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} } - \end{formula} - - \begin{formula}{resistivity} - \desc{Resistivity tensor}{}{} - \desc[german]{Spezifischer Widerstands-tensor}{}{} - \eq{ - \rho = \sigma^{-1} - % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} } - } - \end{formula} - - \begin{formula}{resistivity} - \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor} - \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor} - \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}} - \end{formula} - - % \begin{formula}{qhe} - % \desc{Integer quantum hall effect}{}{} - % \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{} - % \fig{img/qhe-klitzing.jpeg} - % \end{formula} - - \begin{formula}{fqhe} - \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors} - \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler} - \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...} - \end{formula} - - \begin{ttext} - \eng{ - \begin{itemize} - \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer - \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction - \item \textbf{Spin} (QSHE): spin currents instead of charge currents - \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields - \end{itemize} - } - \ger{ - \begin{itemize} - \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig - \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch - \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme - \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld - \end{itemize} - } - \end{ttext} - - - \TODO{sort} - \begin{formula}{impedance_c} - \desc{Impedance of a capacitor}{}{} - \desc[german]{Impedanz eines Kondesnators}{}{} - \eq{Z_{C} = \frac{1}{i\omega C}} - \end{formula} - - \begin{formula}{impedance_l} - \desc{Impedance of an inductor}{}{} - \desc[german]{Impedanz eines Induktors}{}{} - \eq{Z_{L} = i\omega L} - \end{formula} - - \TODO{impedance addition for parallel / linear} - -\Section[ - \eng{Dipole-stuff} - \ger{Dipol-zeug} -]{dipole} - - \begin{formula}{poynting} - \desc{Dipole radiation Poynting vector}{}{} - \desc[german]{Dipolsrahlung Poynting-Vektor}{}{} - \eq{\vec{S} = \left(\frac{\mu_0 p_0^2 \omega^4}{32\pi^2 c}\right)\frac{\sin^2\theta}{r^2} \vec{r}} - \end{formula} - - \begin{formula}{power} - \desc{Time-average power}{}{} - \desc[german]{Zeitlich mittlere Leistung}{}{} - \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}} - \end{formula} diff --git a/src/main.tex b/src/main.tex old mode 100755 new mode 100644 index 43bfa54..2cf49bf --- a/src/main.tex +++ b/src/main.tex @@ -1,27 +1,29 @@ +%! TeX program = lualatex +% (for vimtex) \documentclass[11pt, a4paper]{article} % \usepackage[utf8]{inputenc} -\usepackage[german]{babel} +\usepackage[english]{babel} \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} % ENVIRONMENTS etc \usepackage{adjustbox} -\usepackage{colortbl} % color table -\usepackage{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} % +\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 % @@ -128,20 +158,22 @@ % Quantities % \newrobustcmd{\qtyRef}[1]{% - \hyperref[qty:#1]{\GT{qty:#1}}% + \edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"fqname"}}% + \hyperref[qty:#1]{\expandafter\GT\expandafter{\tempname:#1}}% } % \newrobustcmd{\QtyRef}[1]{% - ${\luavar{quantities["#1"]["symbol"]}}$ \hyperref[qty:#1]{\GT{qty:#1}}% + $\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}% } % Constants % \newrobustcmd{\constRef}[1]{% - \hyperref[const:#1]{\GT{const:#1}}% + \edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"fqname"}}% + \hyperref[const:#1]{\expandafter\GT\expandafter{\tempname:#1}}% } % \newrobustcmd{\ConstRef}[1]{% - $\luavar{constants["#1"]["symbol"]}$ \hyperref[const:#1]{\GT{const:#1}}% + $\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}% } % Element from periodic table % @@ -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_&ersand} - -\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} diff --git a/src/math/calculus.tex b/src/math/calculus.tex index 3247401..b879109 100644 --- a/src/math/calculus.tex +++ b/src/math/calculus.tex @@ -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} + diff --git a/src/math/geometry.tex b/src/math/geometry.tex index a217fa8..f8646c3 100644 --- a/src/math/geometry.tex +++ b/src/math/geometry.tex @@ -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} diff --git a/src/math/linalg.tex b/src/math/linalg.tex index 8755862..ad99fe0 100644 --- a/src/math/linalg.tex +++ b/src/math/linalg.tex @@ -1,12 +1,66 @@ \Section[ \eng{Linear algebra} \ger{Lineare Algebra} - ]{linalg} +]{linalg} + + \Subsection[ + \eng{Matrix basics} + \ger{Matrizen Basics} + ]{matrix} + + \begin{formula}{matrix_matrix_product} + \desc{Matrix-matrix product as sum}{}{} + \desc[german]{Matrix-Matrix Produkt als Summe}{}{} + \eq{C_{ij} = \sum_{k} A_{ik} B_{kj}} + \end{formula} + \begin{formula}{matrix_vector_product} + \desc{Matrix-vector product as sum}{}{} + \desc[german]{Matrix-Vektor Produkt als Summe}{}{} + \eq{\vec{c}_{i} = \sum_{j} A_{ij} \vec{b}_{j}} + \end{formula} + + \begin{formula}{symmetric} + \desc{Symmetric matrix}{}{$A$ $n\times n$ \GT{matrix}} + \desc[german]{Symmetrische matrix}{}{} + \eq{A^\T = A} + \end{formula} + + \begin{formula}{unitary} + \desc{Unitary matrix}{}{} + \desc[german]{Unitäre Matrix}{}{} + \eq{U ^\dagger U = \id} + \end{formula} + + \Subsubsection[ + \eng{Transposed matrix} + \ger{Transponierte Matrix} + ]{transposed} + \begin{formula}{sum} + \desc{Sum}{}{} + \desc[german]{Summe}{}{} + \eq{(A+B)^\T = A^\T + B^\T} + \end{formula} + \begin{formula}{product} + \desc{Product}{}{} + \desc[german]{Produkt}{}{} + \eq{(AB)^\T = B^\T A^\T} + \end{formula} + \begin{formula}{inverse} + \desc{Inverse}{}{} + \desc[german]{Inverse}{}{} + \eq{(A^{-1})^\T = (A^\T)^{-1}} + \end{formula} + \begin{formula}{exponential} + \desc{Exponential}{}{} + \desc[german]{Exponential}{}{} + \eq{\exp(A^\T) = (\exp A)^\T \\ \ln(A^\T)=(\ln A)^\T} + \end{formula} + \Subsection[ \eng{Determinant} \ger{Determinante} - ]{determinant} + ]{determinant} \begin{formula}{2x2} \desc{2x2 matrix}{}{} \desc[german]{2x2 Matrix}{}{} @@ -43,7 +97,16 @@ \Subsection[ - ]{zeug} + ]{misc} + + \begin{formula}{normal_equation} + \desc{Normal equation}{Solves a linear regression problem}{\mat{\theta} hypothesis / weight matrix, \mat{X} design matrix, \vec{y} output vector} + % \desc[german]{}{}{} + \eq{ + \mat{\theta} = (\mat{X}^\T \mat{X})^{-1} \mat{X}^\T \vec{y} + } + \end{formula} + \begin{formula}{inverse_2x2} \desc{Inverse $2\times 2$ matrix}{}{} @@ -54,12 +117,6 @@ } \end{formula} - \begin{formula}{unitary} - \desc{Unitary matrix}{}{} - \desc[german]{Unitäre Matrix}{}{} - \eq{U ^\dagger U = \id} - \end{formula} - \begin{formula}{svd} \desc{Singular value decomposition}{Factorization of complex matrices through rotating \rightarrow rescaling \rightarrow rotation.}{$A$: $m\times n$ matrix, $U$: $m\times m$ unitary matrix, $\Lambda$: $m\times n$ rectangular diagonal matrix with non-negative numbers on the diagonal, $V$: $n\times n$ unitary matrix} \desc[german]{Singulärwertzerlegung}{Faktorisierung einer reellen oder komplexen Matrix durch Rotation \rightarrow Skalierung \rightarrow Rotation.