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refactor sectioning

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matthias@quintern.xyz 2025-03-21 22:48:38 +01:00
parent 2674545117
commit 702fc1eb33
47 changed files with 1196 additions and 1383 deletions
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15
scripts/distributions.py
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@ -24,6 +24,20 @@ def gauss():
ax.legend()
return fig
# LAPLACE
def flaplace(x, mu, b):
return 1 / (2*b) * np.exp(-np.abs(x - mu) / b)
def laplace():
fig, ax = get_fig()
x = np.linspace(-5, 5, 300)
for mu, b in [(0, 1), (0, 2), (0, 5), (-2, 2)]:
y = flaplace(x, mu, b)
label = texvar("mu", mu) + ", " + texvar("b", b)
ax.plot(x, y, label=label)
ax.legend()
return fig
# CAUCHY / LORENTZ
def fcauchy(x, x_0, gamma):
return 1 / (np.pi * gamma * (1 + ((x - x_0)/gamma)**2))
@ -128,6 +142,7 @@ def binomial():
if __name__ == '__main__':
export(gauss(), "distribution_gauss")
export(laplace(), "distribution_laplace")
export(cauchy(), "distribution_cauchy")
export(maxwell(), "distribution_maxwell-boltzmann")
export(gamma(), "distribution_gamma")

15
src/ch/ch.tex
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@ -1,9 +1,8 @@
\Part[
\eng{Chemistry}
\ger{Chemie}
]{ch}
\Section[
\eng{Periodic table}
\ger{Periodensystem}
]{ptable}
\Part{ch}
\desc{Chemistry}{}{}
\desc[german]{Chemie}{}{}
\Section{ptable}
\desc{Periodic table}{}{}
\desc[german]{Periodensystem}{}{}
\drawPeriodicTable

64
src/ch/el.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Electrochemistry}
\ger{Elektrochemie}
]{el}
\Section{el}
\desc{Electrochemistry}{}{}
\desc[german]{Elektrochemie}{}{}
\begin{formula}{chemical_potential}
\desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{free_enthalpy}, \QtyRef{amount}}
\desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
@ -38,10 +38,9 @@
\end{formula}
\Subsection[
\eng{Electrochemical cell}
\ger{Elektrochemische Zelle}
]{cell}
\Subsection{cell}
\desc{Electrochemical cell}{}{}
\desc[german]{Elektrochemische Zelle}{}{}
\eng[galvanic]{galvanic}
\ger[galvanic]{galvanisch}
\eng[electrolytic]{electrolytic}
@ -162,10 +161,9 @@
\end{formula}
\Subsection[
\eng{Ionic conduction in electrolytes}
\ger{Ionische Leitung in Elektrolyten}
]{ion_cond}
\Subsection{ion_cond}
\desc{Ionic conduction in electrolytes}{}{}
\desc[german]{Ionische Leitung in Elektrolyten}{}{}
\eng[z]{charge number}
\ger[z]{Ladungszahl}
\eng[of_i]{of ion $i$}
@ -280,10 +278,9 @@
\eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
\end{formula}
\Subsection[
\eng{Kinetics}
\ger{Kinetik}
]{kin}
\Subsection{kin}
\desc{Kinetics}{}{}
\desc[german]{Kinetik}{}{}
\begin{formula}{transfer_coefficient}
\desc{Transfer coefficient}{}{}
\desc[german]{Durchtrittsfaktor}{Transferkoeffizient\\Anteil des Potentials der sich auf die freie Reaktionsenthalpie des anodischen Prozesses auswirkt}{}
@ -307,10 +304,9 @@
\eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
\end{formula}
\Subsubsection[
\eng{Mass transport}
\ger{Massentransport}
]{mass}
\Subsubsection{mass}
\desc{Mass transport}{}{}
\desc[german]{Massentransport}{}{}
\begin{formula}{concentration_overpotential}
\desc{Concentration overpotential}{Due to concentration gradient near the electrode, the ions need to \fRef[diffuse]{ch:el:ion_cond:diffusion} to the electrode before reacting}{\ConstRef{universal_gas}, \QtyRef{temperature}, $\c_{0/\txS}$ ion concentration in the electrolyte / at the double layer, $z$ \qtyRef{charge_number}, \ConstRef{faraday}}
\desc[german]{Konzentrationsüberspannung}{Durch einen Konzentrationsgradienten an der Elektrode müssen Ionen erst zur Elektrode \fRef[diffundieren]{ch:el:ion_cond:diffusion}, bevor sie reagieren können}{}
@ -488,15 +484,13 @@
\Subsection[
\eng{Techniques}
\ger{Techniken}
]{tech}
\Subsection{tech}
\desc{Techniques}{}{}
\desc[german]{Techniken}{}{}
\Subsubsection[
\eng{Reference electrodes}
\ger{Referenzelektroden}
]{ref}
\Subsubsection{ref}
\desc{Reference electrodes}{}{}
\desc[german]{Referenzelektroden}{}{}
\begin{ttext}
\eng{Defined as reference for measuring half-cell potententials}
\ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
@ -522,10 +516,9 @@
\Subsubsection[
\eng{Cyclic voltammetry}
\ger{Zyklische Voltammetrie}
]{cv}
\Subsubsection{cv}
\desc{Cyclic voltammetry}{}{}
\desc[german]{Zyklische Voltammetrie}{}{}
\begin{bigformula}{duck}
\desc{Cyclic voltammogram}{}{}
% \desc[german]{}{}{}
@ -647,10 +640,9 @@
\eq{j_\infty = nFD \frac{c^0}{\delta_\text{diff}} = \frac{1}{1.61} nFD^{\frac{2}{3}} v^{\frac{-1}{6}} c^0 \sqrt{\omega}}
\end{formula}
\Subsubsection[
\eng{AC-Impedance}
\ger{AC-Impedanz}
]{ac}
\Subsubsection{ac}
\desc{AC-Impedance}{}{}
\desc[german]{AC-Impedanz}{}{}
\begin{formula}{nyquist}
\desc{Nyquist diagram}{Real and imaginary parts of \qtyRef{impedance} while varying the frequency}{}
\desc[german]{Nyquist-Diagram}{Real und Imaginaärteil der \qtyRef{impedance} während die Frequenz variiert wird}{}

15
src/ch/misc.tex
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@ -1,7 +1,7 @@
\Section[
\eng{Thermoelectricity}
\ger{Thermoelektrizität}
]{thermo}
\Section{thermo}
\desc{Thermoelectricity}{}{}
\desc[german]{Thermoelektrizität}{}{}
\begin{formula}{seebeck}
\desc{Seebeck coefficient}{Thermopower}{$V$ voltage, \QtyRef{temperature}}
\desc[german]{Seebeck-Koeffizient}{}{}
@ -35,10 +35,9 @@
\end{formula}
\Section[
\eng{misc}
\ger{misc}
]{misc}
\Section{misc}
\desc{misc}{}{}
\desc[german]{misc}{}{}
% TODO: hide
\begin{formula}{stoichiometric_coefficient}

129
src/cm/charge_transport.tex
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@ -1,11 +1,10 @@
\Section[
\eng{Charge transport}
\ger{Ladungstransport}
]{charge_transport}
\Subsection[
\eng{Drude model}
\ger{Drude-Modell}
]{drude}
\Section{charge_transport}
\desc{Charge transport}{}{}
\desc[german]{Ladungstransport}{}{}
\Subsection{drude}
\desc{Drude model}{}{}
\desc[german]{Drude-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -48,10 +47,9 @@
\eq{\sigma = \frac{\vec{j}}{\vec{\E}} = \frac{n e^2 \tau}{\masse} = n e \mu}
\end{formula}
\Subsection[
\eng{Sommerfeld model}
\ger{Sommerfeld-Modell}
]{sommerfeld}
\Subsection{sommerfeld}
\desc{Sommerfeld model}{}{}
\desc[german]{Sommerfeld-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -66,10 +64,9 @@
\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}
\Subsection[
\eng{Boltzmann-transport}
\ger{Boltzmann-Transport}
]{boltzmann}
\Subsection{boltzmann}
\desc{Boltzmann-transport}{}{}
\desc[german]{Boltzmann-Transport}{}{}
\begin{ttext}
\eng{Semiclassical description using a probability distribution (\fRef{cm:sc:fermi_dirac}) to describe the particles.}
\ger{Semiklassische Beschreibung, benutzt eine Wahrscheinlichkeitsverteilung (\fRef{cm:sc:fermi_dirac}).}
@ -82,10 +79,9 @@
}
\end{formula}
\Subsection[
\eng{Magneto-transport}
\ger{Magnetotransport}
]{mag}
\Subsection{mag}
\desc{Magneto-transport}{}{}
\desc[german]{Magnetotransport}{}{}
\begin{formula}{cyclotron_frequency}
\desc{Cyclotron frequency}{Moving charge carriers move in cyclic orbits under applied magnetic field}{$q$ \qtyRef{charge}, \QtyRef{magnetic_flux_density}, m \qtyRef[effective]{mass}}
\desc[german]{Zyklotronfrequenz}{Ladungstraäger bewegen sich in einem Magnetfeld auf einer Kreisbahn}{}
@ -98,13 +94,96 @@
% \desc[german]{}{}{}
% \eq{}
% \end{formula}
\TODO{move hall here}
\Subsubsection{hall}
\desc{Hall-Effect}{}{}
\desc[german]{Hall-Effekt}{}{}
\Paragraph{classic}
\desc{Classical Hall-Effect}{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.}{}
\desc[german]{Klassischer Hall-Effekt}{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.}{}
\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}
\Paragraph{quantum}
\desc{Quantum hall effects}{}{}
\desc[german]{Quantenhalleffekte}{}{}
\begin{formula}{types}
\desc{Types of quantum hall effects}{}{}
\desc[german]{Arten von Quantenhalleffekten}{}{}
\ttxt{\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{formula}
\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}
\Subsection[
\eng{misc}
\ger{misc}
]{misc}
\Subsection{misc}
\desc{misc}{}{}
\desc[german]{misc}{}{}
\begin{formula}{tsu_esaki}
\desc{Tsu-Esaki tunneling current}{Describes the current $I_{\txL \leftrightarrow \txR}$ through a barrier}{$\mu_i$ \qtyRef{chemical_potential} at left/right side, $U_i$ voltage on left/right side. Electrons occupy region between $U_i$ and $\mu_i$}
\desc[german]{Tsu-Esaki Tunnelstrom}{Beschreibt den Strom $I_{\txL \leftrightarrow \txR}$ durch eine Barriere }{$\mu_i$ \qtyRef{chemical_potential} links/rechts, $U_i$ Spannung links/rechts. Elektronen besetzen Bereich zwischen $U_i$ und $\mu_i$}

19
src/cm/cm.tex
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@ -1,8 +1,8 @@
\Part[
\eng{Condensed matter physics}
\ger{Festkörperphysik}
]{cm}
\TODO{van hove singularities, debye frequency}
\Part{cm}
\desc{Condensed matter physics}{}{}
\desc[german]{Festkörperphysik}{}{}
\TODO{van hove singularities}
\begin{formula}{dos}
\desc{Density of states (DOS)}{}{\QtyRef{volume}, $N$ number of energy levels, \QtyRef{energy}}
@ -11,12 +11,9 @@
\eq{D(E) = \frac{1}{V}\sum_{i=1}^{N} \delta(E-E(\vec{k_i}))}
\end{formula}
\Section[
\eng{Bonds}
\ger{Bindungen}
]{bond}
\Section{bond}
\desc{Bonds}{}{}
\desc[german]{Bindungen}{}{}
\begin{formula}{metallic}
\desc{Metallic bond}{}{}
\desc[german]{Metallbindung}{}{}

42
src/cm/crystal.tex
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@ -1,11 +1,11 @@
\Section[
\eng{Crystals}
\ger{Kristalle}
]{crystal}
\Subsection[
\eng{Bravais lattice}
\ger{Bravais-Gitter}
]{bravais}
\Section{crystal}
\desc{Crystals}{}{}
\desc[german]{Kristalle}{}{}
\Subsection{bravais}
\desc{Bravais lattice}{}{}
\desc[german]{Bravais-Gitter}{}{}
\Eng[lattice_system]{Lattice system}
\Ger[lattice_system]{Gittersystem}
\Eng[crystal_family]{Crystal system}
@ -197,14 +197,9 @@
\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}
\Subsection{reci}
\desc{Reciprocal lattice}{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}{}
\desc[german]{Reziprokes Gitter}{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}{}
\begin{formula}{vectors}
\desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
@ -222,10 +217,9 @@
\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}
\Subsection{scatter}
\desc{Scattering processes}{}{}
\desc[german]{Streuprozesse}{}{}
\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}{}
@ -235,10 +229,10 @@
}
\end{formula}
\Subsection[
\eng{Lattices}
\ger{Gitter}
]{lat}
\Subsection{lat}
\desc{Lattices}{}{}
\desc[german]{Gitter}{}{}
\begin{formula}{sc}
\desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}}
\desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{}

36
src/cm/egas.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Free electron gas}
\ger{Freies Elektronengase}
]{egas}
\Section{egas}
\desc{Free electron gas}{}{}
\desc[german]{Freies Elektronengase}{}{}
\begin{formula}{desc}
\desc{Description}{\GT{see_also}: \fRef{td:id_qgas}}{}
\desc[german]{Beschreibung}{}{}
@ -31,20 +31,18 @@
\eq{\mu = \frac{q \tau}{m}}
\end{formula}
\Subsection[
\eng{3D electron gas}
\ger{3D Elektronengas}
]{3deg}
\Subsection{3deg}
\desc{3D electron gas}{}{}
\desc[german]{3D Elektronengas}{}{}
\begin{formula}{dos}
\desc{Density of states}{}{}
\desc[german]{Zustandsdichte}{}{}
\eq{D_\text{3D}(E) = \frac{1}{2\pi^2} \left(\frac{2m}{\hbar^2}\right)^{3/2} \sqrt{E}}
\end{formula}
\Subsection[
\eng{2D electron gas}
\ger{2D Elektronengas}
]{2deg}
\Subsection{2deg}
\desc{2D electron gas}{}{}
\desc[german]{2D Elektronengas}{}{}
\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{
@ -71,10 +69,9 @@
\eq{D_\text{2D}(E) = \frac{m}{\pi\hbar^2}}
\end{formula}
\Subsection[
\eng{1D electron gas / quantum wire}
\ger{1D Eleltronengas / Quantendraht}
]{1deg}
\Subsection{1deg}
\desc{1D electron gas / quantum wire}{}{}
\desc[german]{1D Eleltronengas / Quantendraht}{}{}
\begin{formula}{energy}
\desc{Energy}{}{}
@ -90,10 +87,9 @@
\TODO{condunctance}
\Subsection[
\eng{0D electron gas / quantum dot}
\ger{0D Elektronengase / Quantenpunkt}
]{0deg}
\Subsection{0deg}
\desc{0D electron gas / quantum dot}{}{}
\desc[german]{0D Elektronengase / Quantenpunkt}{}{}
\begin{formula}{dos}
\desc{Density of states}{}{}
\desc[german]{Zustandsdichte}{}{}

8
src/cm/mat.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Material physics}
\ger{Materialphysik}
]{mat}
\Section{mat}
\desc{Material physics}{}{}
\desc[german]{Materialphysik}{}{}
\begin{formula}{tortuosity}
\desc{Tortuosity}{Degree of the winding of a transport path through a porous material. \\ Multiple definitions exist}{$l$ path length, $L$ distance of the end points}

34
src/cm/misc.tex
View File

@ -1,15 +1,10 @@
\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}
\Section{band}
\desc{Band theory}{}{}
\desc[german]{Bändermodell}{}{}
\Subsection{hybrid_orbitals}
\desc{Hybrid orbitals}{Hybrid orbitals are linear combinations of other atomic orbitals.}{}
\desc[german]{Hybridorbitale}{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.}{}
% chemmacros package
\begin{formula}{sp}
@ -51,10 +46,9 @@
\Section[
\eng{Diffusion}
\ger{Diffusion}
]{diffusion}
\Section{diffusion}
\desc{Diffusion}{}{}
\desc[german]{Diffusion}{}{}
\begin{formula}{diffusion_coefficient}
\desc{Diffusion coefficient}{}{}
\desc[german]{Diffusionskoeffizient}{}{}
@ -91,10 +85,10 @@
\eq{\pdv{c}{t} = D \pdv[2]{c}{x}}
\end{formula}
\Section[
\eng{\GT{misc}}
\ger{\GT{misc}}
]{misc}
\Section{misc}
% \desc{\GT{misc}}{}{}
% \desc[german]{\GT{misc}}{}{}
\begin{formula}{vdw_material}
\desc{Van-der-Waals material}{2D materials}{}

