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refactor sectioning

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This commit is contained in:
matthias@quintern.xyz 2025-03-21 22:48:38 +01:00
parent 2674545117
commit 702fc1eb33
47 changed files with 1196 additions and 1383 deletions

15
scripts/distributions.py

@ -24,6 +24,20 @@ def gauss():
ax.legend() ax.legend()
return fig 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 # CAUCHY / LORENTZ
def fcauchy(x, x_0, gamma): def fcauchy(x, x_0, gamma):
return 1 / (np.pi * gamma * (1 + ((x - x_0)/gamma)**2)) return 1 / (np.pi * gamma * (1 + ((x - x_0)/gamma)**2))
@ -128,6 +142,7 @@ def binomial():
if __name__ == '__main__': if __name__ == '__main__':
export(gauss(), "distribution_gauss") export(gauss(), "distribution_gauss")
export(laplace(), "distribution_laplace")
export(cauchy(), "distribution_cauchy") export(cauchy(), "distribution_cauchy")
export(maxwell(), "distribution_maxwell-boltzmann") export(maxwell(), "distribution_maxwell-boltzmann")
export(gamma(), "distribution_gamma") export(gamma(), "distribution_gamma")

15
src/ch/ch.tex

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

64
src/ch/el.tex

@ -1,7 +1,7 @@
\Section[ \Section{el}
\eng{Electrochemistry} \desc{Electrochemistry}{}{}
\ger{Elektrochemie} \desc[german]{Elektrochemie}{}{}
]{el}
\begin{formula}{chemical_potential} \begin{formula}{chemical_potential}
\desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{free_enthalpy}, \QtyRef{amount}} \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}{} \desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
@ -38,10 +38,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{cell}
\eng{Electrochemical cell} \desc{Electrochemical cell}{}{}
\ger{Elektrochemische Zelle} \desc[german]{Elektrochemische Zelle}{}{}
]{cell}
\eng[galvanic]{galvanic} \eng[galvanic]{galvanic}
\ger[galvanic]{galvanisch} \ger[galvanic]{galvanisch}
\eng[electrolytic]{electrolytic} \eng[electrolytic]{electrolytic}
@ -162,10 +161,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{ion_cond}
\eng{Ionic conduction in electrolytes} \desc{Ionic conduction in electrolytes}{}{}
\ger{Ionische Leitung in Elektrolyten} \desc[german]{Ionische Leitung in Elektrolyten}{}{}
]{ion_cond}
\eng[z]{charge number} \eng[z]{charge number}
\ger[z]{Ladungszahl} \ger[z]{Ladungszahl}
\eng[of_i]{of ion $i$} \eng[of_i]{of ion $i$}
@ -280,10 +278,9 @@
\eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}} \eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
\end{formula} \end{formula}
\Subsection[ \Subsection{kin}
\eng{Kinetics} \desc{Kinetics}{}{}
\ger{Kinetik} \desc[german]{Kinetik}{}{}
]{kin}
\begin{formula}{transfer_coefficient} \begin{formula}{transfer_coefficient}
\desc{Transfer coefficient}{}{} \desc{Transfer coefficient}{}{}
\desc[german]{Durchtrittsfaktor}{Transferkoeffizient\\Anteil des Potentials der sich auf die freie Reaktionsenthalpie des anodischen Prozesses auswirkt}{} \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}} \eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{mass}
\eng{Mass transport} \desc{Mass transport}{}{}
\ger{Massentransport} \desc[german]{Massentransport}{}{}
]{mass}
\begin{formula}{concentration_overpotential} \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{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}{} \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[ \Subsection{tech}
\eng{Techniques} \desc{Techniques}{}{}
\ger{Techniken} \desc[german]{Techniken}{}{}
]{tech}
\Subsubsection[ \Subsubsection{ref}
\eng{Reference electrodes} \desc{Reference electrodes}{}{}
\ger{Referenzelektroden} \desc[german]{Referenzelektroden}{}{}
]{ref}
\begin{ttext} \begin{ttext}
\eng{Defined as reference for measuring half-cell potententials} \eng{Defined as reference for measuring half-cell potententials}
\ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen} \ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
@ -522,10 +516,9 @@
\Subsubsection[ \Subsubsection{cv}
\eng{Cyclic voltammetry} \desc{Cyclic voltammetry}{}{}
\ger{Zyklische Voltammetrie} \desc[german]{Zyklische Voltammetrie}{}{}
]{cv}
\begin{bigformula}{duck} \begin{bigformula}{duck}
\desc{Cyclic voltammogram}{}{} \desc{Cyclic voltammogram}{}{}
% \desc[german]{}{}{} % \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}} \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} \end{formula}
\Subsubsection[ \Subsubsection{ac}
\eng{AC-Impedance} \desc{AC-Impedance}{}{}
\ger{AC-Impedanz} \desc[german]{AC-Impedanz}{}{}
]{ac}
\begin{formula}{nyquist} \begin{formula}{nyquist}
\desc{Nyquist diagram}{Real and imaginary parts of \qtyRef{impedance} while varying the frequency}{} \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}{} \desc[german]{Nyquist-Diagram}{Real und Imaginaärteil der \qtyRef{impedance} während die Frequenz variiert wird}{}

15
src/ch/misc.tex

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

129
src/cm/charge_transport.tex

@ -1,11 +1,10 @@
\Section[ \Section{charge_transport}
\eng{Charge transport} \desc{Charge transport}{}{}
\ger{Ladungstransport} \desc[german]{Ladungstransport}{}{}
]{charge_transport}
\Subsection[ \Subsection{drude}
\eng{Drude model} \desc{Drude model}{}{}
\ger{Drude-Modell} \desc[german]{Drude-Modell}{}{}
]{drude}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}
@ -48,10 +47,9 @@
\eq{\sigma = \frac{\vec{j}}{\vec{\E}} = \frac{n e^2 \tau}{\masse} = n e \mu} \eq{\sigma = \frac{\vec{j}}{\vec{\E}} = \frac{n e^2 \tau}{\masse} = n e \mu}
\end{formula} \end{formula}
\Subsection[ \Subsection{sommerfeld}
\eng{Sommerfeld model} \desc{Sommerfeld model}{}{}
\ger{Sommerfeld-Modell} \desc[german]{Sommerfeld-Modell}{}{}
]{sommerfeld}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \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}} \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} \end{formula}
\Subsection[ \Subsection{boltzmann}
\eng{Boltzmann-transport} \desc{Boltzmann-transport}{}{}
\ger{Boltzmann-Transport} \desc[german]{Boltzmann-Transport}{}{}
]{boltzmann}
\begin{ttext} \begin{ttext}
\eng{Semiclassical description using a probability distribution (\fRef{cm:sc:fermi_dirac}) to describe the particles.} \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}).} \ger{Semiklassische Beschreibung, benutzt eine Wahrscheinlichkeitsverteilung (\fRef{cm:sc:fermi_dirac}).}
@ -82,10 +79,9 @@
} }
\end{formula} \end{formula}
\Subsection[ \Subsection{mag}
\eng{Magneto-transport} \desc{Magneto-transport}{}{}
\ger{Magnetotransport} \desc[german]{Magnetotransport}{}{}
]{mag}
\begin{formula}{cyclotron_frequency} \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{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}{} \desc[german]{Zyklotronfrequenz}{Ladungstraäger bewegen sich in einem Magnetfeld auf einer Kreisbahn}{}
@ -98,13 +94,96 @@
% \desc[german]{}{}{} % \desc[german]{}{}{}
% \eq{} % \eq{}
% \end{formula} % \end{formula}
\TODO{move hall here}
\Subsubsection{hall}
\desc{Hall-Effect}{}{}
\desc[german]{Hall-Effekt}{}{}
\Subsection[ \Paragraph{classic}
\eng{misc} \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.}{}
\ger{misc} \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.}{}
]{misc} \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{misc}
\desc{misc}{}{}
\desc[german]{misc}{}{}
\begin{formula}{tsu_esaki} \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{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 $\mu_i$} \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