}{} @@ -93,7 +150,7 @@ \end{formula} - \Subection[ + \Subsection[ \eng{Eigenvalues} \ger{Eigenwerte} ]{eigen} diff --git a/src/math/math.tex b/src/math/math.tex new file mode 100644 index 0000000..97ada42 --- /dev/null +++ b/src/math/math.tex @@ -0,0 +1,5 @@ +\Part[ + \eng{Mathematics} + \ger{Mathematik} +]{math} + diff --git a/src/math/probability_theory.tex b/src/math/probability_theory.tex index 093531e..bb17bb8 100644 --- a/src/math/probability_theory.tex +++ b/src/math/probability_theory.tex @@ -102,7 +102,7 @@ \disteq{median}{x_0} \disteq{variance}{\text{\GT{undefined}}} \end{distribution} - + \noindent \begin{ttext} \eng{Also known as \textbf{Cauchy-Lorentz distribution}, \textbf{Lorentz(ian) function}, \textbf{Breit-Wigner distribution}.} \ger{Auch bekannt als \textbf{Cauchy-Lorentz Verteilung}, \textbf{Lorentz Funktion}, \textbf{Breit-Wigner Verteilung}.} @@ -114,9 +114,9 @@ \ger{Binomialverteilung} ]{binomial} \begin{ttext} - \eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \hyperref[sec:pb:distributions::poisson]{poisson distribution}} - \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 diff --git a/src/quantities.tex b/src/quantities.tex index 101ce61..d8fcdc4 100644 --- a/src/quantities.tex +++ b/src/quantities.tex @@ -1,77 +1,119 @@ % if this causes a compilation error, check that none of the units have been redefined -\Eng[si_base_units]{SI base units} -\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} diff --git a/src/quantum_computing.tex b/src/quantum_computing.tex index 967c37f..b39fefc 100644 --- a/src/quantum_computing.tex +++ b/src/quantum_computing.tex @@ -92,12 +92,10 @@ \begin{formula}{circuit} \desc{SQUID}{Superconducting quantum interference device, consists of parallel \hyperref{sec:qc:scq:josephson_junction}{josephson junctions}, can be used to measure extremely weak magnetic fields}{} \desc[german]{SQUID}{Superconducting quantum interference device, besteht aus parralelen \hyperref{sec:qc:scq:josephson_junction}{Josephson Junctions} und kann zur Messung extrem schwacher Magnetfelder genutzt werden}{} - \content{ - \centering - \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{$E_\text{C} = \frac{(2e)^2}{2C}, E_\text{L} = \frac{\varphi_0^2}{2L}, \delta_\text{s} = \frac{\varphi_\text{s}}{\varphi_0}$} diff --git a/src/quantum_mechanics.tex b/src/quantum_mechanics.tex index e6bbce9..005730d 100644 --- a/src/quantum_mechanics.tex +++ b/src/quantum_mechanics.tex @@ -497,6 +497,15 @@ \eq{\psi_k(\vec{r}) = e^{i \vec{k}\cdot \vec{r}} \cdot u_{\vec{k}}(\vec{r})} \end{formula} + \begin{formula}{periodicity} + \desc{Periodicity}{}{\QtyRef{lattice_vector}, \QtyRef{reciprocal_lattice_vector}} + \desc[german]{Periodizität}{}{} + \eq{ + u_\vec{k}(\vec{r} + \vec{R}) = u_\vec{k}(\vec{r}) \\ + \psi_{\vec{k}+\vec{G}}(\vec{r}) = \psi_\vec{k}(\vec{r}) + } + \end{formula} + \Section[ \eng{Symmetries} diff --git a/src/spv.tex b/src/spv.tex new file mode 100644 index 0000000..3226015 --- /dev/null +++ b/src/spv.tex @@ -0,0 +1,41 @@ +\Section[ + \eng{Surface-Photovoltage} + \ger{Oberflächen-Photospannung} +]{spv} + Mechanisms: + \begin{formula}{scr} + \desc{Space-charge regions}{}{} + % \desc[german]{}{}{} + \ttxt{ + \eng{Under illumination, the potential of a space charge region is reduced through the separation of photogenerated charge carriers} + } + \end{formula} + \begin{formula}{dember} + \desc{Dember-Photovoltage}{}{\QtyRef{diffusion_coefficient}} + % \desc[german]{}{}{} + \ttxt{ + \eng{Usually electrons diffuse faster than holes ($D_\txe > D_\txh$) \Rightarrow charge carrier separation} + } + \end{formula} + + \begin{formula}{asymmetric_charge_transfer} + \desc{Asymmetric