56
src/cm/semiconductors.tex
View File

@ -1,8 +1,7 @@
\def\meff{m^{*}}
\Section[
\eng{Semiconductors}
\ger{Halbleiter}
]{sc}
\Section{sc}
\desc{Semiconductors}{}{}
\desc[german]{Halbleiter}{}{}
\begin{formula}{description}
\desc{Description}{}{$n,p$ \fRef{cm:sc:charge_carrier_density:equilibrium}}
\desc[german]{Beschreibung}{}{}
@ -137,10 +136,9 @@
\end{formula}
\TODO{effective mass approx}
\Subsection[
\eng{Doping}
\ger{Dotierung}
]{dope}
\Subsection{dope}
\desc{Doping}{}{}
\desc[german]{Dotierung}{}{}
\begin{formula}{description}
\desc{Description}{}{}
@ -183,14 +181,12 @@
\TODO{plot}
\end{formula}
\Subsection[
\eng{Defects}
\ger{Defekte}
]{defect}
\Subsubsection[
\eng{Point defects}
\ger{Punktdefekte}
]{point}
\Subsection{defect}
\desc{Defects}{}{}
\desc[german]{Defekte}{}{}
\Subsubsection{point}
\desc{Point defects}{}{}
\desc[german]{Punktdefekte}{}{}
\begin{formula}{vacancy}
\desc{Vacancy}{}{}
\desc[german]{Fehlstelle}{}{}
@ -245,10 +241,9 @@
}}
\end{formula}
\Subsubsection[
\eng{Line defects}
\ger{Liniendefekte}
]{line}
\Subsubsection{line}
\desc{Line defects}{}{}
\desc[german]{Liniendefekte}{}{}
\begin{formula}{edge}
\desc{Edge distortion}{}{}
\desc[german]{Stufenversetzung}{}{}
@ -279,10 +274,9 @@
}
\end{formula}
\Subsubsection[
\eng{Area defects}
\ger{Flächendefekte}
]{area}
\Subsubsection{area}
\desc{Area defects}{}{}
\desc[german]{Flächendefekte}{}{}
\begin{formula}{grain_boundary}
\desc{Grain boundary}{}{}
\desc[german]{Korngrenze}{}{}
@ -303,10 +297,9 @@
}}
\end{formula}
\Subsection[
\eng{Devices and junctions}
\ger{Bauelemente und Kontakte}
]{junctions}
\Subsection{junctions}
\desc{Devices and junctions}{}{}
\desc[german]{Bauelemente und Kontakte}{}{}
\begin{formula}{metal-sc}
\desc{Metal-semiconductor junction}{}{}
\desc[german]{Metall-Halbleiter Kontakt}{}{}
@ -350,10 +343,9 @@
\Subsection[
\eng{Excitons}
\ger{Exzitons}
]{exciton}
\Subsection{exciton}
\desc{Excitons}{}{}
\desc[german]{Exzitons}{}{}
\begin{formula}{desc}
\desc{Exciton}{}{}
\desc[german]{Exziton}{}{}

72
src/cm/superconductivity.tex
View File

@ -4,21 +4,15 @@
\def\Tcrit{T_\text{c}}
\def\Bcth{B_\text{c,th}}
\Section[
\eng{Superconductivity}
\ger{Supraleitung}
]{super}
\begin{ttext}
\eng{
\Section{super}
\desc{Superconductivity}{
Materials for which the electric resistance jumps to 0 under a critical temperature $\Tcrit$.
Below $\Tcrit$ they have perfect conductivity and perfect diamagnetism, up until a critical magnetic field $\Bcth$.
}
\ger{
}{}
\desc[german]{Supraleitung}{
Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur $\Tcrit$ auf 0 springt.
Sie verhalten sich dann wie ideale Leiter und ideale Diamagnete, bis zu einem kritischen Feld $\Bcth$.
}
\end{ttext}
}{}
\begin{formula}{type1}
\desc{Type-I superconductor}{}{}
@ -92,10 +86,9 @@
}
\end{formula}
\Subsection[
\eng{London Theory}
\ger{London-Theorie}
]{london}
\Subsection{london}
\desc{London Theory}{}{}
\desc[german]{London-Theorie}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -148,10 +141,9 @@
\eq{\lambda_\txL(T) = \lambda_\txL(0) \frac{1}{\sqrt{1- \left(\frac{T}{T_\txc}\right)^4}}}
\end{formula}
\Subsubsection[
\eng{Macroscopic wavefunction}
\ger{Makroskopische Wellenfunktion}
]{macro}
\Subsubsection{macro}
\desc{Macroscopic wavefunction}{}{}
\desc[german]{Makroskopische Wellenfunktion}{}{}
\begin{formula}{ansatz}
\desc{Ansatz}{}{}
\desc[german]{Ansatz}{}{}
@ -170,10 +162,9 @@
\end{formula}
\Subsubsection[
\eng{Josephson Effect}
\ger{Josephson Effekt}
]{josephson}
\Subsubsection{josephson}
\desc{Josephson Effect}{}{}
\desc[german]{Josephson Effekt}{}{}
\begin{formula}{1st_relation}
\desc{1. Josephson relation}{Dissipationless supercurrent accros junction at zero applied voltage}{$\vecj_\text{C}=\frac{2e}{\hbar}E_\text{J}$ critical current, $\phi$ phase difference accross junction}
\desc[german]{1. Josephson Gleichung}{Dissipationsloser Suprastrom durch die Kreuzung ohne angelegte Spannung}{$\vecj_\text{C}=\frac{2e}{\hbar}E_\text{J}$ kritischer Strom, $\phi$ Phasendifferenz zwischen den Supraleitern}
@ -195,10 +186,9 @@
\Subsection[
\eng{\GL Theory (GLAG)}
\ger{\GL Theorie (GLAG)}
]{gl}
\Subsection{gl}
\desc{\GL Theory (GLAG)}{}{}
\desc[german]{\GL Theorie (GLAG)}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -326,10 +316,9 @@
}}
\end{formula}
\Subsection[
\eng{Microscopic theory}
\ger{Mikroskopische Theorie}
]{micro}
\Subsection{micro}
\desc{Microscopic theory}{}{}
\desc[german]{Mikroskopische Theorie}{}{}
\begin{formula}{isotop_effect}
\desc{Isotope effect}{Superconducting behaviour depends on atomic mass and thereby on the lattice \Rightarrow Microscopic origin}{$\Tcrit$ critial temperature, $M$ isotope mass, $\omega_\text{ph}$}
\desc[german]{Isotopeneffekt}{Supraleitung hängt von der Atommasse und daher von den Gittereigenschaften ab \Rightarrow Mikroskopischer Ursprung}{$\Tcrit$ kritische Temperatur, $M$ Isotopen-Masse, $\omega_\text{ph}$}
@ -347,10 +336,9 @@
}
\end{formula}
\Subsubsection[
\eng{BCS-Theory}
\ger{BCS-Theorie}
]{bcs}
\Subsubsection{bcs}
\desc{BCS-Theory}{}{}
\desc[german]{BCS-Theorie}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -429,10 +417,9 @@
\eq{E \approx 2E_\txF - 2\hbar\omega_\txD \Exp{-\frac{4}{V_0 D(E_\txF)}}}
\end{formula}
\Subsubsection[
\eng{Excitations and finite temperatures}
\ger{Anregungen und endliche Temperatur}
]{excite}
\Subsubsection{excite}
\desc{Excitations and finite temperatures}{}{}
\desc[german]{Anregungen und endliche Temperatur}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -522,10 +509,9 @@
}
\end{formula}
\Subsubsection[
\eng{Flux pinning}
\ger{Haftung von Flusslinien}
]{pinning}
\Subsubsection{pinning}
\desc{Flux pinning}{}{}
\desc[german]{Haftung von Flusslinien}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}

50
src/cm/techniques.tex
View File

@ -1,22 +1,20 @@
\Section[
\eng{Techniques}
\ger{Techniken}
]{tech}
\Section{tech}
\desc{Techniques}{}{}
\desc[german]{Techniken}{}{}
\Subsection[
\eng{Measurement techniques}
\ger{Messtechniken}
]{meas}
\Subsection{meas}
\desc{Measurement techniques}{}{}
\desc[german]{Messtechniken}{}{}
\Eng[name]{Name}
\Ger[name]{Name}
\Eng[application]{Application}
\Ger[application]{Anwendung}
\Subsubsection[
\eng{Raman spectroscopy}
\ger{Raman Spektroskopie}
]{raman}
\Subsubsection{raman}
\desc{Raman spectroscopy}{}{}
\desc[german]{Raman Spektroskopie}{}{}
% TODO remove fqname from minipagetable?
@ -66,19 +64,17 @@
\end{bigformula}
\Subsubsection[
\eng{ARPES}
\ger{ARPES}
]{arpes}
\Subsubsection{arpes}
\desc{ARPES}{}{}
\desc[german]{ARPES}{}{}
what?
in?
how?
plot
\Subsubsection[
\eng{Scanning probe microscopy SPM}
\ger{Rastersondenmikroskopie (SPM)}
]{spm}
\Subsubsection{spm}
\desc{Scanning probe microscopy SPM}{}{}
\desc[german]{Rastersondenmikroskopie (SPM)}{}{}
\begin{ttext}
\eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
\ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
@ -132,10 +128,9 @@
\end{minipage}
\end{bigformula}
\Subsection[
\eng{Fabrication techniques}
\ger{Herstellungsmethoden}
]{fab}
\Subsection{fab}
\desc{Fabrication techniques}{}{}
\desc[german]{Herstellungsmethoden}{}{}
\begin{bigformula}{cvd}
\desc{Chemical vapor deposition (CVD)}{}{}
@ -177,10 +172,9 @@
\end{bigformula}
\Subsubsection[
\eng{Epitaxy}
\ger{Epitaxie}
]{epitaxy}
\Subsubsection{epitaxy}
\desc{Epitaxy}{}{}
\desc[german]{Epitaxie}{}{}
\begin{ttext}
\eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
\ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}

22
src/cm/topo.tex
View File

@ -1,26 +1,20 @@
\Section[
\eng{Topological Materials}
\ger{Topologische Materialien}
]{topo}
\Subsection[
\eng{Berry phase / Geometric phase}
\ger{Berry-Phase / Geometrische Phase}
]{berry_phase}
\Section{topo}
\desc{Topological Materials}{}{}
\desc[german]{Topologische Materialien}{}{}
\begin{ttext}[desc]
\eng{
\Subsection{berry_phase}
\desc{Berry phase / Geometric phase}{
While adiabatically traversing a closed through the parameter space $R(t)$, the wave function of a systems
may pick up an additional phase $\gamma$.\\
If $\vec{R}(t)$ varies adiabatically (slowly) and the system is initially in eigenstate $\ket{n}$,
it will stay in an Eigenstate throughout the process (quantum adiabtic theorem).
}
\ger{
}{}
\desc[german]{Berry-Phase / Geometrische Phase}{
Beim adiabatischem Durchlauf eines geschlossenen Weges durch den Parameterraum $R(t)$ kann die Wellenfunktion eines Systems
eine zusätzliche Phase $\gamma$ erhalten.\\
Wenn $\vec{R}(t)$ adiabatisch (langsam) variiert und das System anfangs im Eigenzustand $\ket{n}$ ist,
bleibt das System während dem Prozess in einem Eigenzustand (Adiabatisches Theorem der Quantenmechanik).
}
\end{ttext}
}{}
\Eng[dynamic_phase]{Dynamical Phase}
\Eng[berry_phase]{Berry Phase}
\Ger[dynamic_phase]{Dynamische Phase}

27
src/cm/vib.tex
View File

@ -1,7 +1,12 @@
\Section[
\eng{Lattice vibrations}
\ger{Gitterschwingungen}
]{vib}
\Section{vib}
\desc{Lattice vibrations}{}{}
\desc[german]{Gitterschwingungen}{}{}
\begin{formula}{speed_of_sound}
\desc{Speed of sound}{Speed with which vibrations propagate through an elastic medium}{}
\desc[german]{Schallgeschwindigkeit}{Geschwindigkeit, mit der sich Vibrationen in einem elastischem Medium ausbreiten}{}
\quantity{v}{\m\per\s}{s}
\end{formula}
\begin{formula}{dispersion_1atom_basis}
\desc{Phonon dispersion of a lattice with a one-atom basis}{same as the dispersion of a linear chain}{$C_n$ force constants between layer $s$ and $s+n$, $M$ \qtyRef{mass} of the reference atom, $a$ \qtyRef{lattice_constant}, $q$ phonon \qtyRef{wavevector}, $u$ Ansatz for the atom displacement}
@ -46,10 +51,9 @@
\eq{C_\txm = 3\NA \kB = 3R \approx \SI{25}{\joule\per\mol\kelvin}}
\end{formula}
\Subsection[
\eng{Einstein model}
\ger{Einstein-Modell}
]{einstein}
\Subsection{einstein}
\desc{Einstein model}{}{}
\desc[german]{Einstein-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -72,10 +76,9 @@
\eq{C_V^\txE = 3N\kB \left( \frac{\hbar\omega_\txE}{\kB T}\right)^2 \frac{\e^{\frac{\hbar\omega_\txE}{\kB T}}}{ \left(\e^{\frac{\hbar\omega_\txE}{\kB T}} - 1\right)^2}}
\end{formula}
\Subsection[
\eng{Debye model}
\ger{Debye-Modell}
]{debye}
\Subsection{debye}
\desc{Debye model}{}{}
\desc[german]{Debye-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}

88
src/comp/ad.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Atomic dynamics}
% \ger{}
]{ad}
\Section{ad}
\desc{Atomic dynamics}{}{}
% \desc[german]{}{}{}
\begin{formula}{hamiltonian}
\desc{Electron Hamiltonian}{}{$\hat{T}$ \fRef{comp:est:kinetic_energy}, $\hat{V}$ \fRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
\desc[german]{Hamiltonian der Elektronen}{}{}
@ -29,10 +29,9 @@
\end{multline}
\end{formula}
\Subsection[
\eng{Born-Oppenheimer Approximation}
\ger{Born-Oppenheimer Näherung}
]{bo}
\Subsection{bo}
\desc{Born-Oppenheimer Approximation}{}{}
\desc[german]{Born-Oppenheimer Näherung}{}{}
\begin{formula}{adiabatic_approx}
\desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move (\absRef{adiabatic_theorem})}{$\Lambda_{ij}$ \fRef{comp:ad:coupling_operator}}
\desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{}
@ -81,10 +80,9 @@
}
\end{formula}
\Subsection[
\eng{Structure optimization}
\ger{Strukturoptimierung}
]{opt}
\Subsection{opt}
\desc{Structure optimization}{}{}
\desc[german]{Strukturoptimierung}{}{}
\begin{formula}{forces}
\desc{Forces}{}{}
\desc[german]{Kräfte}{}{}
@ -139,10 +137,9 @@
}}
\end{formula}
\Subsection[
\eng{Lattice vibrations}
\ger{Gitterschwingungen}
]{latvib}
\Subsection{latvib}
\desc{Lattice vibrations}{}{}
\desc[german]{Gitterschwingungen}{}{}
\begin{formula}{force_constant_matrix}
\desc{Force constant matrix}{}{}
% \desc[german]{}{}{}
@ -159,10 +156,9 @@
% -> DFPT
% finite-difference method
\Subsubsection[
\eng{Finite difference method}
% \ger{}
]{fin_diff}
\Subsubsection{fin_diff}
\desc{Finite difference method}{}{}
% \desc[german]{}{}{}
\begin{formula}{approx}
\desc{Approximation}{Assume forces in equilibrium structure vanish}{$\Delta s$ displacement of atom $J$}
@ -181,10 +177,9 @@
\eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) }
\end{formula}
\Subsubsection[
\eng{Anharmonic approaches}
\ger{Anharmonische Ansätze}
]{anharmonic}
\Subsubsection{anharmonic}
\desc{Anharmonic approaches}{}{}
\desc[german]{Anharmonische Ansätze}{}{}
\begin{formula}{qha}
\desc{Quasi-harmonic approximation}{}{}
@ -205,10 +200,9 @@
\Subsection[
\eng{Molecular Dynamics}
\ger{Molekulardynamik}
]{md} \abbrLink{md}{MD}
\Subsection{md}
\desc{Molecular Dynamics}{}{}
\desc[german]{Molekulardynamik}{}{} \abbrLink{md}{MD}
\begin{formula}{desc}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -236,10 +230,9 @@
}}
\end{formula}
\Subsubsection[
\eng{Ab-initio molecular dynamics}
\ger{Ab-initio molecular dynamics}
]{ab-initio}
\Subsubsection{ab-initio}
\desc{Ab-initio molecular dynamics}{}{}
\desc[german]{Ab-initio molecular dynamics}{}{}
\begin{formula}{bomd}
\abbrLabel{BOMD}
\desc{Born-Oppenheimer MD (BOMD)}{}{}
@ -271,10 +264,9 @@
\end{gather}
\end{formula}
\Subsubsection[
\eng{Force-field MD}
\ger{Force-field MD}
]{ff}
\Subsubsection{ff}
\desc{Force-field MD}{}{}
\desc[german]{Force-field MD}{}{}
\begin{formula}{ffmd}
\desc{Force field MD (FFMD)}{}{}
@ -291,13 +283,9 @@
\Subsubsection[
\eng{Integration schemes}
% \ger{}
]{scheme}
\begin{ttext}
\eng{Procedures for updating positions and velocities to obey the equations of motion.}
\end{ttext}
\Subsubsection{scheme}
\desc{Integration schemes}{Procedures for updating positions and velocities to obey the equations of motion.}{}
\desc[german]{Integrationsmethoden}{Prozeduren zum stückweisen numerischen Lösung der Bewegungsgleichungen}{}
\begin{formula}{euler}
\desc{Euler method}{First-order procedure for solving \abbrRef{ode}s with a given initial value.\\Taylor expansion of $\vecR/\vecv (t+\Delta t)$}{}
@ -337,10 +325,9 @@
}
\end{formula}
\Subsubsection[
\eng{Thermostats and barostats}
\ger{Thermostate und Barostate}
]{stats}
\Subsubsection{stats}
\desc{Thermostats and barostats}{}{}
\desc[german]{Thermostate und Barostate}{}{}
\begin{formula}{velocity_rescaling}
\desc{Velocity rescaling}{Thermostat, keep temperature at $T_0$ by rescaling velocities. Does not allow temperature fluctuations and thus does not obey the \absRef{c_ensemble}}{$T$ target \qtyRef{temperature}, $M$ \qtyRef{mass} of nucleon $I$, $\vecv$ \qtyRef{velocity}, $f$ number of degrees of freedom, $\lambda$ velocity scaling parameter, \ConstRef{boltzmann}}
% \desc[german]{}{}{}
@ -367,10 +354,9 @@
\end{gather}
\end{formula}
\Subsubsection[
\eng{Calculating observables}
\ger{Berechnung von Observablen}
]{obs}
\Subsubsection{obs}
\desc{Calculating observables}{}{}
\desc[german]{Berechnung von Observablen}{}{}
\begin{formula}{spectral_density}
\desc{Spectral density}{Wiener-Khinchin theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{$C$ \absRef{autocorrelation}}
\desc[german]{Spektraldichte}{Wiener-Khinchin Theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{}