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

42
src/cm/crystal.tex

@ -1,11 +1,11 @@
\Section[ \Section{crystal}
\eng{Crystals} \desc{Crystals}{}{}
\ger{Kristalle} \desc[german]{Kristalle}{}{}
]{crystal}
\Subsection[ \Subsection{bravais}
\eng{Bravais lattice} \desc{Bravais lattice}{}{}
\ger{Bravais-Gitter} \desc[german]{Bravais-Gitter}{}{}
]{bravais}
\Eng[lattice_system]{Lattice system} \Eng[lattice_system]{Lattice system}
\Ger[lattice_system]{Gittersystem} \Ger[lattice_system]{Gittersystem}
\Eng[crystal_family]{Crystal system} \Eng[crystal_family]{Crystal system}
@ -197,14 +197,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{reci}
\eng{Reciprocal lattice} \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.}{}
\ger{Reziprokes Gitter} \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.}{}
]{reci}
\begin{ttext}
\eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
\ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
\end{ttext}
\begin{formula}{vectors} \begin{formula}{vectors}
\desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell} \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}} \eq{\vec{G}_{{hkl}} = h \vec{b_1} + k \vec{b_2} + l \vec{b_3}}
\end{formula} \end{formula}
\Subsection[ \Subsection{scatter}
\eng{Scattering processes} \desc{Scattering processes}{}{}
\ger{Streuprozesse} \desc[german]{Streuprozesse}{}{}
]{scatter}
\begin{formula}{matthiessen} \begin{formula}{matthiessen}
\desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{\QtyRef{mobility}, \QtyRef{scattering_time}} \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}{} \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{}
@ -235,10 +229,10 @@
} }
\end{formula} \end{formula}
\Subsection[ \Subsection{lat}
\eng{Lattices} \desc{Lattices}{}{}
\ger{Gitter} \desc[german]{Gitter}{}{}
]{lat}
\begin{formula}{sc} \begin{formula}{sc}
\desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}} \desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}}
\desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{} \desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{}

36
src/cm/egas.tex

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

8
src/cm/mat.tex

@ -1,7 +1,7 @@
\Section[ \Section{mat}
\eng{Material physics} \desc{Material physics}{}{}
\ger{Materialphysik} \desc[german]{Materialphysik}{}{}
]{mat}
\begin{formula}{tortuosity} \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} \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

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

56
src/cm/semiconductors.tex

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

72
src/cm/superconductivity.tex

@ -4,21 +4,15 @@
\def\Tcrit{T_\text{c}} \def\Tcrit{T_\text{c}}
\def\Bcth{B_\text{c,th}} \def\Bcth{B_\text{c,th}}
\Section[ \Section{super}
\eng{Superconductivity} \desc{Superconductivity}{
\ger{Supraleitung}
]{super}
\begin{ttext}
\eng{
Materials for which the electric resistance jumps to 0 under a critical temperature $\Tcrit$. 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 $\Bcth$. 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. 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 $\Bcth$. Sie verhalten sich dann wie ideale Leiter und ideale Diamagnete, bis zu einem kritischen Feld $\Bcth$.
}{}
}
\end{ttext}
\begin{formula}{type1} \begin{formula}{type1}
\desc{Type-I superconductor}{}{} \desc{Type-I superconductor}{}{}
@ -92,10 +86,9 @@
} }
\end{formula} \end{formula}
\Subsection[ \Subsection{london}
\eng{London Theory} \desc{London Theory}{}{}
\ger{London-Theorie} \desc[german]{London-Theorie}{}{}
]{london}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \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}}} \eq{\lambda_\txL(T) = \lambda_\txL(0) \frac{1}{\sqrt{1- \left(\frac{T}{T_\txc}\right)^4}}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{macro}
\eng{Macroscopic wavefunction} \desc{Macroscopic wavefunction}{}{}
\ger{Makroskopische Wellenfunktion} \desc[german]{Makroskopische Wellenfunktion}{}{}
]{macro}
\begin{formula}{ansatz} \begin{formula}{ansatz}
\desc{Ansatz}{}{} \desc{Ansatz}{}{}
\desc[german]{Ansatz}{}{} \desc[german]{Ansatz}{}{}
@ -170,10 +162,9 @@
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{josephson}
\eng{Josephson Effect} \desc{Josephson Effect}{}{}
\ger{Josephson Effekt} \desc[german]{Josephson Effekt}{}{}
]{josephson}
\begin{formula}{1st_relation} \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{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} \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[ \Subsection{gl}
\eng{\GL Theory (GLAG)} \desc{\GL Theory (GLAG)}{}{}
\ger{\GL Theorie (GLAG)} \desc[german]{\GL Theorie (GLAG)}{}{}
]{gl}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}
@ -326,10 +316,9 @@
}} }}
\end{formula} \end{formula}
\Subsection[ \Subsection{micro}
\eng{Microscopic theory} \desc{Microscopic theory}{}{}
\ger{Mikroskopische Theorie} \desc[german]{Mikroskopische Theorie}{}{}
]{micro}
\begin{formula}{isotop_effect} \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{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, $\omega_\text{ph}$} \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} \end{formula}
\Subsubsection[ \Subsubsection{bcs}
\eng{BCS-Theory} \desc{BCS-Theory}{}{}
\ger{BCS-Theorie} \desc[german]{BCS-Theorie}{}{}
]{bcs}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}
@ -429,10 +417,9 @@
\eq{E \approx 2E_\txF - 2\hbar\omega_\txD \Exp{-\frac{4}{V_0 D(E_\txF)}}} \eq{E \approx 2E_\txF - 2\hbar\omega_\txD \Exp{-\frac{4}{V_0 D(E_\txF)}}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{excite}
\eng{Excitations and finite temperatures} \desc{Excitations and finite temperatures}{}{}
\ger{Anregungen und endliche Temperatur} \desc[german]{Anregungen und endliche Temperatur}{}{}
]{excite}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}
@ -522,10 +509,9 @@
} }
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{pinning}
\eng{Flux pinning} \desc{Flux pinning}{}{}
\ger{Haftung von Flusslinien} \desc[german]{Haftung von Flusslinien}{}{}
]{pinning}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}