charge transfer}{}{} + % \desc[german]{}{}{} + \ttxt{ + \eng{Asymmetric transfer rates from bulk to surface states and vice versa leads to charge carrier separation} + } + \end{formula} + \begin{formula}{exciton_dissociation} + \desc{Exciton dissociation}{Important in organic semiconductors with conjugated molecules}{} + % \desc[german]{}{}{} + \ttxt{ + \eng{Excitons dissociate at donor-acceptor heterojunctions and the electron is transferred to the acceptor} + } + \end{formula} + \begin{formula}{surface_dipoles} + \desc{Surface dipoles}{}{} + % \desc[german]{}{}{} + \ttxt{ + \eng{Light can excite electrons, which are then attracted to one part of the molecule. This leads to an orientation of surface dipoles} + } + \end{formula} diff --git a/src/statistical_mechanics.tex b/src/statistical_mechanics.tex index 9cdc3c6..6faa81e 100644 --- a/src/statistical_mechanics.tex +++ b/src/statistical_mechanics.tex @@ -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} diff --git a/src/svgs/convertToPdf.sh b/src/svgs/convertToPdf.sh old mode 100644 new mode 100755 diff --git a/src/test.tex b/src/test.tex new file mode 100644 index 0000000..97337fe --- /dev/null +++ b/src/test.tex @@ -0,0 +1,84 @@ +\part{Testing} + +\paragraph{File loading} +\noindent Lua Aux loaded? \luaAuxLoaded\\ +Translations Aux loaded? \translationsAuxLoaded\\ +Input only: \inputOnlyFile + +\paragraph{Testing GT, GetTranslation, IfTranslationExists, IfTranslation} +\addtranslation{english}{ttest}{This is the english translation of \texttt{ttest}} +\noindent +GT: ttest = \GT{ttest}\\ +GetTranslation: ttest = \GetTranslation{ttest}\\ +Is english? = \IfTranslation{english}{ttest}{yes}{no} \\ +Is german? = \IfTranslation{german}{ttest}{yes}{no} \\ +Is defined = \IfTranslationExists{ttest}{yes}{no} \\ + +\paragraph{Testing translation keys containing macros} +\def\ttest{NAME} +% \addtranslation{english}{\ttest:name}{With variable} +% \addtranslation{german}{\ttest:name}{Mit Variable} +% \addtranslation{english}{NAME:name}{Without variable} +% \addtranslation{german}{NAME:name}{Without Variable} +\DT[\ttest:name]{english}{DT With variable} +\DT[\ttest:name]{german}{DT Mit Variable} +\noindent +GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\ +GetTranslation: {\textbackslash}ttest:name = \GetTranslation{\ttest:name}\\ +Is english? = \IfTranslation{english}{\ttest:name}{yes}{no} \\ +Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\ +Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\ +Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no} + +% \DT[qty:test]{english}{HAHA} + +\paragraph{Testing hyperrefs} +\noindent{This text is labeled with "test" \label{test}}\\ +\hyperref[test]{This should refer to the line above}\\ +Link to quantity which is defined after the reference: \qtyRef{test}\\ +\DT[eq:test]{english}{If you read this, then the translation for eq:test was expandend!} +Link to defined quantity: \qtyRef{mass} +\\ Link to element with name: \ElRef{H} +\begin{equation} + \label{eq:test} + E = mc^2 +\end{equation} + +\paragraph{Testing translation keys with token symbols like undescores} +\noindent +\GT{absolute_undefined_translation_with_underscors}\\ +\gt{relative_undefined_translation_with_underscors}\\ +\GT{absolute_undefined_translation_with_&ersand} + + +\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} + + diff --git a/src/util/environments.tex b/src/util/environments.tex index d627540..6ce3ce0 100644 --- a/src/util/environments.tex +++ b/src/util/environments.tex @@ -1,5 +1,5 @@ % use this to define text in different languages for the key -% the translation for when