8
src/comp/comp.tex
View File

@ -1,4 +1,4 @@
\Part[
\eng{Computational Physics}
\ger{Computergestützte Physik}
]{comp}
\Part{comp}
\desc{Computational Physics}{}{}
\desc[german]{Computergestützte Physik}{}{}

64
src/comp/est.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Electronic structure theory}
% \ger{}
]{est}
\Section{est}
\desc{Electronic structure theory}{}{}
% \desc[german]{}{}{}
\begin{formula}{kinetic_energy}
\desc{Kinetic energy}{of species $i$}{$i$ = nucleons/electrons, $N$ number of particles, $m$ \qtyRef{mass}}
@ -26,10 +26,9 @@
\end{formula}
\Subsection[
\eng{Tight-binding}
\ger{Modell der stark gebundenen Elektronen / Tight-binding}
]{tb}
\Subsection{tb}
\desc{Tight-binding}{}{}
\desc[german]{Modell der stark gebundenen Elektronen / Tight-binding}{}{}
\begin{formula}{assumptions}
\desc{Assumptions}{}{}
\desc[german]{Annahmen}{}{}
@ -49,15 +48,13 @@
\Subsection[
\eng{Density functional theory (DFT)}
\ger{Dichtefunktionaltheorie (DFT)}
]{dft}
\Subsection{dft}
\desc{Density functional theory (DFT)}{}{}
\desc[german]{Dichtefunktionaltheorie (DFT)}{}{}
\abbrLink{dft}{DFT}
\Subsubsection[
\eng{Hartree-Fock}
\ger{Hartree-Fock}
]{hf}
\Subsubsection{hf}
\desc{Hartree-Fock}{}{}
\desc[german]{Hartree-Fock}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@ -117,10 +114,9 @@
}
\end{formula}
\Subsubsection[
\eng{Hohenberg-Kohn Theorems}
\ger{Hohenberg-Kohn Theoreme}
]{hk}
\Subsubsection{hk}
\desc{Hohenberg-Kohn Theorems}{}{}
\desc[german]{Hohenberg-Kohn Theoreme}{}{}
\begin{formula}{hk1}
\desc{Hohenberg-Kohn theorem (HK1)}{}{}
\desc[german]{Hohenberg-Kohn Theorem (HK1)}{}{}
@ -144,10 +140,9 @@
\eq{n(\vecr) = \Braket{\psi_0|\sum_{i=1}^N \delta(\vecr-\vecr_i)|\psi_0}}
\end{formula}
\Subsubsection[
\eng{Kohn-Sham DFT}
\ger{Kohn-Sham DFT}
]{ks}
\Subsubsection{ks}
\desc{Kohn-Sham DFT}{}{}
\desc[german]{Kohn-Sham DFT}{}{}
\abbrLink{ksdft}{KS-DFT}
\begin{formula}{map}
\desc{Kohn-Sham map}{}{}
@ -194,10 +189,9 @@
}
\end{formula}
\Subsubsection[
\eng{Exchange-Correlation functionals}
\ger{Exchange-Correlation Funktionale}
]{xc}
\Subsubsection{xc}
\desc{Exchange-Correlation functionals}{}{}
\desc[german]{Exchange-Correlation Funktionale}{}{}
\begin{formula}{xc}
\desc{Exchange-Correlation functional}{}{}
\desc[german]{Exchange-Correlation Funktional}{}{}
@ -250,10 +244,9 @@
\end{formula}
\Subsubsection[
\eng{Basis sets}
\ger{Basis-Sets}
]{basis}
\Subsubsection{basis}
\desc{Basis sets}{}{}
\desc[german]{Basis-Sets}{}{}
\begin{formula}{plane_wave}
\desc{Plane wave basis}{Plane wave ansatz in \fRef{comp:est:dft:ks:equation}\\Good for periodic structures, allows computation parallelization over a sample points in the \abbrRef{brillouin_zone}}{}
\desc[german]{Ebene Wellen als Basis}{}{}
@ -265,10 +258,9 @@
\eq{E_\text{cutoff} = \frac{\hbar^2 \abs{\veck+\vecG}^2}{2m}}
\end{formula}
\Subsubsection[
\eng{Pseudo-Potential method}
\ger{Pseudopotentialmethode}
]{pseudo}
\Subsubsection{pseudo}
\desc{Pseudo-Potential method}{}{}
\desc[german]{Pseudopotentialmethode}{}{}
\begin{formula}{ansatz}
\desc{Ansatz}{}{}
\desc[german]{Ansatz}{}{}

56
src/comp/ml.tex
View File

@ -1,11 +1,11 @@
\Section[
\eng{Machine-Learning}
\ger{Maschinelles Lernen}
]{ml}
\Subsection[
\eng{Performance metrics}
\ger{Metriken zur Leistungsmessung}
]{performance}
\Section{ml}
\desc{Machine-Learning}{}{}
\desc[german]{Maschinelles Lernen}{}{}
\Subsection{performance}
\desc{Performance metrics}{}{}
\desc[german]{Metriken zur Leistungsmessung}{}{}
\eng[cp]{correct predictions}
\ger[cp]{richtige Vorhersagen}
\eng[fp]{false predictions}
@ -16,13 +16,14 @@
\ger[y]{Wahrheit}
\ger[yhat]{Vorhersage}
\eng[n_desc]{Number of data points}
\ger[n_desc]{Anzahl der Datenpunkte}
\begin{formula}{accuracy}
\desc{Accuracy}{}{}
\desc[german]{Genauigkeit}{}{}
\eq{a = \frac{\tGT{::cp}}{\tGT{::fp} + \tGT{::cp}}}
\end{formula}
\eng{n_desc}{Number of data points}
\ger{n_desc}{Anzahl der Datenpunkte}
\begin{formula}{mean_abs_error}
\desc{Mean absolute error (MAE)}{}{$y$ \GT{::y}, $\hat{y}$ \GT{::yhat}, $n$ \GT{::n_desc}}
\desc[german]{Mittlerer absoluter Fehler (MAE)}{}{}
@ -39,14 +40,12 @@
\eq{\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \left(y_i - \hat{y}_i\right)^2}}
\end{formula}
\Subsection[
\eng{Regression}
\ger{Regression}
]{reg}
\Subsubsection[
\eng{Linear Regression}
\ger{Lineare Regression}
]{linear}
\Subsection{reg}
\desc{Regression}{}{}
\desc[german]{Regression}{}{}
\Subsubsection{linear}
\desc{Linear Regression}{}{}
\desc[german]{Lineare Regression}{}{}
\begin{formula}{eq}
\desc{Linear regression}{Fits the data under the assumption of \fRef[normally distributed errors]{math:pt:distributions:cont:normal}}{$\mat{x}\in\R^{N\times M}$ input data, $\mat{y}\in\R^{N\times L}$ output data, $\mat{b}$ bias, $\vec{\beta}$ weights, $N$ samples, $M$ features, $L$ output variables}
\desc[german]{Lineare Regression}{Fitted Daten unter der Annahme \fRef[normalverteilter Fehler]{math:pt:distributions:cont:normal}}{}
@ -70,10 +69,9 @@
\eq{\vec{\beta} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}}
\end{formula}
\Subsubsection[
\eng{Kernel method}
\ger{Kernelmethode}
]{kernel}
\Subsubsection{kernel}
\desc{Kernel method}{}{}
\desc[german]{Kernelmethode}{}{}
\begin{formula}{kernel_trick}
\desc{Kernel trick}{}{$\vecx_i \in \R^{M_1}$ input vectors, $M_1$ dimension of data vector space, $M_2$ dimension of feature space}
% \desc[german]{}{}{}
@ -103,10 +101,9 @@
\eq{k(\vecx_i, \vecx_j) = \Exp{-\frac{\norm{\vecx_i - \vecx_j}_2^2}{\sigma}}}
\end{formula}
\Subsubsection[
\eng{Bayesian regression}
\ger{Bayes'sche Regression}
]{bayes}
\Subsubsection{bayes}
\desc{Bayesian regression}{}{}
\desc[german]{Bayes'sche Regression}{}{}
\begin{formula}{linear_regression}
\desc{Bayesian linear regression}{}{}
@ -185,9 +182,8 @@
\eq{V_\text{BondOrder}(\vecR_M, \vecR_N) = V_\text{rep}(\vecR_M, \vecR_N) + b_{MNK} V_\text{attr}(\vecR_M, \vecR_N)}
\end{formula}
\Subsection[
\eng{Gradient descent}
\ger{Gradientenverfahren}
]{gd}
\Subsection{gd}
\desc{Gradient descent}{}{}
\desc[german]{Gradientenverfahren}{}{}
\TODO{in lecture 30 CMP}

43
src/comp/qmb.tex
View File

@ -1,11 +1,10 @@
\Section[
\eng{Quantum many-body physics}
\ger{Quanten-Vielteilchenphysik}
]{qmb}
\Subsection[
\eng{Quantum many-body models}
\ger{Quanten-Vielteilchenmodelle}
]{models}
\Section{qmb}
\desc{Quantum many-body physics}{}{}
\desc[german]{Quanten-Vielteilchenphysik}{}{}
\Subsection{models}
\desc{Quantum many-body models}{}{}
\desc[german]{Quanten-Vielteilchenmodelle}{}{}
\begin{formula}{heg}
\desc{Homogeneous electron gas (HEG)}{Also "Jellium"}{}
% \desc[german]{}{}{}
@ -14,26 +13,22 @@
}
\end{formula}
\Subsection[
\eng{Methods}
\ger{Methoden}
]{methods}
\Subsubsection[
\eng{Quantum Monte-Carlo}
\ger{Quantum Monte-Carlo}
]{qmonte-carlo}
\Subsection{methods}
\desc{Methods}{}{}
\desc[german]{Methoden}{}{}
\Subsubsection{qmonte-carlo}
\desc{Quantum Monte-Carlo}{}{}
\desc[german]{Quantum Monte-Carlo}{}{}
\TODO{TODO}
\Subsection[
\eng{Importance sampling}
\ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
]{importance_sampling}
\Subsection{importance_sampling}
\desc{Importance sampling}{}{}
\desc[german]{Importance sampling / Stichprobenentnahme nach Wichtigkeit}{}{}
\TODO{Monte Carlo}
\Subsection[
\eng{Matrix product states}
\ger{Matrix Produktzustände}
]{mps}
\Subsection{mps}
\desc{Matrix product states}{}{}
\desc[german]{Matrix Produktzustände}{}{}

8
src/constants.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Constants}
\ger{Konstanten}
]{constants}
\Section{constants}
\desc{Constants}{}{}
\desc[german]{Konstanten}{}{}
\begin{formula}{planck}
\desc{Planck Constant}{}{}
\desc[german]{Plancksches Wirkumsquantum}{}{}

8
src/ed/ed.tex
View File

@ -1,7 +1,7 @@
\Part[
\eng{Electrodynamics}
\ger{Elektrodynamik}
]{ed}
\Part{ed}
\desc{Electrodynamics}{}{}
\desc[german]{Elektrodynamik}{}{}
% pure electronic stuff in el
% pure magnetic stuff in mag

13
src/ed/el.tex
View File

@ -1,8 +1,7 @@
\Section[
\eng{Electric field}
\ger{Elektrisches Feld}
]{el}
\Section{el}
\desc{Electric field}{}{}
\desc[german]{Elektrisches Feld}{}{}
\begin{formula}{electric_field}
\desc{Electric field}{Surrounds charged particles}{}
\desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{}
@ -29,8 +28,8 @@
\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}{}{}
\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}
}
@ -62,7 +61,7 @@
\begin{formula}{electric_displacement_field}
\desc{Electric displacement field}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_field}, \QtyRef{dielectric_polarization_density}}
\desc[german]{Elektrische Flussdichte / dielektrische Verschiebung}{}{}
\desc[german]{Elektrische Flussdichte}{Dielektrische Verschiebung}{}
\quantity{\vec{D}}{\coulomb\per\m^2=\ampere\s\per\m^2}{v}
\eq{\vec{D} = \epsilon_0 \vec{\E} + \vec{P}}
\end{formula}

29
src/ed/em.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Electromagnetism}
\ger{Elektromagnetismus}
]{em}
\Section{em}
\desc{Electromagnetism}{}{}
\desc[german]{Elektromagnetismus}{}{}
\begin{formula}{vacuum_speed_of_light}
\desc{Speed of light}{in the vacuum}{}
\desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
@ -46,10 +46,9 @@
\end{formula}
\Subsection[
\eng{Maxwell-Equations}
\ger{Maxwell-Gleichungen}
]{maxwell}
\Subsection{maxwell}
\desc{Maxwell-Equations}{}{}
\desc[german]{Maxwell-Gleichungen}{}{}
\begin{formula}{vacuum}
\desc{Vacuum}{microscopic formulation}{}
\desc[german]{Vakuum}{Mikroskopische Formulierung}{}
@ -73,10 +72,9 @@
\end{formula}
\Subsubsection[
\eng{Gauges}
\ger{Eichungen}
]{gauge}
\Subsubsection{gauge}
\desc{Gauges}{}{}
\desc[german]{Eichungen}{}{}
\begin{formula}{coulomb}
\desc{Coulomb gauge}{}{\QtyRef{magnetic_vector_potential}}
\desc[german]{Coulomb-Eichung}{}{}
@ -88,10 +86,9 @@
\TODO{Polarization}
\Subsection[
\eng{Induction}
\ger{Induktion}
]{induction}
\Subsection{induction}
\desc{Induction}{}{}
\desc[german]{Induktion}{}{}
\begin{formula}{farady_law}
\desc{Faraday's law of induction}{}{}
\desc[german]{Faradaysche Induktionsgesetz}{}{}

15
src/ed/mag.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Magnetic field}
\ger{Magnetfeld}
]{mag}
\Section{mag}
\desc{Magnetic field}{}{}
\desc[german]{Magnetfeld}{}{}
\begin{formula}{magnetic_flux}
\desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
@ -98,10 +98,9 @@
\Subsection[
\eng{Magnetic materials}
\ger{Magnetische Materialien}
]{materials}
\Subsection{materials}
\desc{Magnetic materials}{}{}
\desc[german]{Magnetische Materialien}{}{}
\begin{formula}{paramagnetism}
\desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
\desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}

115
src/ed/misc.tex
View File

@ -1,108 +1,6 @@
% 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{Quantum hall effects}
\ger{Quantenhalleffekte}
]{quantum}
\begin{formula}{types}
\desc{Types of quantum hall effects}{}{}
\desc[german]{Arten von Quantenhalleffekten}{}{}
\ttxt{\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{formula}
\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}
\Section[
\eng{Dipole-stuff}
\ger{Dipol-zeug}
]{dipole}
\Section{dipole}
\desc{Dipoles}{}{}
\desc[german]{Dipole}{}{}
\begin{formula}{poynting}
\desc{Dipole radiation Poynting vector}{}{}
@ -116,10 +14,9 @@
\eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
\end{formula}
\Section[
\eng{misc}
\ger{misc}
]{misc}
\Section{misc}
\desc{misc}{}{}
\desc[german]{misc}{}{}
\begin{formula}{impedance_r}
\desc{Impedance of an ohmic resistor}{}{\QtyRef{resistance}}
\desc[german]{Impedanz eines Ohmschen Widerstands}{}{}

8
src/ed/optics.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Optics}
\ger{Optik}
]{optics}
\Section{optics}
\desc{Optics}{}{}
\desc[german]{Optik}{}{}
\begin{ttext}
\eng{Properties of light and its interactions with matter}
\ger{Ausbreitung von Licht und die Interaktion mit Materie}