50
src/cm/techniques.tex

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

22
src/cm/topo.tex

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

27
src/cm/vib.tex

@ -1,7 +1,12 @@
\Section[ \Section{vib}
\eng{Lattice vibrations} \desc{Lattice vibrations}{}{}
\ger{Gitterschwingungen} \desc[german]{Gitterschwingungen}{}{}
]{vib}
\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} \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} \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}} \eq{C_\txm = 3\NA \kB = 3R \approx \SI{25}{\joule\per\mol\kelvin}}
\end{formula} \end{formula}
\Subsection[ \Subsection{einstein}
\eng{Einstein model} \desc{Einstein model}{}{}
\ger{Einstein-Modell} \desc[german]{Einstein-Modell}{}{}
]{einstein}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \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}} \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} \end{formula}
\Subsection[ \Subsection{debye}
\eng{Debye model} \desc{Debye model}{}{}
\ger{Debye-Modell} \desc[german]{Debye-Modell}{}{}
]{debye}
\begin{formula}{description} \begin{formula}{description}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}

88
src/comp/ad.tex

@ -1,7 +1,7 @@
\Section[ \Section{ad}
\eng{Atomic dynamics} \desc{Atomic dynamics}{}{}
% \ger{} % \desc[german]{}{}{}
]{ad}
\begin{formula}{hamiltonian} \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{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}{}{} \desc[german]{Hamiltonian der Elektronen}{}{}
@ -29,10 +29,9 @@
\end{multline} \end{multline}
\end{formula} \end{formula}
\Subsection[ \Subsection{bo}
\eng{Born-Oppenheimer Approximation} \desc{Born-Oppenheimer Approximation}{}{}
\ger{Born-Oppenheimer Näherung} \desc[german]{Born-Oppenheimer Näherung}{}{}
]{bo}
\begin{formula}{adiabatic_approx} \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{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})}{} \desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{}
@ -81,10 +80,9 @@
} }
\end{formula} \end{formula}
\Subsection[ \Subsection{opt}
\eng{Structure optimization} \desc{Structure optimization}{}{}
\ger{Strukturoptimierung} \desc[german]{Strukturoptimierung}{}{}
]{opt}
\begin{formula}{forces} \begin{formula}{forces}
\desc{Forces}{}{} \desc{Forces}{}{}
\desc[german]{Kräfte}{}{} \desc[german]{Kräfte}{}{}
@ -139,10 +137,9 @@
}} }}
\end{formula} \end{formula}
\Subsection[ \Subsection{latvib}
\eng{Lattice vibrations} \desc{Lattice vibrations}{}{}
\ger{Gitterschwingungen} \desc[german]{Gitterschwingungen}{}{}
]{latvib}
\begin{formula}{force_constant_matrix} \begin{formula}{force_constant_matrix}
\desc{Force constant matrix}{}{} \desc{Force constant matrix}{}{}
% \desc[german]{}{}{} % \desc[german]{}{}{}
@ -159,10 +156,9 @@
% -> DFPT % -> DFPT
% finite-difference method % finite-difference method
\Subsubsection[ \Subsubsection{fin_diff}
\eng{Finite difference method} \desc{Finite difference method}{}{}
% \ger{} % \desc[german]{}{}{}
]{fin_diff}
\begin{formula}{approx} \begin{formula}{approx}
\desc{Approximation}{Assume forces in equilibrium structure vanish}{$\Delta s$ displacement of atom $J$} \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) } \eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) }
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{anharmonic}
\eng{Anharmonic approaches} \desc{Anharmonic approaches}{}{}
\ger{Anharmonische Ansätze} \desc[german]{Anharmonische Ansätze}{}{}
]{anharmonic}
\begin{formula}{qha} \begin{formula}{qha}
\desc{Quasi-harmonic approximation}{}{} \desc{Quasi-harmonic approximation}{}{}
@ -205,10 +200,9 @@
\Subsection[ \Subsection{md}
\eng{Molecular Dynamics} \desc{Molecular Dynamics}{}{}
\ger{Molekulardynamik} \desc[german]{Molekulardynamik}{}{} \abbrLink{md}{MD}
]{md} \abbrLink{md}{MD}
\begin{formula}{desc} \begin{formula}{desc}
\desc{Description}{}{} \desc{Description}{}{}
\desc[german]{Beschreibung}{}{} \desc[german]{Beschreibung}{}{}
@ -236,10 +230,9 @@
}} }}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{ab-initio}
\eng{Ab-initio molecular dynamics} \desc{Ab-initio molecular dynamics}{}{}
\ger{Ab-initio molecular dynamics} \desc[german]{Ab-initio molecular dynamics}{}{}
]{ab-initio}
\begin{formula}{bomd} \begin{formula}{bomd}
\abbrLabel{BOMD} \abbrLabel{BOMD}
\desc{Born-Oppenheimer MD (BOMD)}{}{} \desc{Born-Oppenheimer MD (BOMD)}{}{}
@ -271,10 +264,9 @@
\end{gather} \end{gather}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{ff}
\eng{Force-field MD} \desc{Force-field MD}{}{}
\ger{Force-field MD} \desc[german]{Force-field MD}{}{}
]{ff}
\begin{formula}{ffmd} \begin{formula}{ffmd}
\desc{Force field MD (FFMD)}{}{} \desc{Force field MD (FFMD)}{}{}
@ -291,13 +283,9 @@
\Subsubsection[ \Subsubsection{scheme}
\eng{Integration schemes} \desc{Integration schemes}{Procedures for updating positions and velocities to obey the equations of motion.}{}
% \ger{} \desc[german]{Integrationsmethoden}{Prozeduren zum stückweisen numerischen Lösung der Bewegungsgleichungen}{}
]{scheme}
\begin{ttext}
\eng{Procedures for updating positions and velocities to obey the equations of motion.}
\end{ttext}
\begin{formula}{euler} \begin{formula}{euler}
\desc{Euler method}{First-order procedure for solving \abbrRef{ode}s with a given initial value.\\Taylor expansion of $\vecR/\vecv (t+\Delta t)$}{} \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} \end{formula}
\Subsubsection[ \Subsubsection{stats}
\eng{Thermostats and barostats} \desc{Thermostats and barostats}{}{}
\ger{Thermostate und Barostate} \desc[german]{Thermostate und Barostate}{}{}
]{stats}
\begin{formula}{velocity_rescaling} \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{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]{}{}{} % \desc[german]{}{}{}
@ -367,10 +354,9 @@
\end{gather} \end{gather}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{obs}
\eng{Calculating observables} \desc{Calculating observables}{}{}
\ger{Berechnung von Observablen} \desc[german]{Berechnung von Observablen}{}{}
]{obs}
\begin{formula}{spectral_density} \begin{formula}{spectral_density}
\desc{Spectral density}{Wiener-Khinchin theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{$C$ \absRef{autocorrelation}} \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}}{} \desc[german]{Spektraldichte}{Wiener-Khinchin Theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{}