the environment ends. +% the translation for is printed when the environment ends. % (temporarily change fqname to the \fqname: 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}}") diff --git a/src/util/macros.tex b/src/util/macros.tex index a7757e1..dc0450e 100644 --- a/src/util/macros.tex +++ b/src/util/macros.tex @@ -2,13 +2,6 @@ \def\gooditem{\item[{$\color{neutral_red}\bullet$}]} \def\baditem{\item[{$\color{neutral_green}\bullet$}]} -% put an explanation above an equal sign -% [1]: equality sign (or anything else) -% 2: text (not in math mode!) -\newcommand{\explUnderEq}[2][=]{% - \underset{\substack{\uparrow\\\mathrlap{\text{\hspace{-1em}#2}}}}{#1}} -\newcommand{\explOverEq}[2][=]{% - \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}} % COMMON SYMBOLS WITH SUPER/SUBSCRIPTS, VECTOR ARROWS ETC. % \def\laplace{\Delta} % Laplace operator @@ -102,6 +95,19 @@ \def\qdots{\quad\dots\quad} \def\qRarrow{\quad\Rightarrow\quad} +% ANNOTATIONS +% put an explanation above an equal sign +% [1]: equality sign (or anything else) +% 2: text (not in math mode!) +\newcommand{\explUnderEq}[2][=]{% + \underset{\substack{\uparrow\\\mathrlap{\text{\hspace{-1em}#2}}}}{#1}} +\newcommand{\explOverEq}[2][=]{% + \overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}} +\newcommand{\eqnote}[1]{ + \text{\color{dark2}#1} +} + + % DELIMITERS \DeclarePairedDelimiter{\abs}{\lvert}{\rvert} \DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} @@ -109,13 +115,21 @@ % OPERATORS \DeclareMathOperator{\e}{e} -\DeclareMathOperator{\T}{T} % transposed +\def\T{\text{T}} % transposed \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\const}{const} \DeclareMathOperator{\erf}{erf} \DeclareMathOperator{\erfc}{erfc} \DeclareMathOperator{\cov}{cov} +% \DeclareMathOperator{\arcsin}{arcsin} +% \DeclareMathOperator{\arccos}{arccos} +% \DeclareMathOperator{\arctan}{arctan} +\DeclareMathOperator{\arccot}{arccot} +\DeclareMathOperator{\arsinh}{arsinh} +\DeclareMathOperator{\arcosh}{arcosh} +\DeclareMathOperator{\artanh}{artanh} +\DeclareMathOperator{\arcoth}{arcoth} % diff, for integrals and stuff % \DeclareMathOperator{\dd}{d} \renewcommand*\d{\mathop{}\!\mathrm{d}} @@ -129,3 +143,14 @@ \newcommand\Sin[1]{\CmdWithParenthesis{\sin}{#1}} \newcommand\Cos[1]{\CmdWithParenthesis{\cos}{#1}} \newcommand\Order[1]{\CmdWithParenthesis{\mathcal{O}}{#1}} + +% VECTOR AND MATRIX +% use vecA to force an arrow +\NewCommandCopy{\vecA}{\vec} +% extra {} assure they can b directly used after _ +%% arrow/underline +\newcommand\mat[1]{{\ensuremath{\underline{#1}}}} +\renewcommand\vec[1]{{\ensuremath{\vecA{#1}}}} +%% bold +% \newcommand\mat[1]{{\ensuremath{\bm{#1}}}} +% \renewcommand\vec[1]{{\ensuremath{\bm{#1}}}} diff --git a/src/util/periodic_table.tex b/src/util/periodic_table.tex index 91e79b8..a41f667 100644 --- a/src/util/periodic_table.tex +++ b/src/util/periodic_table.tex @@ -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 } } diff --git a/src/util/translation.tex b/src/util/translation.tex index 9628e5c..28c0cb7 100644 --- a/src/util/translation.tex +++ b/src/util/translation.tex @@ -36,7 +36,7 @@ \newrobustcmd{\GT}[1]{%\expandafter\GetTranslation\expandafter{#1}} \IfTranslationExists{#1}{% \expandafter\GetTranslation\expandafter{#1}% - }{% + }{% ?? \detokenize{#1}% }% } diff --git a/src/util/translations.tex b/src/util/translations.tex index 5e86101..4571df4 100644 --- a/src/util/translations.tex +++ b/src/util/translations.tex @@ -35,6 +35,9 @@ \Eng[see_also]{See also} \Ger[see_also]{Siehe auch} +\Eng[for]{for} +\Ger[for]{für} + \Eng[and_therefore]{and therefore} \Ger[and_therefore]{und damit}