16
src/main.tex
View File

@ -122,7 +122,7 @@
\input{util/translations.tex}
% \InputOnly{cm}
% \InputOnly{test}
\Input{math/math}
\Input{math/linalg}
@ -171,10 +171,9 @@
\Input{ch/misc}
\newpage
\Part[
\eng{Appendix}
\ger{Anhang}
]{appendix}
\Part{appendix}
\desc{Appendix}{}{}
\desc[german]{Anhang}{}{}
\begin{formula}{world}
\desc{World formula}{}{}
\desc[german]{Weltformel}{}{}
@ -186,10 +185,9 @@
% \listofquantities
\listoffigures
\listoftables
\Section[
\eng{List of elements}
\ger{Liste der Elemente}
]{elements}
\Section{elements}
\desc{List of elements}{}{}
\desc[german]{Liste der Elemente}{}{}
\printAllElements
\newpage
\Input{test}

104
src/math/calculus.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Calculus}
\ger{Analysis}
]{cal}
\Section{cal}
\desc{Calculus}{}{}
\desc[german]{Analysis}{}{}
% \begin{formula}{shark}
% \desc{Shark-midnight formula}{\emoji{shark}-s}{}
@ -12,14 +12,12 @@
% \end{formula}
\Subsection[
\eng{Fourier analysis}
\ger{Fourieranalyse}
]{fourier}
\Subsubsection[
\eng{Fourier series}
\ger{Fourierreihe}
]{series}
\Subsection{fourier}
\desc{Fourier analysis}{}{}
\desc[german]{Fourieranalyse}{}{}
\Subsubsection{series}
\desc{Fourier series}{}{}
\desc[german]{Fourierreihe}{}{}
\begin{formula}{series} \absLabel[fourier_series]
\desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
\desc[german]{Fourierreihe}{Komplexe Darstellung}{}
@ -53,35 +51,33 @@
\end{formula}
\Subsubsection[
\eng{Fourier transformation}
\ger{Fouriertransformation}
]{trafo}
\Subsubsection{trafo}
\desc{Fourier transformation}{}{}
\desc[german]{Fouriertransformation}{}{}
\begin{formula}{transform} \absLabel[fourier_transform]
\desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
\desc[german]{Fouriertransformierte}{}{}
\eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
\end{formula}
\Eng[linear_in]{linear in}
\Ger[linear_in]{linear in}
\GT{for} $f\in L^1(\R^n)$:
\begin{enumerate}[i)]
\item $f \mapsto \hat{f}$ \GT{linear_in} $f$
\item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
\item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
\item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
\end{enumerate}
\begin{formula}{properties}
\desc{Properties}{}{\GT{for} $f\in L^1(\R^n)$}
\desc[german]{Eigenschaften}{}{}
\Eng[linear_in]{linear in}
\Ger[linear_in]{linear in}
\begin{enumerate}[i)]
\item $f \mapsto \hat{f}$ \GT{linear_in} $f$
\item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
\item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
\item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
\end{enumerate}
\end{formula}
\Subsubsection[
\eng{Convolution}
\ger{Faltung / Konvolution}
]{conv}
\begin{ttext}
\eng{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}
\ger{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}
\end{ttext}
\Subsubsection{conv}
\desc{Convolution}{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}{}
\desc[german]{Faltung / Konvolution}{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}{}
\begin{formula}{def}
\desc{Definition}{}{}
\desc[german]{Definition}{}{}
@ -120,10 +116,9 @@
\end{formula}
\Subsection[
\eng{Misc}
\ger{Verschiedenes}
]{misc}
\Subsection{misc}
\desc{Misc}{}{}
\desc[german]{Verschiedenes}{}{}
\begin{formula}{stirling-approx}
\desc{Stirling approximation}{}{}
@ -154,10 +149,9 @@
\end{formula}
\Subsection[
\eng{Logarithm}
\ger{Logarithmus}
]{log}
\Subsection{log}
\desc{Logarithm}{}{}
\desc[german]{Logarithmus}{}{}
\begin{formula}{identities}
\desc{Logarithm identities}{}{}
\desc[german]{Logarithmus Identitäten}{Logarithmus Rechenregeln}{}
@ -178,19 +172,17 @@
}
\end{formula}
\Subsection[
\eng{Vector calculus}
\ger{Vektor Analysis}
]{vec}
\Subsection{vec}
\desc{Vector calculus}{}{}
\desc[german]{Vektor Analysis}{}{}
\begin{formula}{laplace}
\desc{Laplace operator}{}{}
\desc[german]{Laplace-Operator}{}{}
\eq{\laplace = \Grad^2 = \pdv[2]{}{x} + \pdv[2]{}{y} + \pdv[2]{}{z}}
\end{formula}
\Subsubsection[
\eng{Spherical symmetry}
\ger{Kugelsymmetrie}
]{sphere}
\Subsubsection{sphere}
\desc{Spherical symmetry}{}{}
\desc[german]{Kugelsymmetrie}{}{}
\begin{formula}{coordinates}
\desc{Spherical coordinates}{}{}
\desc[german]{Kugelkoordinaten}{}{}
@ -214,10 +206,9 @@
\end{formula}
\Subsection[
\eng{Integrals}
\ger{Integralrechnung}
]{integral}
\Subsection{integral}
\desc{Integrals}{}{}
\desc[german]{Integralrechnung}{}{}
\begin{formula}{partial}
\desc{Partial integration}{}{}
\desc[german]{Partielle integration}{}{}
@ -247,10 +238,9 @@
\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}
\Subsubsection{list}
\desc{List of common integrals}{}{}
\desc[german]{Liste nützlicher Integrale}{}{}
% Put links to other integrals here
\fRef{math:cal:log:integral}

29
src/math/geometry.tex
View File

@ -1,12 +1,11 @@
\Section[
\eng{Geometry}
\ger{Geometrie}
]{geo}
\Section{geo}
\desc{Geometry}{}{}
\desc[german]{Geometrie}{}{}
\Subsection[
\eng{Trigonometry}
\ger{Trigonometrie}
]{trig}
\Subsection{trig}
\desc{Trigonometry}{}{}
\desc[german]{Trigonometrie}{}{}
\begin{formula}{exponential_function}
\desc{Exponential function}{}{}
@ -41,10 +40,9 @@
\eq{\cosh(x) &= \cos{ix} \\ &= \frac{e^{x}+e^{-x}}{2}}
\end{formula}
\Subsection[
\eng{Various theorems}
\ger{Verschiedene Theoreme}
]{theorems}
\Subsection{theorems}
\desc{Various theorems}{}{}
\desc[german]{Verschiedene Theoreme}{}{}
\begin{formula}{sum}
\desc{Hypthenuse in the unit circle}{}{}
\desc[german]{Hypothenuse im Einheitskreis}{}{}
@ -78,10 +76,9 @@
\end{formula}
\Subsubsection[
\eng{Table of values}
\ger{Wertetabelle}
]{value_table}
\Subsubsection{value_table}
\desc{Table of values}{}{}
\desc[german]{Wertetabelle}{}{}
\begingroup
\setlength{\tabcolsep}{0.9em} % horizontal
\renewcommand{\arraystretch}{2} % vertical

43
src/math/linalg.tex
View File

@ -1,12 +1,11 @@
\Section[
\eng{Linear algebra}
\ger{Lineare Algebra}
]{linalg}
\Section{linalg}
\desc{Linear algebra}{}{}
\desc[german]{Lineare Algebra}{}{}
\Subsection[
\eng{Matrix basics}
\ger{Matrizen Basics}
]{matrix}
\Subsection{matrix}
\desc{Matrix basics}{}{}
\desc[german]{Matrizen Basics}{}{}
\begin{formula}{matrix_matrix_product}
\desc{Matrix-matrix product as sum}{}{}
@ -31,10 +30,9 @@
\eq{U ^\dagger U = \id}
\end{formula}
\Subsubsection[
\eng{Transposed matrix}
\ger{Transponierte Matrix}
]{transposed}
\Subsubsection{transposed}
\desc{Transposed matrix}{}{}
\desc[german]{Transponierte Matrix}{}{}
\begin{formula}{sum}
\desc{Sum}{}{}
\desc[german]{Summe}{}{}
@ -57,10 +55,9 @@
\end{formula}
\Subsection[
\eng{Determinant}
\ger{Determinante}
]{determinant}
\Subsection{determinant}
\desc{Determinant}{}{}
\desc[german]{Determinante}{}{}
\begin{formula}{2x2}
\desc{2x2 matrix}{}{}
\desc[german]{2x2 Matrix}{}{}
@ -95,10 +92,9 @@
\end{formula}
\Subsection[
\eng{Misc}
\ger{Misc}
]{misc}
\Subsection{misc}
\desc{Misc}{}{}
\desc[german]{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}
@ -157,10 +153,9 @@
\end{formula}
\Subsection[
\eng{Eigenvalues}
\ger{Eigenwerte}
]{eigen}
\Subsection{eigen}
\desc{Eigenvalues}{}{}
\desc[german]{Eigenwerte}{}{}
\begin{formula}{values}
\desc{Eigenvalue equation}{}{$\lambda$ eigenvalue, $v$ eigenvector}
\desc[german]{Eigenwert-Gleichung}{}{$\lambda$ Eigenwert, $v$ Eigenvektor}

8
src/math/math.tex
View File

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

286
src/math/probability_theory.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Probability theory}
\ger{Wahrscheinlichkeitstheorie}
]{pt}
\Section{pt}
\desc{Probability theory}{}{}
\desc[german]{Wahrscheinlichkeitstheorie}{}{}
\begin{formula}{mean}
\absLabel
@ -70,33 +70,30 @@
\eq{\binom{n}{k} = \frac{n!}{k!(n-k)!}}
\end{formula}
\Subsection[
\eng{Distributions}
\ger{Verteilungen}
]{distributions}
\Subsubsection[
\eng{Continuous probability distributions}
\ger{Kontinuierliche Wahrscheinlichkeitsverteilungen}
]{cont}
\Subsection{distributions}
\desc{Distributions}{}{}
\desc[german]{Verteilungen}{}{}
\Subsubsection{cont}
\desc{Continuous probability distributions}{}{}
\desc[german]{Kontinuierliche Wahrscheinlichkeitsverteilungen}{}{}
\begin{bigformula}{normal}
\absLabel[normal_distribution]
\desc{Gauß/Normal distribution}{}{}
\desc[german]{Gauß/Normal-Verteilung}{}{}
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_gauss.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
\disteq{support}{x \in \R}
\disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
\disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
\disteq{mean}{\mu}
\disteq{median}{\mu}
\disteq{variance}{\sigma^2}
\end{distribution}
\includegraphics{img/distribution_gauss.pdf}
}{
\begin{distribution}
\disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
\disteq{support}{x \in \R}
\disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
\disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
\disteq{mean}{\mu}
\disteq{median}{\mu}
\disteq{variance}{\sigma^2}
\end{distribution}
}
\end{bigformula}
\begin{formula}{standard_normal}
@ -110,63 +107,77 @@
\absLabel[multivariate_normal_distribution]
\desc{Multivariate normal distribution}{Multivariate Gaussian distribution}{$\vec{\mu}$ \absRef{mean}, $\mat{\Sigma}$ \absRef{covariance}}
\desc[german]{Mehrdimensionale Normalverteilung}{Multivariate Normalverteilung}{}
\TODO{k-variate normal plot}
\begin{distribution}
\disteq{parameters}{\vec{\mu} \in \R^k,+\quad \mat{\Sigma} \in \R^{k\times k}}
\disteq{support}{\vec{x} \in \vec{\mu} + \text{span}(\mat{\Sigma})}
\disteq{pdf}{\mathcal{N}(\vec{\mu}, \mat{\Sigma}) = \frac{1}{(2\pi)^{k/2}} \frac{1}{\sqrt{\det{\Sigma}}} \Exp{-\frac{1}{2} \left(\vecx-\vec{\mu}\right)^\T \mat{\Sigma}^{-1} \left(\vecx-\vec{\mu}\right)}}
\disteq{mean}{\vec{\mu}}
\disteq{variance}{\mat{\Sigma}}
\end{distribution}
\fsplit[0.3]{
\TODO{k-variate normal plot}
}{
\begin{distribution}
\disteq{parameters}{\vec{\mu} \in \R^k,+\quad \mat{\Sigma} \in \R^{k\times k}}
\disteq{support}{\vec{x} \in \vec{\mu} + \text{span}(\mat{\Sigma})}
\disteq{pdf}{\mathcal{N}(\vec{\mu}, \mat{\Sigma}) = \frac{1}{(2\pi)^{k/2}} \frac{1}{\sqrt{\det{\Sigma}}} \Exp{-\frac{1}{2} \left(\vecx-\vec{\mu}\right)^\T \mat{\Sigma}^{-1} \left(\vecx-\vec{\mu}\right)}}
\disteq{mean}{\vec{\mu}}
\disteq{variance}{\mat{\Sigma}}
\end{distribution}
}
\end{bigformula}
\begin{formula}{laplace}
\begin{bigformula}{laplace}
\absLabel[laplace_distribution]
\desc{Laplace-distribution}{}{}
\desc[german]{Laplace-Verteilung}{}{}
\TODO{TODO}
\end{formula}
\desc{Laplace-distribution}{Double exponential distribution}{}
\desc[german]{Laplace-Verteilung}{Doppelexponentialverteilung}{}
\fsplit[\distleftwidth]{
\centering
\includegraphics{img/distribution_laplace.pdf}
}{
\begin{distribution}
\disteq{parameters}{\mu \in \R,\quad b > 0 \in \R}
\disteq{support}{x \in \R}
\disteq{pdf}{\frac{1}{\sqrt{2b}}\Exp{-\frac{\abs{x-\mu}}{b}}}
% \disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
\disteq{mean}{\mu}
\disteq{median}{\mu}
\disteq{variance}{2b^2}
\end{distribution}
}
\end{bigformula}
\begin{bigformula}{cauchy}
\absLabel[lorentz_distribution]
\desc{Cauchys / Lorentz distribution}{Also known as Cauchy-Lorentz distribution, Lorentz(ian) function, Breit-Wigner distribution.}{}
\desc[german]{Cauchy / Lorentz-Verteilung}{Auch bekannt als Cauchy-Lorentz Verteilung, Lorentz Funktion, Breit-Wigner Verteilung.}{}
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_cauchy.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
\disteq{support}{x \in \R}
\disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
\disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
\disteq{mean}{\text{\GT{undefined}}}
\disteq{median}{x_0}
\disteq{variance}{\text{\GT{undefined}}}
\end{distribution}
\includegraphics{img/distribution_cauchy.pdf}
}{
\begin{distribution}
\disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
\disteq{support}{x \in \R}
\disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
\disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
\disteq{mean}{\text{\GT{undefined}}}
\disteq{median}{x_0}
\disteq{variance}{\text{\GT{undefined}}}
\end{distribution}
}
\end{bigformula}
\begin{bigformula}{maxwell-boltzmann}
\absLabel[maxwell-boltzmann_distribution]
\desc{Maxwell-Boltzmann distribution}{}{}
\desc[german]{Maxwell-Boltzmann Verteilung}{}{}
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{a > 0}
\disteq{support}{x \in (0, \infty)}
\disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
\disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
\disteq{mean}{2a \frac{2}{\pi}}
\disteq{median}{}
\disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
\end{distribution}
\includegraphics{img/distribution_maxwell-boltzmann.pdf}
}{
\begin{distribution}
\disteq{parameters}{a > 0}
\disteq{support}{x \in (0, \infty)}
\disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
\disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
\disteq{mean}{2a \frac{2}{\pi}}
% \disteq{median}{}
\disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
\end{distribution}
}
\end{bigformula}
@ -174,48 +185,45 @@
\absLabel[gamma_distribution]
\desc{Gamma Distribution}{with $\lambda$ parameter}{$\Gamma$ \fRef{math:cal:integral:list:gamma_function}, $\gamma$ \fRef{math:cal:integral:list:lower_incomplete_gamma_function}}
\desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{}
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_gamma.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{\alpha > 0, \lambda > 0}
\disteq{support}{x\in(0,1)}
\disteq{pdf}{\frac{\lambda^\alpha}{\Gamma(\alpha) x^{\alpha-1} \e^{-\lambda x}}}
\disteq{cdf}{\frac{1}{\Gamma(\alpha) \gamma(\alpha, \lambda x)}}
\disteq{mean}{\frac{\alpha}{\lambda}}
\disteq{variance}{\frac{\alpha}{\lambda^2}}
\end{distribution}
\includegraphics{img/distribution_gamma.pdf}
}{
\begin{distribution}
\disteq{parameters}{\alpha > 0, \lambda > 0}
\disteq{support}{x\in(0,1)}
\disteq{pdf}{\frac{\lambda^\alpha}{\Gamma(\alpha) x^{\alpha-1} \e^{-\lambda x}}}
\disteq{cdf}{\frac{1}{\Gamma(\alpha) \gamma(\alpha, \lambda x)}}
\disteq{mean}{\frac{\alpha}{\lambda}}
\disteq{variance}{\frac{\alpha}{\lambda^2}}
\end{distribution}
}
\end{bigformula}
\begin{bigformula}{beta}
\absLabel[beta_distribution]
\desc{Beta Distribution}{}{$\txB$ \fRef{math:cal:integral:list:beta_function} / \fRef{math:cal:integral:list:incomplete_beta_function}}
\desc[german]{Beta Verteilung}{}{}
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_beta.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{\alpha \in \R, \beta \in \R}
\disteq{support}{x\in[0,1]}
\disteq{pdf}{\frac{x^{\alpha-1} (1-x)^{\beta-1}}{\txB(\alpha,\beta)}}
\disteq{cdf}{\frac{\txB(x;\alpha,\beta)}{\txB(\alpha,\beta)}}
\disteq{mean}{\frac{\alpha}{\alpha+\beta}}
% \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
\disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
\end{distribution}
\includegraphics{img/distribution_beta.pdf}
}{
\begin{distribution}
\disteq{parameters}{\alpha \in \R, \beta \in \R}
\disteq{support}{x\in[0,1]}
\disteq{pdf}{\frac{x^{\alpha-1} (1-x)^{\beta-1}}{\txB(\alpha,\beta)}}
\disteq{cdf}{\frac{\txB(x;\alpha,\beta)}{\txB(\alpha,\beta)}}
\disteq{mean}{\frac{\alpha}{\alpha+\beta}}
% \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
\disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
\end{distribution}
}
\end{bigformula}
\Subsubsection[
\eng{Discrete probability distributions}
\ger{Diskrete Wahrscheinlichkeitsverteilungen}
]{discrete}
\Subsubsection{discrete}
\desc{Discrete probability distributions}{}{}
\desc[german]{Diskrete Wahrscheinlichkeitsverteilungen}{}{}
\begin{bigformula}{binomial}
\absLabel[binomial_distribution]
\desc{Binomial distribution}{}{}
@ -224,42 +232,40 @@
\eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \absRef[poisson distribution]{poisson_distribution}}
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \absRef[Poissonverteilung]{poisson_distribution}}
\end{ttext}\\
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_binomial.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
\disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
\disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
% \disteq{cdf}{\text{regularized incomplete beta function}}
\disteq{mean}{np}
\disteq{median}{\floor{np} \text{ or } \ceil{np}}
\disteq{variance}{npq = np(1-p)}
\end{distribution}
\includegraphics{img/distribution_binomial.pdf}
}{
\begin{distribution}
\disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
\disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
\disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
% \disteq{cdf}{\text{regularized incomplete beta function}}
\disteq{mean}{np}
\disteq{median}{\floor{np} \text{ or } \ceil{np}}
\disteq{variance}{npq = np(1-p)}
\end{distribution}
}
\end{bigformula}
\begin{bigformula}{poisson}
\absLabel[poisson_distribution]
\desc{Poisson distribution}{}{}
\desc[german]{Poissonverteilung}{}{}
\begin{minipage}{\distleftwidth}
\begin{figure}[H]
\fsplit[\distleftwidth]{
\centering
\includegraphics[width=\textwidth]{img/distribution_poisson.pdf}
\end{figure}
\end{minipage}
\begin{distribution}
\disteq{parameters}{\lambda \in (0,\infty)}
\disteq{support}{k \in \N}
\disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
\disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
\disteq{mean}{\lambda}
\disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
\disteq{variance}{\lambda}
\end{distribution}
\includegraphics{img/distribution_poisson.pdf}
}{
\begin{distribution}
\disteq{parameters}{\lambda \in (0,\infty)}
\disteq{support}{k \in \N}
\disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
\disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
\disteq{mean}{\lambda}
\disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
\disteq{variance}{\lambda}
\end{distribution}
}
\end{bigformula}
@ -277,10 +283,9 @@
% \end{distribution}
\Subsection[
\eng{Central limit theorem}
\ger{Zentraler Grenzwertsatz}
]{cls}
\Subsection{cls}
\desc{Central limit theorem}{}{}
\desc[german]{Zentraler Grenzwertsatz}{}{}
\begin{ttext}
\eng{
Suppose $X_1, X_2, \dots$ is a sequence of independent and identically distributed random variables with $\braket{X_i} = \mu$ and $(\Delta X_i)^2 = \sigma^2 < \infty$.
@ -294,10 +299,9 @@
}
\end{ttext}
\Subsection[
\eng{Propagation of uncertainty / error}
\ger{Fehlerfortpflanzung}
]{error}
\Subsection{error}
\desc{Propagation of uncertainty / error}{}{}
\desc[german]{Fehlerfortpflanzung}{}{}
\begin{formula}{generalised}
\desc{Generalized error propagation}{}{$V$ \fRef{math:pt:covariance} matrix, $J$ \fRef{math:cal:jacobi-matrix}}
\desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fRef{math:pt:covariance} Matrix, $J$ \fRef{cal:jacobi-matrix}}{}
@ -328,10 +332,9 @@
\eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
\end{formula}
\Subsection[
\eng{Maximum likelihood estimation}
\ger{Maximum likelihood Methode}
]{mle}
\Subsection{mle}
\desc{Maximum likelihood estimation}{}{}
\desc[german]{Maximum likelihood Methode}{}{}
\begin{formula}{likelihood}
\desc{Likelihood function}{Likelihood of observing $x$ when parameter is $\theta$\\in general not normalized!}{$\rho$ \fRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ depending on parameter $\theta$, $\Theta$ parameter space}
\desc[german]{Likelihood Funktion}{"Plausibilität" $x$ zu messen, wenn der Parameter $\theta$ ist\\nicht normalisiert!}{$\rho$ \fRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ hängt ab von Parameter $\theta$, $\Theta$ Parameterraum}
@ -348,10 +351,9 @@
\eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)}
\end{formula}
\Subsection[
\eng{Bayesian probability theory}
\ger{Bayessche Wahrscheinlichkeitstheorie}
]{bayesian}
\Subsection{bayesian}
\desc{Bayesian probability theory}{}{}
\desc[german]{Bayessche Wahrscheinlichkeitstheorie}{}{}
\begin{formula}{prior}
\desc{Prior distribution}{Expected distribution before conducting the experiment}{$\theta$ parameter}
\desc[german]{Prior Verteilung}{}{}