8
src/comp/comp.tex

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

64
src/comp/est.tex

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

56
src/comp/ml.tex

@ -1,11 +1,11 @@
\Section[ \Section{ml}
\eng{Machine-Learning} \desc{Machine-Learning}{}{}
\ger{Maschinelles Lernen} \desc[german]{Maschinelles Lernen}{}{}
]{ml}
\Subsection[ \Subsection{performance}
\eng{Performance metrics} \desc{Performance metrics}{}{}
\ger{Metriken zur Leistungsmessung} \desc[german]{Metriken zur Leistungsmessung}{}{}
]{performance}
\eng[cp]{correct predictions} \eng[cp]{correct predictions}
\ger[cp]{richtige Vorhersagen} \ger[cp]{richtige Vorhersagen}
\eng[fp]{false predictions} \eng[fp]{false predictions}
@ -16,13 +16,14 @@
\ger[y]{Wahrheit} \ger[y]{Wahrheit}
\ger[yhat]{Vorhersage} \ger[yhat]{Vorhersage}
\eng[n_desc]{Number of data points}
\ger[n_desc]{Anzahl der Datenpunkte}
\begin{formula}{accuracy} \begin{formula}{accuracy}
\desc{Accuracy}{}{} \desc{Accuracy}{}{}
\desc[german]{Genauigkeit}{}{} \desc[german]{Genauigkeit}{}{}
\eq{a = \frac{\tGT{::cp}}{\tGT{::fp} + \tGT{::cp}}} \eq{a = \frac{\tGT{::cp}}{\tGT{::fp} + \tGT{::cp}}}
\end{formula} \end{formula}
\eng{n_desc}{Number of data points}
\ger{n_desc}{Anzahl der Datenpunkte}
\begin{formula}{mean_abs_error} \begin{formula}{mean_abs_error}
\desc{Mean absolute error (MAE)}{}{$y$ \GT{::y}, $\hat{y}$ \GT{::yhat}, $n$ \GT{::n_desc}} \desc{Mean absolute error (MAE)}{}{$y$ \GT{::y}, $\hat{y}$ \GT{::yhat}, $n$ \GT{::n_desc}}
\desc[german]{Mittlerer absoluter Fehler (MAE)}{}{} \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}} \eq{\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \left(y_i - \hat{y}_i\right)^2}}
\end{formula} \end{formula}
\Subsection[ \Subsection{reg}
\eng{Regression} \desc{Regression}{}{}
\ger{Regression} \desc[german]{Regression}{}{}
]{reg} \Subsubsection{linear}
\Subsubsection[ \desc{Linear Regression}{}{}
\eng{Linear Regression} \desc[german]{Lineare Regression}{}{}
\ger{Lineare Regression}
]{linear}
\begin{formula}{eq} \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{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}}{} \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}} \eq{\vec{\beta} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{kernel}
\eng{Kernel method} \desc{Kernel method}{}{}
\ger{Kernelmethode} \desc[german]{Kernelmethode}{}{}
]{kernel}
\begin{formula}{kernel_trick} \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{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]{}{}{} % \desc[german]{}{}{}
@ -103,10 +101,9 @@
\eq{k(\vecx_i, \vecx_j) = \Exp{-\frac{\norm{\vecx_i - \vecx_j}_2^2}{\sigma}}} \eq{k(\vecx_i, \vecx_j) = \Exp{-\frac{\norm{\vecx_i - \vecx_j}_2^2}{\sigma}}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{bayes}
\eng{Bayesian regression} \desc{Bayesian regression}{}{}
\ger{Bayes'sche Regression} \desc[german]{Bayes'sche Regression}{}{}
]{bayes}
\begin{formula}{linear_regression} \begin{formula}{linear_regression}
\desc{Bayesian 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)} \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} \end{formula}
\Subsection[ \Subsection{gd}
\eng{Gradient descent} \desc{Gradient descent}{}{}
\ger{Gradientenverfahren} \desc[german]{Gradientenverfahren}{}{}
]{gd}
\TODO{in lecture 30 CMP} \TODO{in lecture 30 CMP}

43
src/comp/qmb.tex

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

8
src/constants.tex

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

8
src/ed/ed.tex

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

13
src/ed/el.tex

@ -1,8 +1,7 @@
\Section[ \Section{el}
\eng{Electric field} \desc{Electric field}{}{}
\ger{Elektrisches Feld} \desc[german]{Elektrisches Feld}{}{}
]{el}
\begin{formula}{electric_field} \begin{formula}{electric_field}
\desc{Electric field}{Surrounds charged particles}{} \desc{Electric field}{Surrounds charged particles}{}
\desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{} \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}{} \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} \end{formula}
\begin{formula}{relative_permittivity} \begin{formula}{relative_permittivity}
\desc{Relative permittivity / Dielectric constant}{}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}} \desc{Relative permittivity}{Dielectric constant}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}}
\desc[german]{Relative Permittivität / Dielectric constant}{}{} \desc[german]{Relative Permittivität}{Dielectric constant}{}
\eq{ \eq{
\epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0} \epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0}
} }
@ -62,7 +61,7 @@
\begin{formula}{electric_displacement_field} \begin{formula}{electric_displacement_field}
\desc{Electric displacement field}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_field}, \QtyRef{dielectric_polarization_density}} \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} \quantity{\vec{D}}{\coulomb\per\m^2=\ampere\s\per\m^2}{v}
\eq{\vec{D} = \epsilon_0 \vec{\E} + \vec{P}} \eq{\vec{D} = \epsilon_0 \vec{\E} + \vec{P}}
\end{formula} \end{formula}

29
src/ed/em.tex

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

15
src/ed/mag.tex

@ -1,7 +1,7 @@
\Section[ \Section{mag}
\eng{Magnetic field} \desc{Magnetic field}{}{}
\ger{Magnetfeld} \desc[german]{Magnetfeld}{}{}
]{mag}
\begin{formula}{magnetic_flux} \begin{formula}{magnetic_flux}
\desc{Magnetic flux}{}{$\vec{A}$ \GT{area}} \desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
@ -98,10 +98,9 @@
\Subsection[ \Subsection{materials}
\eng{Magnetic materials} \desc{Magnetic materials}{}{}
\ger{Magnetische Materialien} \desc[german]{Magnetische Materialien}{}{}
]{materials}
\begin{formula}{paramagnetism} \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{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}{} \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}