72
src/mechanics.tex
View File

@ -1,12 +1,11 @@
\Part[
\eng{Mechanics}
\ger{Mechanik}
]{mech}
\Part{mech}
\desc{Mechanics}{}{}
\desc[german]{Mechanik}{}{}
\Section[
\eng{Newton}
\ger{Newton}
]{newton}
\Section{newton}
\desc{Newton}{}{}
\desc[german]{Newton}{}{}
\begin{formula}{newton_laws}
\desc{Newton's laws}{}{}
\desc[german]{Newtonsche Gesetze}{}{}
@ -31,10 +30,9 @@
}
\end{formula}
\Section[
\eng{Misc}
\ger{Verschiedenes}
]{misc}
\Section{misc}
\desc{Misc}{}{}
\desc[german]{Verschiedenes}{}{}
\begin{formula}{hook}
\desc{Hooke's law}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ spring length}
\desc[german]{Hookesches Gesetz}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ Federlänge}
@ -50,28 +48,36 @@
\end{formula}
\def\lagrange{\mathcal{L}}
\Section[
\eng{Lagrange formalism}
\ger{Lagrange Formalismus}
]{lagrange}
\begin{ttext}[desc]
\eng{The Lagrange formalism is often the most simple approach the get the equations of motion,
because with suitable generalied coordinates obtaining the Lagrange function is often relatively easy.
\Section{lagrange}
\desc{Lagrange formalism}{}{}
\desc[german]{Lagrange Formalismus}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
\ttxt{
\eng{The Lagrange formalism is often the most simple approach the get the equations of motion,
because with suitable generalied coordinates obtaining the Lagrange function is often relatively easy.
}
\ger{Der Lagrange-Formalsismus ist oft der einfachste Weg die Bewegungsgleichungen zu erhalten,
da das Aufstellen der Lagrange-Funktion mit geeigneten generalisierten Koordinaten oft relativ einfach ist.
}
}
\ger{Der Lagrange-Formalsismus ist oft der einfachste Weg die Bewegungsgleichungen zu erhalten,
da das Aufstellen der Lagrange-Funktion mit geeigneten generalisierten Koordinaten oft relativ einfach ist.
}
\end{ttext}
\begin{ttext}[generalized_coords]
\eng{
The generalized coordinates are choosen so that the cronstraints are automatically fullfilled.
For example, the generalized coordinate for a 2D pendelum is $q=\varphi$, with $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
}
\ger{
Die generalisierten Koordinaten werden so gewählt, dass die Zwangsbedingungen automatisch erfüllt sind.
Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
}
\end{ttext}
\end{formula}
\begin{formula}{generalized_coordinates}
\desc{Generalized coordinates}{}{}
\desc[german]{Generalisierte Koordinaten}{}{}
\absLabel
\begin{ttext}[generalized_coords]
\eng{
The generalized coordinates are choosen so that the cronstraints are automatically fullfilled.
For example, the generalized coordinate for a 2D pendelum is $q=\varphi$, with $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
}
\ger{
Die generalisierten Koordinaten werden so gewählt, dass die Zwangsbedingungen automatisch erfüllt sind.
Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
}
\end{ttext}
\end{formula}
\begin{formula}{lagrangian} \absLabel
\desc{Lagrange function}{}{$T$ kinetic energy, $V$ potential energy }
\desc[german]{Lagrange-Funktion}{}{$T$ kinetische Energie, $V$ potentielle Energie}

8
src/particle.tex
View File

@ -1,7 +1,7 @@
\Part[
\eng{Particle physics}
\ger{Teilchenphysik}
]{particle}
\Part{particle}
\desc{Particle physics}{}{}
\desc[german]{Teilchenphysik}{}{}
\begin{formula}{electron_mass}
\desc{Electron mass}{}{}

26
src/pkg/mqformula.sty
View File

@ -54,16 +54,6 @@
% 1: key
\newenvironment{formulainternal}[1]{
\mqfqname@enter{#1}
% [1]: language
% 2: name
% 3: description
% 4: definitions/links
\newcommand{\desc}[4][english]{
% language, name, description, definitions
\ifblank{##2}{}{\dt{##1}{##2}}
\ifblank{##3}{}{\dt[desc]{##1}{##3}}
\ifblank{##4}{}{\dt[defs]{##1}{##4}}
}
\directlua{n_formulaEntries = 0}
% makes this formula referencable with \abbrRef{<name>}
@ -196,11 +186,10 @@
\par\noindent\ignorespaces
% \textcolor{gray}{\hrule}
% \vspace{0.5\baselineskip}
\textbf{
\raggedright
\GT{\fqname}
}
\IfTranslationExists{\fqname:desc}{
\textbf{%
\raggedright\GT{\fqname}\ignorespaces%
}%
\IfTranslationExists{\fqname:desc}{\ignorespaces%
: {\color{fg1} \GT{\fqname:desc}}
}{}
\hfill
@ -228,13 +217,6 @@
\newenvironment{formulagroup}[1]{
\mqfqname@enter{#1}
\newcommand{\desc}[4][english]{
% language, name, description, definitions
\ifblank{##2}{}{\dt{##1}{##2}}
\ifblank{##3}{}{\dt[desc]{##1}{##3}}
\ifblank{##4}{}{\dt[defs]{##1}{##4}}
}
\par\noindent
\begin{minipage}{\textwidth} % using a minipage to now allow line breaks within the bigformula
\mqfqname@label

64
src/pkg/mqfqname.sty
View File

@ -93,45 +93,57 @@
\directlua{fqnameLeaveOnlyFirstN(#1)}%
}
% Define translations for the current fqname
% [1]: language
% 2: name
% 3: description -> :desc
% 4: definitions/links -> :defs
\newcommand{\desc}[4][english]{
% language, name, description, definitions
\ifblank{#2}{}{\dt{#1}{#2}}
\ifblank{#3}{}{\dt[desc]{#1}{#3}}
\ifblank{#4}{}{\dt[defs]{#1}{#4}}
}
% SECTIONING
% start <section>, get heading from translation, set label
% fqname is the fully qualified name of all sections and formulas, the keys of all previous sections joined with a ':'
% fqname is secFqname:<key> where <key> is the key/id of some environment, like formula
% [1]: code to run after setting \fqname, but before the \part, \section etc
% 2: key
\newcommand{\Part}[2][desc]{
\newpage
\mqfqname@leaveOnlyFirstN{0}
% 1: depth
% 2: key
% 3: Latex section command
\newcommand\mqfqname@section[3]{
\mqfqname@leaveOnlyFirstN{#1}
\mqfqname@enter{#2}
#1
% this is necessary so that \part/\section... takes the fully expanded string. Otherwise the pdf toc will have just the fqname
\edef\fqnameText{\GT{\fqname}}
\part{\fqnameText}
#3{\fqnameText}
\mqfqname@label
\IfTranslationExists{\fqname:desc}{
{\color{fg1} \GT{\fqname:desc}}
}{}
}
\newcommand{\Section}[2][]{
\mqfqname@leaveOnlyFirstN{1}
\mqfqname@enter{#2}
#1
\edef\fqnameText{\GT{\fqname}}
\section{\fqnameText}
\mqfqname@label
\newcommand{\Part}[1]{
\newpage
\mqfqname@section{0}{#1}{\part}
}
\newcommand{\Subsection}[2][]{
\mqfqname@leaveOnlyFirstN{2}
\mqfqname@enter{#2}
#1
\edef\fqnameText{\GT{\fqname}}
\subsection{\fqnameText}
\mqfqname@label
\newcommand{\Section}[1]{
\mqfqname@section{1}{#1}{\section}
}
\newcommand{\Subsubsection}[2][]{
\mqfqname@leaveOnlyFirstN{3}
\mqfqname@enter{#2}
#1
\edef\fqnameText{\GT{\fqname}}
\subsubsection{\fqnameText}
\mqfqname@label
\newcommand{\Subsection}[1]{
\mqfqname@section{2}{#1}{\subsection}
}
\newcommand{\Subsubsection}[1]{
\mqfqname@section{3}{#1}{\subsubsection}
}
\newcommand{\Paragraph}[1]{
\mqfqname@section{4}{#1}{\paragraph}
}
\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}

19
src/pkg/mqperiodictable.sty
View File

@ -33,15 +33,13 @@ end
% 3: period
% 4: column
\newenvironment{element}[4]{
% [1]: language
% 2: name
% 3: description
% 4: definitions/links
\newcommand{\desc}[4][english]{
\ifblank{##2}{}{\DT[el:#1]{##1}{##2}}
\ifblank{##3}{}{\DT[el:#1_desc]{##1}{##3}}
\ifblank{##4}{}{\DT[el:#1_defs]{##1}{##4}}
% force the fqname to el
\directlua{
old_sections = sections
sections = {}
table.insert(sections, "el")
}
\mqfqname@update
\directLuaAuxExpand{
elementAdd(\luastring{#1}, \luastring{#2}, \luastring{#3}, \luastring{#4})
}
@ -55,6 +53,11 @@ end
\edef\lastElementName{#1}
}{
\ignorespacesafterend
% restore fqname
\directlua{
sections = old_sections
}
\mqfqname@update
}
% LIST