115
src/ed/misc.tex

@ -1,108 +1,6 @@
% TODO move \Section{dipole}
\Section[ \desc{Dipoles}{}{}
\eng{Hall-Effect} \desc[german]{Dipole}{}{}
\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}
\begin{formula}{poynting} \begin{formula}{poynting}
\desc{Dipole radiation Poynting vector}{}{} \desc{Dipole radiation Poynting vector}{}{}
@ -116,10 +14,9 @@
\eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}} \eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
\end{formula} \end{formula}
\Section[ \Section{misc}
\eng{misc} \desc{misc}{}{}
\ger{misc} \desc[german]{misc}{}{}
]{misc}
\begin{formula}{impedance_r} \begin{formula}{impedance_r}
\desc{Impedance of an ohmic resistor}{}{\QtyRef{resistance}} \desc{Impedance of an ohmic resistor}{}{\QtyRef{resistance}}
\desc[german]{Impedanz eines Ohmschen Widerstands}{}{} \desc[german]{Impedanz eines Ohmschen Widerstands}{}{}

8
src/ed/optics.tex

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

16
src/main.tex

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

88
src/math/calculus.tex

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

29
src/math/geometry.tex

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

43
src/math/linalg.tex

@ -1,12 +1,11 @@
\Section[ \Section{linalg}
\eng{Linear algebra} \desc{Linear algebra}{}{}
\ger{Lineare Algebra} \desc[german]{Lineare Algebra}{}{}
]{linalg}
\Subsection[
\eng{Matrix basics} \Subsection{matrix}
\ger{Matrizen Basics} \desc{Matrix basics}{}{}
]{matrix} \desc[german]{Matrizen Basics}{}{}
\begin{formula}{matrix_matrix_product} \begin{formula}{matrix_matrix_product}
\desc{Matrix-matrix product as sum}{}{} \desc{Matrix-matrix product as sum}{}{}
@ -31,10 +30,9 @@
\eq{U ^\dagger U = \id} \eq{U ^\dagger U = \id}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{transposed}
\eng{Transposed matrix} \desc{Transposed matrix}{}{}
\ger{Transponierte Matrix} \desc[german]{Transponierte Matrix}{}{}
]{transposed}
\begin{formula}{sum} \begin{formula}{sum}
\desc{Sum}{}{} \desc{Sum}{}{}
\desc[german]{Summe}{}{} \desc[german]{Summe}{}{}
@ -57,10 +55,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{determinant}
\eng{Determinant} \desc{Determinant}{}{}
\ger{Determinante} \desc[german]{Determinante}{}{}
]{determinant}
\begin{formula}{2x2} \begin{formula}{2x2}
\desc{2x2 matrix}{}{} \desc{2x2 matrix}{}{}
\desc[german]{2x2 Matrix}{}{} \desc[german]{2x2 Matrix}{}{}
@ -95,10 +92,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{misc}
\eng{Misc} \desc{Misc}{}{}
\ger{Misc} \desc[german]{Misc}{}{}
]{misc}
\begin{formula}{normal_equation} \begin{formula}{normal_equation}
\desc{Normal equation}{Solves a linear regression problem}{\mat{\theta} hypothesis / weight matrix, \mat{X} design matrix, \vec{y} output vector} \desc{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} \end{formula}
\Subsection[ \Subsection{eigen}
\eng{Eigenvalues} \desc{Eigenvalues}{}{}
\ger{Eigenwerte} \desc[german]{Eigenwerte}{}{}
]{eigen}
\begin{formula}{values} \begin{formula}{values}
\desc{Eigenvalue equation}{}{$\lambda$ eigenvalue, $v$ eigenvector} \desc{Eigenvalue equation}{}{$\lambda$ eigenvalue, $v$ eigenvector}
\desc[german]{Eigenwert-Gleichung}{}{$\lambda$ Eigenwert, $v$ Eigenvektor} \desc[german]{Eigenwert-Gleichung}{}{$\lambda$ Eigenwert, $v$ Eigenvektor}