241
src/qm/atom.tex
View File

@ -1,100 +1,114 @@
\def\vecr{{\vec{r}}}
\def\abohr{a_\textrm{B}}
\Section[
\eng{Hydrogen Atom}
\ger{Wasserstoffatom}
]{h}
\Section{h}
\desc{Hydrogen Atom}{}{}
\desc[german]{Wasserstoffatom}{}{}
\begin{formula}{reduced_mass}
\desc{Reduced mass}{}{}
\desc[german]{Reduzierte Masse}{}{}
\eq{\mu = \frac{\masse m_\textrm{K}}{\masse + m_\textrm{K}} \explOverEq[\approx]{$\masse \ll m_\textrm{K}$} \masse}
\end{formula}
\begin{formula}{reduced_mass}
\desc{Reduced mass}{}{}
\desc[german]{Reduzierte Masse}{}{}
\eq{\mu = \frac{\masse m_\textrm{K}}{\masse + m_\textrm{K}} \explOverEq[\approx]{$\masse \ll m_\textrm{K}$} \masse}
\end{formula}
\begin{formula}{potential}
\desc{Coulumb potential}{For a single electron atom}{$Z$ atomic number}
\desc[german]{Coulumb potential}{Für ein Einelektronenatom}{$Z$ Ordnungszahl/Kernladungszahl}
\eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
\end{formula}
\begin{formula}{hamiltonian}
\desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{}
% \eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
\eq{
\hat{H} &= -\frac{\hbar^2}{2\mu} {\Grad_\vecr}^2 - V(\vecr) \\
&= \frac{\hat{p}_r^2}{2\mu} + \frac{\hat{L}^2}{2\mu r} + V(r)
}
\end{formula}
\begin{formula}{potential}
\desc{Coulumb potential}{For a single electron atom}{$Z$ atomic number}
\desc[german]{Coulumb potential}{Für ein Einelektronenatom}{$Z$ Ordnungszahl/Kernladungszahl}
\eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
\end{formula}
\begin{formula}{hamiltonian}
\desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{}
% \eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
\eq{
\hat{H} &= -\frac{\hbar^2}{2\mu} {\Grad_\vecr}^2 - V(\vecr) \\
&= \frac{\hat{p}_r^2}{2\mu} + \frac{\hat{L}^2}{2\mu r} + V(r)
}
\end{formula}
\begin{formula}{wave_function}
\desc{Wave function}{}{$R_{nl}(r)$ \fRef{qm:h:radial}, $Y_{lm}$ \fRef{qm:spherical_harmonics}}
\desc[german]{Wellenfunktion}{}{}
\eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
\end{formula}
\begin{formula}{wave_function}
\desc{Wave function}{}{$R_{nl}(r)$ \fRef{qm:h:radial}, $Y_{lm}$ \fRef{qm:spherical_harmonics}}
\desc[german]{Wellenfunktion}{}{}
\eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
\end{formula}
\begin{formula}{radial}
\desc{Radial part}{}{$L_r^s(x)$ Laguerre-polynomials}
\desc[german]{Radialanteil}{}{$L_r^s(x)$ Laguerre-Polynome}
\eq{
R_{nl} &= - \sqrt{\frac{(n-l-1)!(2\kappa)^3}{2n[(n+l)!]^3}} (2\kappa r)^l \e^{-\kappa r} L_{n+1}^{2l+1}(2\kappa r)
\shortintertext{\GT{with}}
\kappa &= \frac{\sqrt{2\mu\abs{E}}}{\hbar} = \frac{Z}{n \abohr}
}
\end{formula}
\begin{formula}{radial}
\desc{Radial part}{}{$L_r^s(x)$ Laguerre-polynomials}
\desc[german]{Radialanteil}{}{$L_r^s(x)$ Laguerre-Polynome}
\eq{
R_{nl} &= - \sqrt{\frac{(n-l-1)!(2\kappa)^3}{2n[(n+l)!]^3}} (2\kappa r)^l \e^{-\kappa r} L_{n+1}^{2l+1}(2\kappa r)
\shortintertext{\GT{with}}
\kappa &= \frac{\sqrt{2\mu\abs{E}}}{\hbar} = \frac{Z}{n \abohr}
}
\end{formula}
\begin{formula}{energy}
\desc{Energy eigenvalues}{}{}
\desc[german]{Energieeigenwerte}{}{}
\eq{E_n &= \frac{Z^2\mu e^4}{n^2(4\pi\epsilon_0)^2 2\hbar^2} = -E_\textrm{H}\frac{Z^2}{n^2}}
\end{formula}
\begin{formula}{energy}
\desc{Energy eigenvalues}{}{}
\desc[german]{Energieeigenwerte}{}{}
\eq{E_n &= \frac{Z^2\mu e^4}{n^2(4\pi\epsilon_0)^2 2\hbar^2} = -E_\textrm{H}\frac{Z^2}{n^2}}
\end{formula}
\begin{formula}{rydberg_constant_heavy}
\desc{Rydberg constant}{for heavy atoms}{\ConstRef{electron_mass}, \ConstRef{charge}, \ConstRef{vacuum_permittivity}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
\desc[german]{Rydberg-Konstante}{für schwere Atome}{}
\constant{R_\infty}{exp}{
\val{10973731.568157(12)}{\per\m}
}
\eq{
R_\infty = \frac{m_e e^4}{8\epsilon_0^2 h^3 c}
}
\end{formula}
\begin{formula}{rydberg_constant_heavy}
\desc{Rydberg constant}{for heavy atoms}{\ConstRef{electron_mass}, \ConstRef{charge}, \ConstRef{vacuum_permittivity}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
\desc[german]{Rydberg-Konstante}{für schwere Atome}{}
\constant{R_\infty}{exp}{
\val{10973731.568157(12)}{\per\m}
}
\eq{
R_\infty = \frac{m_e e^4}{8\epsilon_0^2 h^3 c}
}
\end{formula}
\begin{formula}{rydberg_constant_corrected}
\desc{Rydberg constant}{corrected for nucleus mass $M$}{\ConstRef{rydberg_constant_heavy}, $\mu = \left(\frac{1}{m_\txe} + \frac{1}{M}\right)^{-1}$ \GT{reduced_mass}, \ConstRef{electron_mass}}
\desc[german]{Rydberg Konstante}{korrigiert für Kernmasse $M$}{}
\eq{R_\txM = \frac{\mu}{m_\txe} R_\infty}
\end{formula}
\begin{formula}{rydberg_constant_corrected}
\desc{Rydberg constant}{corrected for nucleus mass $M$}{\ConstRef{rydberg_constant_heavy}, $\mu = \left(\frac{1}{m_\txe} + \frac{1}{M}\right)^{-1}$ \GT{reduced_mass}, \ConstRef{electron_mass}}
\desc[german]{Rydberg Konstante}{korrigiert für Kernmasse $M$}{}
\eq{R_\txM = \frac{\mu}{m_\txe} R_\infty}
\end{formula}
\begin{formula}{rydberg_energy}
\desc{Rydberg energy}{Energy unit}{\ConstRef{rydberg_constant_heavy}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
\desc[german]{Rydberg-Energy}{Energie Einheit}{}
\eq{1\,\text{Ry} = hc\,R_\infty}
\end{formula}
\begin{formula}{rydberg_energy}
\desc{Rydberg energy}{Energy unit}{\ConstRef{rydberg_constant_heavy}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
\desc[german]{Rydberg-Energy}{Energie Einheit}{}
\eq{1\,\text{Ry} = hc\,R_\infty}
\end{formula}
\begin{formula}{bohr_radius}
\desc{Bohr radius}{}{\ConstRef{vacuum_permittivity}, \ConstRef{electron_mass}}
\desc[german]{Bohrscher Radius}{}{}
\constant{a_0}{exp}{
\val{5.29177210544(82) \xE{-11}}{\m}
}
\eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
\end{formula}
\begin{formula}{bohr_radius}
\desc{Bohr radius}{}{\ConstRef{vacuum_permittivity}, \ConstRef{electron_mass}}
\desc[german]{Bohrscher Radius}{}{}
\constant{a_0}{exp}{
\val{5.29177210544(82) \xE{-11}}{\m}
}
\eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
\end{formula}
\begin{formula}{hunds_rules}
\desc{Hund's rules}{Angular momentum configuration rules for electrons in atomic orbitals in the atom's ground state}{}
\desc[german]{Hundsche Regeln}{Drehimpulskonfiguration für Elektronen in Atomorbitalen im Grundzustand des Atoms }{}
\ttxt{\eng{
\begin{enumerate}
\item Full shells: $J=0$
\item $S$ takes the maximum possible value
\item For equal $S$ configurations, the one where $L$ is maximized is taken
\item Outermost shell half filled or less \Rightarrow $J$ minimized: $J=\abs{L-S}$ \\
Outermost shell more than half filled \Rightarrow $J$ maximized $J=L+S$
\end{enumerate}
}\ger{
\begin{enumerate}
\item Volle Schalen haben Gesamtdrehimpuls 0: $J=0$
\item $S$ nimmt den höchstmöglichsten Wert an
\item Für gleiche $S$ wird $L$ maximiert
\item Äußerste Schale halb oder weniger gefüllt \Rightarrow $J$ minimiert: $J=\abs{L-S}$\\
Äußerste Schale mehr als halb gefüllt \Rightarrow $J$ maximiert: $J=L+S$
\end{enumerate}
}}
\end{formula}
\Subsection[
\eng{Corrections}
\ger{Korrekturen}
]{corrections}
\Subsection{corrections}
\desc{Corrections}{}{}
\desc[german]{Korrekturen}{}{}
\Subsubsection[
\eng{Darwin term}
\ger{Darwin-Term}
]{darwin}
\begin{ttext}[desc]
\eng{Relativisitc correction: Accounts for interaction with nucleus (non-zero wavefunction at nucleaus position)}
\ger{Relativistische Korrektur: Berücksichtigt die Interatkion mit dem Kern (endliche Wellenfunktion bei der Kernposition)}
\end{ttext}
\Subsubsection{darwin}
\desc{Darwin term}{Relativisitc correction: Accounts for interaction with nucleus (non-zero wavefunction at nucleaus position)}{}
\desc[german]{Darwin-Term}{Relativistische Korrektur: Berücksichtigt die Interatkion mit dem Kern (endliche Wellenfunktion bei der Kernposition)}{}
\begin{formula}{energy_shift}
\desc{Energy shift}{}{}
\desc[german]{Energieverschiebung}{}{}
@ -107,14 +121,9 @@
\eq{\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c} \approx \frac{1}{137}}
\end{formula}
\Subsubsection[
\eng{Spin-orbit coupling (LS-coupling)}
\ger{Spin-Bahn-Kopplung (LS-Kopplung)}
]{ls_coupling}
\begin{ttext}[desc]
\eng{The interaction of the electron spin with the electrostatic field of the nuclei lead to energy shifts.}
\ger{The Wechselwirkung zwischen dem Elektronenspin und dem elektrostatischen Feld des Kerns führt zu Energieverschiebungen.}
\end{ttext}
\Subsubsection{ls_coupling}
\desc{Spin-orbit coupling (LS-coupling)}{The interaction of the electron spin with the electrostatic field of the nuclei lead to energy shifts.}{}
\desc[german]{Spin-Bahn-Kopplung (LS-Kopplung)}{The Wechselwirkung zwischen dem Elektronenspin und dem elektrostatischen Feld des Kerns führt zu Energieverschiebungen.}{}
\begin{formula}{energy_shift}
\desc{Energy shift}{}{}
@ -122,20 +131,15 @@
\eq{\Delta E_\text{LS} = \frac{\mu_0 Z e^2}{8\pi \masse^2\,r^3} \braket{\vec{S} \cdot \vec{L}}}
\end{formula}
\begin{formula}{sl}
\desc{\TODO{name}}{}{}
\desc[german]{??}{}{}
\desc{Spin-orbit coupling}{}{}
\desc[german]{Spin-Bahn-Kopplung}{}{}
\eq{\braket{\vec{S} \cdot \vec{L}} &= \frac{1}{2} \braket{[J^2-L^2-S^2]} \nonumber \\
&= \frac{\hbar^2}{2}[j(j+1) -l(l+1) -s(s+1)]}
\end{formula}
\Subsubsection[
\eng{Fine-structure}
\ger{Feinstruktur}
]{fine_structure}
\begin{ttext}[desc]
\eng{The fine-structure combines \fRef[relativistic corrections]{qm:h:corrections:darwin} and \fRef{qm:h:corrections:ls_coupling}.}
\ger{Die Feinstruktur vereint \fRef[relativistische Korrekturen]{qm:h:corrections:darwin} und \fRef{qm:h:corrections:ls_coupling}.}
\end{ttext}
\Subsubsection{fine_structure}
\desc{Fine-structure}{The fine-structure combines \fRef[relativistic corrections]{qm:h:corrections:darwin} and \fRef{qm:h:corrections:ls_coupling}.}{}
\desc[german]{Feinstruktur}{Die Feinstruktur vereint \fRef[relativistische Korrekturen]{qm:h:corrections:darwin} und \fRef{qm:h:corrections:ls_coupling}.}{}
\begin{formula}{energy_shift}
\desc{Energy shift}{}{}
\desc[german]{Energieverschiebung}{}{}
@ -143,28 +147,18 @@
\end{formula}
\Subsubsection[
\eng{Lamb-shift}
\ger{Lamb-Shift}
]{lamb_shift}
\begin{ttext}[desc]
\eng{The interaction of the electron with virtual photons emitted/absorbed by the nucleus leads to a (very small) shift in the energy level.}
\ger{The Wechselwirkung zwischen dem Elektron und vom Kern absorbierten/emittierten virtuellen Photonen führt zu einer (sehr kleinen) Energieverschiebung.}
\end{ttext}
\Subsubsection{lamb_shift}
\desc{Lamb-shift}{The interaction of the electron with virtual photons emitted/absorbed by the nucleus leads to a (very small) shift in the energy level.}{}
\desc[german]{Lamb-Shift}{The Wechselwirkung zwischen dem Elektron und vom Kern absorbierten/emittierten virtuellen Photonen führt zu einer (sehr kleinen) Energieverschiebung.}{}
\begin{formula}{energy}
\desc{Potential energy}{}{$\delta r$ pertubation of $r$}
\desc[german]{Potentielle Energy}{}{$\delta r$ Schwankung von $r$}
\eq{\braket{E_\textrm{pot}} = -\frac{Z e^2}{4\pi\epsilon_0} \Braket{\frac{1}{r+\delta r}}}
\end{formula}
\Subsubsection[
\eng{Hyperfine structure}
\ger{Hyperfeinstruktur}
]{hyperfine_structure}
\begin{ttext}[desc]
\eng{Interaction of the nucleus spin with the magnetic field created by the electron leads to energy shifts. (Lifts degeneracy) }
\ger{Wechselwirkung von Kernspin mit dem vom Elektron erzeugten Magnetfeld spaltet Energieniveaus}
\end{ttext}
\Subsubsection{hyperfine_structure}
\desc{Hyperfine structure}{Interaction of the nucleus spin with the magnetic field created by the electron leads to energy shifts. (Lifts degeneracy) }{}
\desc[german]{Hyperfeinstruktur}{Wechselwirkung von Kernspin mit dem vom Elektron erzeugten Magnetfeld spaltet Energieniveaus}{}
\begin{formula}{nuclear_spin}
\desc{Nuclear spin}{}{}
\desc[german]{Kernspin}{}{}
@ -199,17 +193,14 @@
\end{formula}
\TODO{landé factor}
\Subsection[
\eng{Effects in magnetic field}
\ger{Effekte im Magnetfeld}
]{mag_effects}
\Subsection{mag_effects}
\desc{Effects in magnetic field}{}{}
\desc[german]{Effekte im Magnetfeld}{}{}
\TODO{all}
\\\TODO{Hunds rules}
\Subsection[
\eng{misc}
\ger{Sonstiges}
]{other}
\Subsection{other}
\desc{misc}{}{}
\desc[german]{Sonstiges}{}{}
\begin{formula}{auger_effect}
\desc{Auger-Meitner-Effekt}{Auger-Effect}{}
\desc[german]{Auger-Meitner-Effekt}{Auger-Effekt}{}

8
src/qm/misc.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Other}
\ger{Sonstiges}
]{misc}
\Section{misc}
\desc{Other}{}{}
\desc[german]{Sonstiges}{}{}
\begin{formula}{RWA}
\desc{Rotating Wave Approximation (RWS)}{Rapidly oscilating terms are neglected}{$\omega_\text{L}$ light frequency, $\omega_0$ transition frequency}
\desc[german]{Rotating Wave Approximation / Drehwellennäherung (RWS)}{Schnell oscillierende Terme werden vernachlässigt}{$\omega_\text{L}$ Frequenz des Lichtes, $\omega_0$ Übergangsfrequenz}

196
src/qm/qm.tex
View File

@ -5,18 +5,23 @@
\def\sigmaybraket{-i \ket{0}\bra{1} + i \ket{1}\bra{0}}
\def\sigmazbraket{\ket{0}\bra{0} - \ket{1}\bra{1}}
\Part[
\eng{Quantum Mechanics}
\ger{Quantenmechanik}
]{qm}
\Section[
\eng{Basics}
\ger{Basics}
]{basics}
\Subsection[
\eng{Operators}
\ger{Operatoren}
]{op}
\Part{qm}
\desc{Quantum Mechanics}{}{}
\desc[german]{Quantenmechanik}{}{}
\Section{basics}
\desc{Basics}{}{}
\desc[german]{Basics}{}{}
\begin{formula}{correspondence_principle}
\desc{Correspondence principle}{}{}
\desc[german]{Korrespondenzprinzip}{}{}
\ttxt{
\ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
\eng{The equations of motion of classical mechanics can be derived from quantum mechanics in the limit of large quantum numbers.}
}
\end{formula}
\Subsection{op}
\desc{Operators}{}{}
\desc[german]{Operatoren}{}{}
\Ger[row_vector]{Zeilenvektor}
\Ger[column_vector]{Spaltenvektor}
\Eng[column_vector]{Column vector}
@ -53,14 +58,9 @@
\eq{\hat{A} = \hat{A}^\dagger}
\end{formula}
\Subsubsection[
\eng{Measurement}
\ger{Messung}
]{measurement}
\begin{ttext}
\eng{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}
\ger{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}
\end{ttext}
\Subsubsection{measurement}
\desc{Measurement}{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}{}
\desc[german]{Messung}{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}{}
\begin{formula}{name}
\desc{Measurement probability}{Probability to measure $\psi$ in state $\lambda$}{}
\desc[german]{Messwahrscheinlichkeit}{Wahrscheinlichkeit, $\psi$ im Zustand $\lambda$ zu messen}{}
@ -73,10 +73,9 @@
\end{formula}
\Subsubsection[
\eng{Pauli matrices}
\ger{Pauli-Matrizen}
]{pauli_matrices}
\Subsubsection{pauli_matrices}
\desc{Pauli matrices}{}{}
\desc[german]{Pauli-Matrizen}{}{}
\begin{formula}{pauli_matrices}
\desc{Pauli matrices}{}{}
\desc[german]{Pauli Matrizen}{}{}
@ -91,10 +90,10 @@
% $\sigma_y$ PHASE
% $\sigma_z$ Sign
\Subsection[
\ger{Wahrscheinlichkeitstheorie}
\eng{Probability theory}
]{probability}
\Subsection{probability}
\desc{Wahrscheinlichkeitstheorie}{}{}
\desc[german]{Probability theory}{}{}
\begin{formula}{conservation_of_probability}
\desc{Continuity equation}{}{$\rho$ density of a conserved quantity $q$, $j$ flux density of $q$}
\desc[german]{Kontinuitätsgleichung}{}{$\rho$ Dichte einer Erhaltungsgröße $q$, $j$ Fluß von $q$}
@ -102,9 +101,9 @@
\end{formula}
\begin{formula}{state_probability}
\desc{State probability}{}{}
\desc[german]{Zustandswahrscheinlichkeit}{}{}
\eq{TODO}
\desc{State probability}{Probability to measure eigenvale $n$}{$P_n$ projector, $n$ normalized eigenvalue of measurement operator with one-dimensional eigenspace}
\desc[german]{Zustandswahrscheinlichkeit}{Wahrscheinlicht, den Eigenwert $n$ zu messen}{$P_n$ Projektor, $n$ normalisierter Eigenwert des Messoperators mit ein-dimensionalem Eigenraum}
\eq{p_n = \Braket{\psi|P_n|\psi} = \Braket{\psi|n}\Braket{n|\psi} = \abs{\Braket{n|\psi}}^2 }
\end{formula}
\begin{formula}{dispersion}
@ -124,10 +123,9 @@
\end{formula}
\Subsection[
\eng{Commutator}
\ger{Kommutator}
]{commutator}
\Subsection{commutator}
\desc{Commutator}{}{}
\desc[german]{Kommutator}{}{}
\begin{formula}{commutator}
\desc{Commutator}{}{}
\desc[german]{Kommutator}{}{}
@ -174,10 +172,9 @@
}
\end{formula}
\Section[
\eng{Schrödinger equation}
\ger{Schrödingergleichung}
]{se}
\Section{se}
\desc{Schrödinger equation}{}{}
\desc[german]{Schrödingergleichung}{}{}
\abbrLink{se}{SE}
\begin{formula}{energy_operator}
\desc{Energy operator}{}{}
@ -228,11 +225,9 @@
}}
\end{formula}
\Subsection[
\eng{Time evolution}
\ger{Zeitentwicklug}
]{time}
The time evolution of the Hamiltonian is given by:
\Subsection{time}
\desc{Time evolution}{}{}
\desc[german]{Zeitentwicklug}{}{}
\begin{formula}{time_evolution_op}
\desc{Time evolution operator}{}{$U$ unitary}
\desc[german]{Zeitentwicklungsoperator}{}{$U$ unitär}
@ -255,18 +250,15 @@
\TODO{unitary transformation of time dependent H}
\Subsubsection[
\eng{Schrödinger- and Heisenberg-pictures}
\ger{Schrödinger- und Heisenberg-Bild}
]{s_h_pictures}
\eng[s_h_pictures_desc]{
\Subsubsection{s_h_pictures}
\desc{Schrödinger- and Heisenberg-pictures}{
In the \textbf{Schrödinger picture}, the time dependecy is in the states
while in the \textbf{Heisenberg picture} the observables (operators) are time dependent.
}
\ger[s_h_pictures_desc]{Im Schrödinger-Bild sind die Zustände zeitabhänig, im Heisenberg-Bild
}{}
\desc[german]{Schrödinger- und Heisenberg-Bild}{
Im Schrödinger-Bild sind die Zustände zeitabhänig, im Heisenberg-Bild
sind die Observablen (Operatoren) zeitabhänig
}
\gt{s_h_pictures_desc}\\
}{}
\begin{formula}{schroediner_time_evolution}
\desc{Schrödinger time evolution}{}{}
\desc[german]{Schrödinger Zeitentwicklug}{}{}
@ -285,12 +277,11 @@
}
\end{formula}
\Subsubsection[
\eng{Ehrenfest theorem}
\ger{Ehrenfest-Theorem}
]{ehrenfest_theorem}
\Subsubsection{ehrenfest_theorem}
\desc{Ehrenfest theorem}{\GT{see_also} \fRef{qm:se:time:ehrenfest_theorem:correspondence_principle}}{}
\desc[german]{Ehrenfest-Theorem}{}{}
\absLink{}{ehrenfest_theorem}
\GT{see_also} \fRef{qm:se:time:ehrenfest_theorem:correspondence_principle}
\begin{formula}{ehrenfest_theorem}
\desc{Ehrenfest theorem}{applies to both pictures}{}
\desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{}
@ -304,27 +295,13 @@
\eq{m\odv[2]{}{t}\braket{x} = -\braket{\nabla V(x)} = \braket{F(x)}}
\end{formula}
% \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time}
% TODO: wo gehört das hin?
\begin{formula}{correspondence_principle}
\desc{Correspondence principle}{}{}
\desc[german]{Korrespondenzprinzip}{}{}
\ttxt{
\ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
\eng{The classical mechanics can be derived from quantum mechanics in the limit of large quantum numbers.}
}
\end{formula}
\Section[
\eng{Pertubation theory}
\ger{Störungstheorie}
]{qm_pertubation}
\begin{ttext}
\eng{The following holds true if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}
\ger{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}
\end{ttext}
\Section{qm_pertubation}
\desc{Pertubation theory}{Applies if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}{}
\desc[german]{Störungstheorie}{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}{}
\begin{formula}{pertubation_hamiltonian}
\desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{}
@ -368,10 +345,9 @@
\end{formula}
\Section[
\eng{Harmonic oscillator}
\ger{Harmonischer Oszillator}
]{hosc}
\Section{hosc}
\desc{Harmonic oscillator}{}{}
\desc[german]{Harmonischer Oszillator}{}{}
\begin{formula}{hamiltonian}
\desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{}
@ -387,10 +363,9 @@
\eq{E_n = \hbar\omega \Big(\frac{1}{2} + n\Big)}
\end{formula}
\Subsection[
\ger{Erzeugungs und Vernichtungsoperatoren / Leiteroperatoren}
\eng{Creation and Annihilation operators / Ladder operators}
]{c_a_ops}
\Subsection{c_a_ops}
\desc{Erzeugungs und Vernichtungsoperatoren / Leiteroperatoren}{}{}
\desc[german]{Creation and Annihilation operators / Ladder operators}{}{}
\begin{formula}{c_a_ops_def}
\desc{Particle number operator/occupation number operator}{}{$\ket{n}$ = Fock states, $\hat{a}$ = Annihilation operator, $\hat{a}^\dagger$ = Creation operator}
\desc[german]{Teilchenzahloperator/Besetzungszahloperator}{}{$\ket{n}$ = Fock-Zustände, $\hat{a}$ = Vernichtungsoperator, $\hat{a}^\dagger$ = Erzeugungsoperator}
@ -445,10 +420,9 @@
}
\end{formula}
\Subsubsection[
\eng{Harmonischer Oszillator}
\ger{Harmonic Oscillator}
]{hosc}
\Subsubsection{hosc}
\desc{Harmonischer Oszillator}{}{}
\desc[german]{Harmonic Oscillator}{}{}
\begin{formula}{c_a_ops}
\desc{Harmonic oscillator}{}{}
\desc[german]{Harmonischer Oszillator}{}{}
@ -475,24 +449,21 @@
% E_n=( \frac{1}{2} +n)\hbar\omega
% \end{equation}
\Section[
\eng{Angular momentum}
\ger{Drehmoment}
]{angular_momentum}
\Section{angular_momentum}
\desc{Angular momentum}{}{}
\desc[german]{Drehmoment}{}{}
\Subsection[
\eng{Aharanov-Bohm effect}
\ger{Aharanov-Bohm Effekt}
]{aharanov_bohm}
\Subsection{aharanov_bohm}
\desc{Aharanov-Bohm effect}{}{}
\desc[german]{Aharanov-Bohm Effekt}{}{}
\begin{formula}{phase}
\desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{\QtyRef{magnetic_vector_potential}, \QtyRef{magnetic_flux}}
\desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{}
\eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
\end{formula}
\Section[
\eng{Periodic potentials}
\ger{Periodische Potentiale}
]{periodic}
\Section{periodic}
\desc{Periodic potentials}{}{}
\desc[german]{Periodische Potentiale}{}{}
\begin{formula}{bloch_waves}
\desc{Bloch waves}{
Solve the stat. SG in periodic potential with period
@ -519,24 +490,18 @@
\end{formula}
\Section[
\eng{Symmetries}
\ger{Symmetrien}
]{symmetry}
\begin{ttext}[desc]
\eng{Most symmetry operators are \fRef[unitary]{math:linalg:matrix:unitary} because the norm of a state must be invariant under transformations of space, time and spin.}
\ger{Die meisten Symmetrieoperatoren sind \fRef[unitär]{math:linalg:matrix:unitary}, da die Norm eines Zustands invariant unter Raum-, Zeit- und Spin-Transformationen sein muss.}
\end{ttext}
\Section{symmetry}
\desc{Symmetries}{Most symmetry operators are \fRef[unitary]{math:linalg:matrix:unitary} because the norm of a state must be invariant under transformations of space, time and spin.}{}
\desc[german]{Symmetrien}{Die meisten Symmetrieoperatoren sind \fRef[unitär]{math:linalg:matrix:unitary}, da die Norm eines Zustands invariant unter Raum-, Zeit- und Spin-Transformationen sein muss.}{}
\begin{formula}{invariance}
\desc{Invariance}{$\hat{H}$ is invariant under a symmetrie described by $\hat{U}$ if this holds}{}
\desc[german]{Invarianz}{$\hat{H}$ is invariant unter der von $\hat{U}$ beschriebenen Symmetrie wenn gilt:}{}
\eq{\hat{U}\hat{H}\hat{U}^\dagger = \hat{H} \Leftrightarrow [\hat{U}, \hat{H}] = 0}
\end{formula}
\Subsection[
\eng{Time-reversal symmetry}
\ger{Zeitumkehrungssymmetrie}
]{time_reversal}
\Subsection{time_reversal}
\desc{Time-reversal symmetry}{}{}
\desc[german]{Zeitumkehrungssymmetrie}{}{}
\begin{formula}{time}
\desc{Time-reversal symmetry}{}{}
@ -550,10 +515,9 @@
\eq{T^2 = -1}
\end{formula}
\Section[
\eng{Two-level systems (TLS)}
\ger{Zwei-Niveau System (TLS)}
]{tls}
\Section{tls}
\desc{Two-level systems (TLS)}{}{}
\desc[german]{Zwei-Niveau System (TLS)}{}{}
\begin{formula}{james_cummings}
\desc{James-Cummings Hamiltonian}{TLS interacting with optical cavity}{$\hat{E} = E_\text{ZPF}(\hat{a} + \hat{a}^\dagger)$ field operator with bosonic ladder operators, $\hat{S} = \hat{\sigma}^\dagger + \hat{\sigma}$ polarization operator with ladder operators of the TLS}
\desc[german]{James-Cummings Hamiltonian}{TLS interagiert mit resonantem Lichtfeld}{$\hat{E} = E_\text{ZPF}(\hat{a} + \hat{a}^\dagger)$ Feldoperator mit bosonischen Leiteroperatoren, $\hat{S} = \hat{\sigma}^\dagger + \hat{\sigma}$ Polarisationsoperator mit Leiteroperatoren des TLS}

42
src/quantities.tex
View File

@ -3,15 +3,13 @@
% 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
\Section[
\eng{Physical quantities}
\ger{Physikalische Größen}
]{quantities}
\Section{quantities}
\desc{Physical quantities}{}{}
\desc[german]{Physikalische Größen}{}{}
\Subsection[
\eng{SI quantities}
\ger{SI-Basisgrößen}
]{si}
\Subsection{si}
\desc{SI quantities}{}{}
\desc[german]{SI-Basisgrößen}{}{}
\begin{formula}{time}
\desc{Time}{}{}
\desc[german]{Zeit}{}{}
@ -54,10 +52,9 @@
\quantity{I_\text{V}}{\candela}{s}
\end{formula}
\Subsection[
\eng{Mechanics}
\ger{Mechanik}
]{mech}
\Subsection{mech}
\desc{Mechanics}{}{}
\desc[german]{Mechanik}{}{}
\begin{formula}{force}
\desc{Force}{}{}
\desc[german]{Kraft}{}{}
@ -89,10 +86,9 @@
\end{formula}
\Subsection[
\eng{Thermodynamics}
\ger{Thermodynamik}
]{td}
\Subsection{td}
\desc{Thermodynamics}{}{}
\desc[german]{Thermodynamik}{}{}
\begin{formula}{volume}
\desc{Volume}{$d$ dimensional Volume}{}
\desc[german]{Volumen}{$d$ dimensionales Volumen}{}
@ -110,10 +106,9 @@
\quantity{\rho}{\kg\per\m^3}{s}
\end{formula}
\Subsection[
\eng{Electrodynamics}
\ger{Elektrodynamik}
]{el}
\Subsection{el}
\desc{Electrodynamics}{}{}
\desc[german]{Elektrodynamik}{}{}
\begin{formula}{charge}
\desc{Charge}{}{}
\desc[german]{Ladung}{}{}
@ -197,10 +192,9 @@
\quantity{L}{\henry=\kg\m^2\per\s^2\ampere^2=\weber\per\ampere=\volt\s\per\ampere=\ohm\s}{s}
\end{formula}
\Subsection[
\eng{Others}
\ger{Sonstige}
]{other}
\Subsection{other}
\desc{Others}{}{}
\desc[german]{Sonstige}{}{}
\begin{formula}{area}
\desc{Area}{}{}
\desc[german]{Fläche}{}{}