8
src/math/math.tex

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

148
src/math/probability_theory.tex

@ -1,7 +1,7 @@
\Section[ \Section{pt}
\eng{Probability theory} \desc{Probability theory}{}{}
\ger{Wahrscheinlichkeitstheorie} \desc[german]{Wahrscheinlichkeitstheorie}{}{}
]{pt}
\begin{formula}{mean} \begin{formula}{mean}
\absLabel \absLabel
@ -70,24 +70,20 @@
\eq{\binom{n}{k} = \frac{n!}{k!(n-k)!}} \eq{\binom{n}{k} = \frac{n!}{k!(n-k)!}}
\end{formula} \end{formula}
\Subsection[ \Subsection{distributions}
\eng{Distributions} \desc{Distributions}{}{}
\ger{Verteilungen} \desc[german]{Verteilungen}{}{}
]{distributions} \Subsubsection{cont}
\Subsubsection[ \desc{Continuous probability distributions}{}{}
\eng{Continuous probability distributions} \desc[german]{Kontinuierliche Wahrscheinlichkeitsverteilungen}{}{}
\ger{Kontinuierliche Wahrscheinlichkeitsverteilungen}
]{cont}
\begin{bigformula}{normal} \begin{bigformula}{normal}
\absLabel[normal_distribution] \absLabel[normal_distribution]
\desc{Gauß/Normal distribution}{}{} \desc{Gauß/Normal distribution}{}{}
\desc[german]{Gauß/Normal-Verteilung}{}{} \desc[german]{Gauß/Normal-Verteilung}{}{}
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_gauss.pdf} \includegraphics{img/distribution_gauss.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R} \disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
\disteq{support}{x \in \R} \disteq{support}{x \in \R}
@ -97,6 +93,7 @@
\disteq{median}{\mu} \disteq{median}{\mu}
\disteq{variance}{\sigma^2} \disteq{variance}{\sigma^2}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
\begin{formula}{standard_normal} \begin{formula}{standard_normal}
@ -110,7 +107,9 @@
\absLabel[multivariate_normal_distribution] \absLabel[multivariate_normal_distribution]
\desc{Multivariate normal distribution}{Multivariate Gaussian distribution}{$\vec{\mu}$ \absRef{mean}, $\mat{\Sigma}$ \absRef{covariance}} \desc{Multivariate normal distribution}{Multivariate Gaussian distribution}{$\vec{\mu}$ \absRef{mean}, $\mat{\Sigma}$ \absRef{covariance}}
\desc[german]{Mehrdimensionale Normalverteilung}{Multivariate Normalverteilung}{} \desc[german]{Mehrdimensionale Normalverteilung}{Multivariate Normalverteilung}{}
\fsplit[0.3]{
\TODO{k-variate normal plot} \TODO{k-variate normal plot}
}{
\begin{distribution} \begin{distribution}
\disteq{parameters}{\vec{\mu} \in \R^k,+\quad \mat{\Sigma} \in \R^{k\times k}} \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{support}{\vec{x} \in \vec{\mu} + \text{span}(\mat{\Sigma})}
@ -118,25 +117,37 @@
\disteq{mean}{\vec{\mu}} \disteq{mean}{\vec{\mu}}
\disteq{variance}{\mat{\Sigma}} \disteq{variance}{\mat{\Sigma}}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
\begin{formula}{laplace} \begin{bigformula}{laplace}
\absLabel[laplace_distribution] \absLabel[laplace_distribution]
\desc{Laplace-distribution}{}{} \desc{Laplace-distribution}{Double exponential distribution}{}
\desc[german]{Laplace-Verteilung}{}{} \desc[german]{Laplace-Verteilung}{Doppelexponentialverteilung}{}
\TODO{TODO} \fsplit[\distleftwidth]{
\end{formula} \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} \begin{bigformula}{cauchy}
\absLabel[lorentz_distribution] \absLabel[lorentz_distribution]
\desc{Cauchys / Lorentz distribution}{Also known as Cauchy-Lorentz distribution, Lorentz(ian) function, Breit-Wigner 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.}{} \desc[german]{Cauchy / Lorentz-Verteilung}{Auch bekannt als Cauchy-Lorentz Verteilung, Lorentz Funktion, Breit-Wigner Verteilung.}{}
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_cauchy.pdf} \includegraphics{img/distribution_cauchy.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{x_0 \in \R,\quad \gamma \in \R} \disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
\disteq{support}{x \in \R} \disteq{support}{x \in \R}
@ -146,27 +157,27 @@
\disteq{median}{x_0} \disteq{median}{x_0}
\disteq{variance}{\text{\GT{undefined}}} \disteq{variance}{\text{\GT{undefined}}}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
\begin{bigformula}{maxwell-boltzmann} \begin{bigformula}{maxwell-boltzmann}
\absLabel[maxwell-boltzmann_distribution] \absLabel[maxwell-boltzmann_distribution]
\desc{Maxwell-Boltzmann distribution}{}{} \desc{Maxwell-Boltzmann distribution}{}{}
\desc[german]{Maxwell-Boltzmann Verteilung}{}{} \desc[german]{Maxwell-Boltzmann Verteilung}{}{}
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf} \includegraphics{img/distribution_maxwell-boltzmann.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{a > 0} \disteq{parameters}{a > 0}
\disteq{support}{x \in (0, \infty)} \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{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{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{mean}{2a \frac{2}{\pi}}
\disteq{median}{} % \disteq{median}{}
\disteq{variance}{\frac{a^2(3\pi-8)}{\pi}} \disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
@ -174,12 +185,10 @@
\absLabel[gamma_distribution] \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{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}{} \desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{}
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_gamma.pdf} \includegraphics{img/distribution_gamma.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{\alpha > 0, \lambda > 0} \disteq{parameters}{\alpha > 0, \lambda > 0}
\disteq{support}{x\in(0,1)} \disteq{support}{x\in(0,1)}
@ -188,18 +197,17 @@
\disteq{mean}{\frac{\alpha}{\lambda}} \disteq{mean}{\frac{\alpha}{\lambda}}
\disteq{variance}{\frac{\alpha}{\lambda^2}} \disteq{variance}{\frac{\alpha}{\lambda^2}}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
\begin{bigformula}{beta} \begin{bigformula}{beta}
\absLabel[beta_distribution] \absLabel[beta_distribution]
\desc{Beta Distribution}{}{$\txB$ \fRef{math:cal:integral:list:beta_function} / \fRef{math:cal:integral:list:incomplete_beta_function}} \desc{Beta Distribution}{}{$\txB$ \fRef{math:cal:integral:list:beta_function} / \fRef{math:cal:integral:list:incomplete_beta_function}}
\desc[german]{Beta Verteilung}{}{} \desc[german]{Beta Verteilung}{}{}
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_beta.pdf} \includegraphics{img/distribution_beta.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{\alpha \in \R, \beta \in \R} \disteq{parameters}{\alpha \in \R, \beta \in \R}
\disteq{support}{x\in[0,1]} \disteq{support}{x\in[0,1]}
@ -209,13 +217,13 @@
% \disteq{median}{\frac{}{}} % pretty complicated, probably not needed % \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
\disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}} \disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
\Subsubsection[ \Subsubsection{discrete}
\eng{Discrete probability distributions} \desc{Discrete probability distributions}{}{}
\ger{Diskrete Wahrscheinlichkeitsverteilungen} \desc[german]{Diskrete Wahrscheinlichkeitsverteilungen}{}{}
]{discrete}
\begin{bigformula}{binomial} \begin{bigformula}{binomial}
\absLabel[binomial_distribution] \absLabel[binomial_distribution]
\desc{Binomial distribution}{}{} \desc{Binomial distribution}{}{}
@ -224,12 +232,10 @@
\eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \absRef[poisson distribution]{poisson_distribution}} \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}} \ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \absRef[Poissonverteilung]{poisson_distribution}}
\end{ttext}\\ \end{ttext}\\
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_binomial.pdf} \includegraphics{img/distribution_binomial.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p} \disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
\disteq{support}{k \in \{0,\,1,\,\dots,\,n\}} \disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
@ -239,18 +245,17 @@
\disteq{median}{\floor{np} \text{ or } \ceil{np}} \disteq{median}{\floor{np} \text{ or } \ceil{np}}
\disteq{variance}{npq = np(1-p)} \disteq{variance}{npq = np(1-p)}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
\begin{bigformula}{poisson} \begin{bigformula}{poisson}
\absLabel[poisson_distribution] \absLabel[poisson_distribution]
\desc{Poisson distribution}{}{} \desc{Poisson distribution}{}{}
\desc[german]{Poissonverteilung}{}{} \desc[german]{Poissonverteilung}{}{}
\begin{minipage}{\distleftwidth} \fsplit[\distleftwidth]{
\begin{figure}[H]
\centering \centering
\includegraphics[width=\textwidth]{img/distribution_poisson.pdf} \includegraphics{img/distribution_poisson.pdf}
\end{figure} }{
\end{minipage}
\begin{distribution} \begin{distribution}
\disteq{parameters}{\lambda \in (0,\infty)} \disteq{parameters}{\lambda \in (0,\infty)}
\disteq{support}{k \in \N} \disteq{support}{k \in \N}
@ -260,6 +265,7 @@
\disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}} \disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
\disteq{variance}{\lambda} \disteq{variance}{\lambda}
\end{distribution} \end{distribution}
}
\end{bigformula} \end{bigformula}
@ -277,10 +283,9 @@
% \end{distribution} % \end{distribution}
\Subsection[ \Subsection{cls}
\eng{Central limit theorem} \desc{Central limit theorem}{}{}
\ger{Zentraler Grenzwertsatz} \desc[german]{Zentraler Grenzwertsatz}{}{}
]{cls}
\begin{ttext} \begin{ttext}
\eng{ \eng{
Suppose $X_1, X_2, \dots$ is a sequence of independent and identically distributed random variables with $\braket{X_i} = \mu$ and $(\Delta X_i)^2 = \sigma^2 < \infty$. 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} \end{ttext}
\Subsection[ \Subsection{error}
\eng{Propagation of uncertainty / error} \desc{Propagation of uncertainty / error}{}{}
\ger{Fehlerfortpflanzung} \desc[german]{Fehlerfortpflanzung}{}{}
]{error}
\begin{formula}{generalised} \begin{formula}{generalised}
\desc{Generalized error propagation}{}{$V$ \fRef{math:pt:covariance} matrix, $J$ \fRef{math:cal:jacobi-matrix}} \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}}{} \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}} \eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
\end{formula} \end{formula}
\Subsection[ \Subsection{mle}
\eng{Maximum likelihood estimation} \desc{Maximum likelihood estimation}{}{}
\ger{Maximum likelihood Methode} \desc[german]{Maximum likelihood Methode}{}{}
]{mle}
\begin{formula}{likelihood} \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{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} \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)} \eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)}
\end{formula} \end{formula}
\Subsection[ \Subsection{bayesian}
\eng{Bayesian probability theory} \desc{Bayesian probability theory}{}{}
\ger{Bayessche Wahrscheinlichkeitstheorie} \desc[german]{Bayessche Wahrscheinlichkeitstheorie}{}{}
]{bayesian}
\begin{formula}{prior} \begin{formula}{prior}
\desc{Prior distribution}{Expected distribution before conducting the experiment}{$\theta$ parameter} \desc{Prior distribution}{Expected distribution before conducting the experiment}{$\theta$ parameter}
\desc[german]{Prior Verteilung}{}{} \desc[german]{Prior Verteilung}{}{}