131
src/quantum_computing.tex
View File

@ -1,12 +1,11 @@
\Part[
\eng{Quantum Computing}
\ger{Quantencomputing}
]{qc}
\Part{qc}
\desc{Quantum Computing}{}{}
\desc[german]{Quantencomputing}{}{}
\Section[
\eng{Qubits}
\ger{Qubits}
]{qubit}
\Section{qubit}
\desc{Qubits}{}{}
\desc[german]{Qubits}{}{}
\begin{formula}{bloch_sphere}
\desc{Bloch sphere}{}{}
\desc[german]{Bloch-Sphäre}{}{}
@ -17,10 +16,9 @@
}
\end{formula}
\Section[
\eng{Gates}
\ger{Gates}
]{gates}
\Section{gates}
\desc{Gates}{}{}
\desc[german]{Gates}{}{}
\begin{formula}{gates}
\desc{Gates}{}{}
\desc[german]{Gates}{}{}
@ -40,23 +38,16 @@
% \item \gt{bitphaseflip}: $\hat{Y} = \sigma_y = \sigmaymatrix$
% \item \gt{phaseflip}: $\hat{Z} = \sigma_z = \sigmazmatrix$ \item \gt{hadamard}: $\hat{H} = \frac{1}{\sqrt{2}}(\hat{X}-\hat{Z}) = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$
% \end{itemize}
\Section[
\eng{Superconducting qubits}
\ger{Supraleitende qubits}
]{scq}
\Section{scq}
\desc{Superconducting qubits}{}{}
\desc[german]{Supraleitende qubits}{}{}
\Subsection[
\eng{Building blocks}
\ger{Bauelemente}
]{elements}
\Subsubsection[
\eng{Josephson Junction}
\ger{Josephson-Kontakt}
]{josephson_junction}
\begin{ttext}[desc]
\eng{When two superconductors are separated by a thin isolator, Cooper pairs can tunnel through the insulator. The Josephson junction is a non-linear inductor.}
\ger{Wenn zwei Supraleiter durch einen dünnen Isolator getrennt sind, können Cooper-Paare durch den Isolator tunneln. Der Josephson-Kontakt ist ein nicht-linearer Induktor.}
\end{ttext}
\Subsection{elements}
\desc{Building blocks}{}{}
\desc[german]{Bauelemente}{}{}
\Subsubsection{josephson_junction}
\desc{Josephson Junction}{When two superconductors are separated by a thin isolator, Cooper pairs can tunnel through the insulator. The Josephson junction is a non-linear inductor.}{}
\desc[german]{Josephson-Kontakt}{Wenn zwei Supraleiter durch einen dünnen Isolator getrennt sind, können Cooper-Paare durch den Isolator tunneln. Der Josephson-Kontakt ist ein nicht-linearer Induktor.}{}
\begin{formula}{hamiltonian}
\desc{Josephson-Hamiltonian}{}{}
@ -78,10 +69,9 @@
\eq{\odv{\hat{\delta}}{t}=\frac{1}{i\hbar}[\hat{H},\hat{\delta}] = -\frac{2eU}{i\hbar}[\hat{n},\hat{\delta}] = \frac{1}{\varphi_0} U}
\end{formula}
\Subsubsection[
\eng{SQUID}
\ger{SQUID}
]{squid}
\Subsubsection{squid}
\desc{SQUID}{}{}
\desc[german]{SQUID}{}{}
\ctikzsubcircuitdef{squidloop}{n, s, nw, ne, se, sw}{
% start at top
coordinate(#1-n)
@ -107,10 +97,9 @@
\eq{\hat{H} &= -E_{\text{J}1} \cos\hat{\phi}_{1} - E_{\text{J}2} \cos\hat{\phi}_{2}}
\end{formula}
\Subsection[
\eng{Josephson junction based qubits}
\ger{Qubits mit Josephson-Junctions}
]{josephson_qubit}
\Subsection{josephson_qubit}
\desc{Josephson junction based qubits}{}{}
\desc[german]{Qubits mit Josephson-Junctions}{}{}
\begin{formula}{circuit}
\desc{General circuit}{}{}
@ -194,20 +183,18 @@
\end{bigformula}
\Subsection[
\eng{Charge based qubits}
\ger{Ladungsbasierte Qubits}
]{charge}
\Subsection{charge}
\desc{Charge based qubits}{}{}
\desc[german]{Ladungsbasierte Qubits}{}{}
\begin{bigformula}{comparison}
\desc{Comparison of charge qubit states}{}{}
\desc[german]{Vergleich der Zustände von Ladungsbasierten Qubits}{}{}
\fig{img/qubit_transmon.pdf}
\end{bigformula}
\Subsubsection[
\eng{Cooper Pair Box (CPB) qubit}
\ger{Cooper Paar Box (QPB) Qubit}
]{cpb}
\Subsubsection{cpb}
\desc{Cooper Pair Box (CPB) qubit}{}{}
\desc[german]{Cooper Paar Box (QPB) Qubit}{}{}
\begin{ttext}
\eng{
= voltage bias junction\\= charge qubit?
@ -245,10 +232,9 @@
&=\sum_n \left[4 E_C (n-n_\text{g})^2 \ket{n}\bra{n} - \frac{E_\text{J}}{2}\ket{n}\bra{n+1}+\ket{n+1}\bra{n}\right] }
\end{formula}
\Subsubsection[
\eng{Transmon qubit}
\ger{Transmon Qubit}
]{transmon}
\Subsubsection{transmon}
\desc{Transmon qubit}{}{}
\desc[german]{Transmon Qubit}{}{}
\begin{formula}{circuit}
\desc{Transmon qubit}{
Josephson junction with a shunt \textbf{capacitance}.
@ -279,10 +265,9 @@
\eq{\hat{H} &= 4 E_C\hat{n}^2 - E_\text{J} \cos\hat{\phi}}
\end{formula}
\Subsubsection[
\eng{Tunable Transmon qubit}
\ger{Tunable Transmon Qubit}
]{tunable}
\Subsubsection{tunable}
\desc{Tunable Transmon qubit}{}{}
\desc[german]{Tunable Transmon Qubit}{}{}
\begin{formula}{circuit}
\desc{Frequency tunable transmon}{By using a \fRef{qc:scq:elements:squid} instead of a \fRef{qc:scq:elements:josephson_junction}, the qubit is frequency tunable through an external field}{}
\desc[german]{}{Durch Nutzung eines \fRef{qc:scq:elements:squid} anstatt eines \fRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{}
@ -309,19 +294,17 @@
\Subsection[
\eng{Inductive qubits}
\ger{Induktive Qubits}
]{inductive}
\Subsection{inductive}
\desc{Inductive qubits}{}{}
\desc[german]{Induktive Qubits}{}{}
\begin{bigformula}{comparison}
\desc{Comparison of other qubit states}{}{}
\desc[german]{Vergleich der Zustände von anderen Qubits}{}{}
\fig{img/qubit_flux_onium.pdf}
\end{bigformula}
\Subsubsection[
\eng{Phase qubit}
\ger{Phase Qubit}
]{phase}
\Subsubsection{phase}
\desc{Phase qubit}{}{}
\desc[german]{Phase Qubit}{}{}
\begin{formula}{circuit}
\desc{Phase qubit}{}{}
\desc[german]{Phase Qubit}{}{}
@ -348,10 +331,9 @@
\eq{\hat{H} = E_C \hat{n}^2 - E_J \cos \hat{\delta} + E_L(\hat{\delta} - \delta_s)^2}
\end{formula}
\Subsubsection[
\eng{Flux qubit}
\ger{Flux Qubit}
]{flux}
\Subsubsection{flux}
\desc{Flux qubit}{}{}
\desc[german]{Flux Qubit}{}{}
\begin{formula}{circuit}
\desc{Flux qubit / Persistent current qubit}{}{}
\desc[german]{Flux Qubit / Persistent current qubit}{}{}
@ -384,10 +366,9 @@
\end{formula}
\Subsubsection[
\eng{Fluxonium qubit}
\ger{Fluxonium Qubit}
]{fluxonium}
\Subsubsection{fluxonium}
\desc{Fluxonium qubit}{}{}
\desc[german]{Fluxonium Qubit}{}{}
\begin{formula}{circuit}
\desc{Fluxonium qubit}{
Josephson junction with a shunt \textbf{inductance}. Instead of having to tunnel, cooper pairs can move to the island via the inductance.
@ -418,10 +399,9 @@
\Section[
\eng{Two-level system}
\ger{Zwei-Niveau System}
]{stuff}
\Section{stuff}
\desc{Two-level system}{}{}
\desc[german]{Zwei-Niveau System}{}{}
\begin{formula}{resonance_frequency}
\desc{Resonance frequency}{}{}
@ -444,10 +424,9 @@
\end{ttext}
\end{formula}
\Section[
\eng{Noise and decoherence}
\ger{Noise und Dekohärenz}
]{noise}
\Section{noise}
\desc{Noise and decoherence}{}{}
\desc[german]{Noise und Dekohärenz}{}{}
\begin{formula}{long}
\desc{Longitudinal relaxation rate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{}
\desc[german]{Longitudinale Relaxationsrate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{}

8
src/spv.tex
View File

@ -1,7 +1,7 @@
\Section[
\eng{Surface-Photovoltage}
\ger{Oberflächen-Photospannung}
]{spv}
\Section{spv}
\desc{Surface-Photovoltage}{}{}
\desc[german]{Oberflächen-Photospannung}{}{}
Mechanisms:
\begin{formula}{scr}
\desc{Space-charge regions}{}{}

169
src/statistical_mechanics.tex
View File

@ -1,7 +1,7 @@
\Part[
\eng{Statistichal Mechanics}
\ger{Statistische Mechanik}
]{stat}
\Part{stat}
\desc{Statistichal Mechanics}{}{}
\desc[german]{Statistische Mechanik}{}{}
\begin{ttext}
\eng{
@ -20,10 +20,9 @@
\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}
\Section{entropy}
\desc{Entropy}{}{}
\desc[german]{Entropie}{}{}
\begin{formula}{properties}
\desc{Positive-definite and additive}{}{}
@ -64,10 +63,9 @@
\eq{p = T \pdv{S}{V}_E}
\end{formula}
\Part[
\eng{Thermodynamics}
\ger{Thermodynamik}
]{td}
\Part{td}
\desc{Thermodynamics}{}{}
\desc[german]{Thermodynamik}{}{}
\begin{formula}{therm_wavelength}
\desc{Thermal wavelength}{}{}
@ -75,10 +73,9 @@
\eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
\end{formula}
\Section[
\eng{Processes}
\ger{Prozesse}
]{process}
\Section{process}
\desc{Processes}{}{}
\desc[german]{Prozesse}{}{}
\begin{ttext}
\eng{
\begin{itemize}
@ -106,10 +103,9 @@
}
\end{ttext}
\Subsection[
\eng{Irreversible gas expansion (Gay-Lussac experiment)}
\ger{Irreversible Gasexpansion (Gay-Lussac-Versuch)}
]{gay}
\Subsection{gay}
\desc{Irreversible gas expansion (Gay-Lussac experiment)}{}{}
\desc[german]{Irreversible Gasexpansion (Gay-Lussac-Versuch)}{}{}
\begin{bigformula}{experiment}
\desc{Gay-Lussac experiment}{}{}
@ -151,10 +147,9 @@
\TODO{Joule-Thompson Prozess}
\Section[
\eng{Phase transitions}
\ger{Phasenübergänge}
]{phases}
\Section{phases}
\desc{Phase transitions}{}{}
\desc[german]{Phasenübergänge}{}{}
\begin{ttext}
\eng{
@ -189,10 +184,9 @@
\eq{f = c - p + 2}
\end{formula}
\Subsubsection[
\eng{Osmosis}
\ger{Osmose}
]{osmosis}
\Subsubsection{osmosis}
\desc{Osmosis}{}{}
\desc[german]{Osmose}{}{}
\begin{ttext}
\eng{
Osmosis is the spontaneous net movement or diffusion of solvent molecules
@ -215,10 +209,9 @@
\end{formula}
\Subsection[
\eng{Material properties}
\ger{Materialeigenschaften}
]{props}
\Subsection{props}
\desc{Material properties}{}{}
\desc[german]{Materialeigenschaften}{}{}
\begin{formula}{heat_capacity}
\desc{Heat capacity}{}{\QtyRef{heat}}
\desc[german]{Wärmekapazität}{}{}
@ -269,15 +262,13 @@
\Section[
\eng{Laws of thermodynamics}
\ger{Hauptsätze der Thermodynamik}
]{laws}
\Section{laws}
\desc{Laws of thermodynamics}{}{}
\desc[german]{Hauptsätze der Thermodynamik}{}{}
\Subsection[
\eng{Zeroeth law}
\ger{Nullter Hauptsatz}
]{law0}
\Subsection{law0}
\desc{Zeroeth law}{}{}
\desc[german]{Nullter Hauptsatz}{}{}
\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.}
@ -291,10 +282,9 @@
A \ggwarrow C \quad\wedge\quad B \ggwarrow C \quad\Rightarrow\quad A \ggwarrow B
\end{equation}
\Subsection[
\eng{First law}
\ger{Erster Hauptsatz}
]{law1}
\Subsection{law1}
\desc{First law}{}{}
\desc[german]{Erster Hauptsatz}{}{}
\begin{ttext}
\eng{In a process without transfer of matter, the change in internal energy, $\Delta U$, of a thermodynamic system is equal to the energy gained as heat, $Q$, less the thermodynamic work, W, done by the system on its surroundings.}
\ger{In einem abgeschlossenem System ist die Änderung der inneren Energie $U$ gleich der gewonnenen Wärme $Q$ minus der vom System an der Umgebung verrichteten Arbeit $W$.}
@ -310,10 +300,9 @@
\end{formula}
\Subsection[
\eng{Second law}
\ger{Zweiter Hauptsatz}
]{law2}
\Subsection{law2}
\desc{Second law}{}{}
\desc[german]{Zweiter Hauptsatz}{}{}
\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.\\
@ -324,10 +313,9 @@
\textbf{Kelvin}: Es ist unmöglich, eine periodisch arbeitende Maschine zu konstruieren, die weiter nichts bewirkt als Hebung einer Last und Abkühlung eines Wärmereservoirs.
}
\end{ttext}
\Subsection[
\eng{Third law}
\ger{Dritter Hauptsatz}
]{law3}
\Subsection{law3}
\desc{Third law}{}{}
\desc[german]{Dritter Hauptsatz}{}{}
\begin{ttext}
\eng{It is impussible to cool a system to absolute zero.}
\ger{Es ist unmöglich, ein System bis zum absoluten Nullpunkt abzukühlen.}
@ -343,10 +331,9 @@
}
\end{formula}
\Section[
\eng{Ensembles}
\ger{Ensembles}
]{ensembles}
\Section{ensembles}
\desc{Ensembles}{}{}
\desc[german]{Ensembles}{}{}
\Eng[const_variables]{Constant variables}
\Ger[const_variables]{Konstante Variablen}
@ -425,10 +412,9 @@
\end{formula}
\Subsection[
\eng{Potentials}
\ger{Potentiale}
]{pots}
\Subsection{pots}
\desc{Potentials}{}{}
\desc[german]{Potentiale}{}{}
\begin{formula}{internal_energy}
\desc{Internal energy}{}{}
\desc[german]{Innere Energie}{}{}
@ -484,10 +470,9 @@
}
\end{formula}
\Section[
\eng{Ideal gas}
\ger{Ideales Gas}
]{id_gas}
\Section{id_gas}
\desc{Ideal gas}{}{}
\desc[german]{Ideales Gas}{}{}
\begin{ttext}
\eng{The ideal gas consists of non-interacting, undifferentiable particles.}
\ger{Das ideale Gas besteht aus nicht-wechselwirkenden, ununterscheidbaren Teilchen.}
@ -550,10 +535,9 @@
\eq{\braket{v^2} = \int_0^\infty \d v\,v^2 w(v) = \frac{3\kB T}{m}}
\end{formula}
\Subsubsection[
\eng{Molecule gas}
\ger{Molekülgas}
]{molecule_gas}
\Subsubsection{molecule_gas}
\desc{Molecule gas}{}{}
\desc[german]{Molekülgas}{}{}
\begin{formula}{desc}
\desc{Molecule gas}{2 particles of mass $M$ connected by a ``spring'' with distance $L$}{}
@ -592,15 +576,13 @@
\TODO{Diagram für verschiedene Temperaturen, Weiler Skript p.83}
\Section[
\eng{Real gas}
\ger{Reales Gas}
]{real_gas}
\Section{real_gas}
\desc{Real gas}{}{}
\desc[german]{Reales Gas}{}{}
\Subsection[
\eng{Virial expansion}
\ger{Virialentwicklung}
]{virial}
\Subsection{virial}
\desc{Virial expansion}{}{}
\desc[german]{Virialentwicklung}{}{}
\begin{ttext}
\eng{Expansion of the pressure $p$ in a power series of the density $\rho$.}
\ger{Entwicklung desw Drucks $p$ in eine Potenzreihe der Dichte $\rho$.}
@ -633,10 +615,9 @@
\eq{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
\end{formula}
\Subsection[
\eng{Van der Waals equation}
\ger{Van der Waals Gleichung}
]{vdw}
\Subsection{vdw}
\desc{Van der Waals equation}{}{}
\desc[german]{Van der Waals Gleichung}{}{}
\begin{ttext}
\eng{Assumes a hard-core potential with a weak attraction.}
\ger{Annahme eines Harte-Kugeln Potentials mit einer schwachen Anziehung}
@ -654,10 +635,9 @@
\TODO{sometimes N is included in a, b}
\Section[
\eng{Ideal quantum gas}
\ger{Ideales Quantengas}
]{id_qgas}
\Section{id_qgas}
\desc{Ideal quantum gas}{}{}
\desc[german]{Ideales Quantengas}{}{}
\def\bosfer{$\pm$: {$\text{bos} \atop \text{fer}$}}
\begin{formula}{fugacity}
@ -746,10 +726,9 @@
\eq{\left. \begin{array}{l}g_\nu(z)\\f_\nu(z)\end{array}\right\} \coloneq \frac{1}{\Gamma(\nu)} \int_0^\infty \d x\, \frac{x^{\nu-1}}{\e^x z^{-1} \mp 1}}
\end{formula}
\Subsection[
\eng{Bosons}
\ger{Bosonen}
]{bos}
\Subsection{bos}
\desc{Bosons}{}{}
\desc[german]{Bosonen}{}{}
\begin{formula}{partition-sum}
\desc{Partition sum}{}{$p \in\N_0$}
\desc[german]{Zustandssumme}{}{$p \in\N_0$}
@ -762,10 +741,9 @@
\end{formula}
\Subsection[
\eng{Fermions}
\ger{Fermionen}
]{fer}
\Subsection{fer}
\desc{Fermions}{}{}
\desc[german]{Fermionen}{}{}
\begin{formula}{partition_sum}
\desc{Partition sum}{}{$p = 0,\,1$}
\desc[german]{Zustandssumme}{}{$p = 0,\,1$}
@ -815,10 +793,9 @@
\eq{v = \frac{N}{V} = \frac{g}{\lambda^3}f_{3/2}(z)}
\end{formula}
\Subsubsection[
\eng{Strong degeneracy}
\ger{Starke Entartung}
]{degenerate}
\Subsubsection{degenerate}
\desc{Strong degeneracy}{}{}
\desc[german]{Starke Entartung}{}{}
\eng[low_temps]{for low temperatures $T \ll T_\text{F}$}
\ger[low_temps]{für geringe Temperaturen $T\ll T_\text{F}$}

30
src/test.tex
View File

@ -103,3 +103,33 @@ Link to defined quantity: \qtyRef{mass}
\end{formula}
\newpage
\Section{layout}
\desc{Layout Test}{}{}
\desc[german]{}{}{}
\begin{formula}{tt1}
\desc{Formula}{Desc}{Defs}
\eq{E=mc^2}
\end{formula}
\begin{bigformula}{tt2}
\desc{Big formula}{Desc}{Defs}
\eq{E=mc^3}
\end{bigformula}
\begin{formulagroup}{tt3}
\desc{Formula group}{Desc}{Defs}
\begin{formula}{tt1}
\desc{Formula}{Desc}{Defs}
\eq{E=mc^2}
\end{formula}
\begin{bigformula}{tt2}
\desc{Big formula}{Desc}{Defs}
\eq{E=mc^3}
\end{bigformula}
\end{formulagroup}

20
src/util/environments.tex
View File

@ -29,8 +29,8 @@
%
% DISTRIBUTION
%
\def\distrightwidth{0.45\textwidth}
\def\distleftwidth{0.45\textwidth}
\def\distrightwidth{0.45}
\def\distleftwidth{0.45}
% Table for distributions
% create entries for parameters using \disteq
@ -57,16 +57,14 @@
& ##2 \\ \hline
}
\hfill
\begin{minipage}{\distrightwidth}
\begingroup
\setlength{\tabcolsep}{0.9em} % horizontal
\renewcommand{\arraystretch}{2} % vertical
\begin{tabular}{|l|>{$\displaystyle}c<{$}|}
\hline
\begingroup
\setlength{\tabcolsep}{0.9em} % horizontal
\renewcommand{\arraystretch}{2} % vertical
\begin{tabular}{|l|>{$\displaystyle}c<{$}|}
\hline
}{
\end{tabular}
\endgroup
\end{minipage}
\end{tabular}
\endgroup
}
% A 2 column table in a minipage