42
src/mechanics.tex

@ -1,12 +1,11 @@
\Part[ \Part{mech}
\eng{Mechanics} \desc{Mechanics}{}{}
\ger{Mechanik} \desc[german]{Mechanik}{}{}
]{mech}
\Section[
\eng{Newton} \Section{newton}
\ger{Newton} \desc{Newton}{}{}
]{newton} \desc[german]{Newton}{}{}
\begin{formula}{newton_laws} \begin{formula}{newton_laws}
\desc{Newton's laws}{}{} \desc{Newton's laws}{}{}
\desc[german]{Newtonsche Gesetze}{}{} \desc[german]{Newtonsche Gesetze}{}{}
@ -31,10 +30,9 @@
} }
\end{formula} \end{formula}
\Section[ \Section{misc}
\eng{Misc} \desc{Misc}{}{}
\ger{Verschiedenes} \desc[german]{Verschiedenes}{}{}
]{misc}
\begin{formula}{hook} \begin{formula}{hook}
\desc{Hooke's law}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ spring length} \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} \desc[german]{Hookesches Gesetz}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ Federlänge}
@ -50,18 +48,25 @@
\end{formula} \end{formula}
\def\lagrange{\mathcal{L}} \def\lagrange{\mathcal{L}}
\Section[ \Section{lagrange}
\eng{Lagrange formalism} \desc{Lagrange formalism}{}{}
\ger{Lagrange Formalismus} \desc[german]{Lagrange Formalismus}{}{}
]{lagrange} \begin{formula}{description}
\begin{ttext}[desc] \desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
\ttxt{
\eng{The Lagrange formalism is often the most simple approach the get the equations of motion, \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. 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, \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. da das Aufstellen der Lagrange-Funktion mit geeigneten generalisierten Koordinaten oft relativ einfach ist.
} }
\end{ttext} }
\end{formula}
\begin{formula}{generalized_coordinates}
\desc{Generalized coordinates}{}{}
\desc[german]{Generalisierte Koordinaten}{}{}
\absLabel
\begin{ttext}[generalized_coords] \begin{ttext}[generalized_coords]
\eng{ \eng{
The generalized coordinates are choosen so that the cronstraints are automatically fullfilled. The generalized coordinates are choosen so that the cronstraints are automatically fullfilled.
@ -72,6 +77,7 @@
Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$. 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{ttext}
\end{formula}
\begin{formula}{lagrangian} \absLabel \begin{formula}{lagrangian} \absLabel
\desc{Lagrange function}{}{$T$ kinetic energy, $V$ potential energy } \desc{Lagrange function}{}{$T$ kinetic energy, $V$ potential energy }
\desc[german]{Lagrange-Funktion}{}{$T$ kinetische Energie, $V$ potentielle Energie} \desc[german]{Lagrange-Funktion}{}{$T$ kinetische Energie, $V$ potentielle Energie}

8
src/particle.tex

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

26
src/pkg/mqformula.sty

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

64
src/pkg/mqfqname.sty

@ -93,45 +93,57 @@
\directlua{fqnameLeaveOnlyFirstN(#1)}% \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 % SECTIONING
% start <section>, get heading from translation, set label % 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 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 % 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 % [1]: code to run after setting \fqname, but before the \part, \section etc
% 2: key % 2: key
\newcommand{\Part}[2][desc]{
\newpage % 1: depth
\mqfqname@leaveOnlyFirstN{0} % 2: key
% 3: Latex section command
\newcommand\mqfqname@section[3]{
\mqfqname@leaveOnlyFirstN{#1}
\mqfqname@enter{#2} \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 % 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}} \edef\fqnameText{\GT{\fqname}}
\part{\fqnameText} #3{\fqnameText}
\mqfqname@label \mqfqname@label
\IfTranslationExists{\fqname:desc}{
{\color{fg1} \GT{\fqname:desc}}
}{}
} }
\newcommand{\Section}[2][]{
\mqfqname@leaveOnlyFirstN{1}
\mqfqname@enter{#2} \newcommand{\Part}[1]{
#1 \newpage
\edef\fqnameText{\GT{\fqname}} \mqfqname@section{0}{#1}{\part}
\section{\fqnameText}
\mqfqname@label
} }
\newcommand{\Subsection}[2][]{ \newcommand{\Section}[1]{
\mqfqname@leaveOnlyFirstN{2} \mqfqname@section{1}{#1}{\section}
\mqfqname@enter{#2}
#1
\edef\fqnameText{\GT{\fqname}}
\subsection{\fqnameText}
\mqfqname@label
} }
\newcommand{\Subsubsection}[2][]{ \newcommand{\Subsection}[1]{
\mqfqname@leaveOnlyFirstN{3} \mqfqname@section{2}{#1}{\subsection}
\mqfqname@enter{#2} }
#1 \newcommand{\Subsubsection}[1]{
\edef\fqnameText{\GT{\fqname}} \mqfqname@section{3}{#1}{\subsubsection}
\subsubsection{\fqnameText} }
\mqfqname@label \newcommand{\Paragraph}[1]{
\mqfqname@section{4}{#1}{\paragraph}
} }
\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}} \newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}

19
src/pkg/mqperiodictable.sty

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

109
src/qm/atom.tex

@ -1,10 +1,9 @@
\def\vecr{{\vec{r}}} \def\vecr{{\vec{r}}}
\def\abohr{a_\textrm{B}} \def\abohr{a_\textrm{B}}
\Section[ \Section{h}
\eng{Hydrogen Atom} \desc{Hydrogen Atom}{}{}
\ger{Wasserstoffatom} \desc[german]{Wasserstoffatom}{}{}
]{h}
\begin{formula}{reduced_mass} \begin{formula}{reduced_mass}
\desc{Reduced mass}{}{} \desc{Reduced mass}{}{}
@ -81,20 +80,35 @@
\eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}} \eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
\end{formula} \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[ \Subsection{corrections}
\eng{Corrections} \desc{Corrections}{}{}
\ger{Korrekturen} \desc[german]{Korrekturen}{}{}
]{corrections}
\Subsubsection[ \Subsubsection{darwin}
\eng{Darwin term} \desc{Darwin term}{Relativisitc correction: Accounts for interaction with nucleus (non-zero wavefunction at nucleaus position)}{}
\ger{Darwin-Term} \desc[german]{Darwin-Term}{Relativistische Korrektur: Berücksichtigt die Interatkion mit dem Kern (endliche Wellenfunktion bei der Kernposition)}{}
]{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}
\begin{formula}{energy_shift} \begin{formula}{energy_shift}
\desc{Energy shift}{}{} \desc{Energy shift}{}{}
\desc[german]{Energieverschiebung}{}{} \desc[german]{Energieverschiebung}{}{}
@ -107,14 +121,9 @@
\eq{\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c} \approx \frac{1}{137}} \eq{\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c} \approx \frac{1}{137}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{ls_coupling}
\eng{Spin-orbit coupling (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.}{}
\ger{Spin-Bahn-Kopplung (LS-Kopplung)} \desc[german]{Spin-Bahn-Kopplung (LS-Kopplung)}{The Wechselwirkung zwischen dem Elektronenspin und dem elektrostatischen Feld des Kerns führt zu Energieverschiebungen.}{}
]{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}
\begin{formula}{energy_shift} \begin{formula}{energy_shift}
\desc{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}}} \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} \end{formula}
\begin{formula}{sl} \begin{formula}{sl}
\desc{\TODO{name}}{}{} \desc{Spin-orbit coupling}{}{}
\desc[german]{??}{}{} \desc[german]{Spin-Bahn-Kopplung}{}{}
\eq{\braket{\vec{S} \cdot \vec{L}} &= \frac{1}{2} \braket{[J^2-L^2-S^2]} \nonumber \\ \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)]} &= \frac{\hbar^2}{2}[j(j+1) -l(l+1) -s(s+1)]}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{fine_structure}
\eng{Fine-structure} \desc{Fine-structure}{The fine-structure combines \fRef[relativistic corrections]{qm:h:corrections:darwin} and \fRef{qm:h:corrections:ls_coupling}.}{}
\ger{Feinstruktur} \desc[german]{Feinstruktur}{Die Feinstruktur vereint \fRef[relativistische Korrekturen]{qm:h:corrections:darwin} und \fRef{qm:h:corrections:ls_coupling}.}{}
]{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}
\begin{formula}{energy_shift} \begin{formula}{energy_shift}
\desc{Energy shift}{}{} \desc{Energy shift}{}{}
\desc[german]{Energieverschiebung}{}{} \desc[german]{Energieverschiebung}{}{}
@ -143,28 +147,18 @@
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{lamb_shift}
\eng{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.}{}
\ger{Lamb-Shift} \desc[german]{Lamb-Shift}{The Wechselwirkung zwischen dem Elektron und vom Kern absorbierten/emittierten virtuellen Photonen führt zu einer (sehr kleinen) Energieverschiebung.}{}
]{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}
\begin{formula}{energy} \begin{formula}{energy}
\desc{Potential energy}{}{$\delta r$ pertubation of $r$} \desc{Potential energy}{}{$\delta r$ pertubation of $r$}
\desc[german]{Potentielle Energy}{}{$\delta r$ Schwankung von $r$} \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}}} \eq{\braket{E_\textrm{pot}} = -\frac{Z e^2}{4\pi\epsilon_0} \Braket{\frac{1}{r+\delta r}}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{hyperfine_structure}
\eng{Hyperfine structure} \desc{Hyperfine structure}{Interaction of the nucleus spin with the magnetic field created by the electron leads to energy shifts. (Lifts degeneracy) }{}
\ger{Hyperfeinstruktur} \desc[german]{Hyperfeinstruktur}{Wechselwirkung von Kernspin mit dem vom Elektron erzeugten Magnetfeld spaltet Energieniveaus}{}
]{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}
\begin{formula}{nuclear_spin} \begin{formula}{nuclear_spin}
\desc{Nuclear spin}{}{} \desc{Nuclear spin}{}{}
\desc[german]{Kernspin}{}{} \desc[german]{Kernspin}{}{}
@ -199,17 +193,14 @@
\end{formula} \end{formula}
\TODO{landé factor} \TODO{landé factor}
\Subsection[ \Subsection{mag_effects}
\eng{Effects in magnetic field} \desc{Effects in magnetic field}{}{}
\ger{Effekte im Magnetfeld} \desc[german]{Effekte im Magnetfeld}{}{}
]{mag_effects}
\TODO{all} \TODO{all}
\\\TODO{Hunds rules}
\Subsection[ \Subsection{other}
\eng{misc} \desc{misc}{}{}
\ger{Sonstiges} \desc[german]{Sonstiges}{}{}
]{other}
\begin{formula}{auger_effect} \begin{formula}{auger_effect}
\desc{Auger-Meitner-Effekt}{Auger-Effect}{} \desc{Auger-Meitner-Effekt}{Auger-Effect}{}
\desc[german]{Auger-Meitner-Effekt}{Auger-Effekt}{} \desc[german]{Auger-Meitner-Effekt}{Auger-Effekt}{}

8
src/qm/misc.tex

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

194
src/qm/qm.tex

@ -5,18 +5,23 @@
\def\sigmaybraket{-i \ket{0}\bra{1} + i \ket{1}\bra{0}} \def\sigmaybraket{-i \ket{0}\bra{1} + i \ket{1}\bra{0}}
\def\sigmazbraket{\ket{0}\bra{0} - \ket{1}\bra{1}} \def\sigmazbraket{\ket{0}\bra{0} - \ket{1}\bra{1}}
\Part[ \Part{qm}
\eng{Quantum Mechanics} \desc{Quantum Mechanics}{}{}
\ger{Quantenmechanik} \desc[german]{Quantenmechanik}{}{}
]{qm} \Section{basics}
\Section[ \desc{Basics}{}{}
\eng{Basics} \desc[german]{Basics}{}{}
\ger{Basics} \begin{formula}{correspondence_principle}
]{basics} \desc{Correspondence principle}{}{}
\Subsection[ \desc[german]{Korrespondenzprinzip}{}{}
\eng{Operators} \ttxt{
\ger{Operatoren} \ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
]{op} \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[row_vector]{Zeilenvektor}
\Ger[column_vector]{Spaltenvektor} \Ger[column_vector]{Spaltenvektor}
\Eng[column_vector]{Column vector} \Eng[column_vector]{Column vector}
@ -53,14 +58,9 @@
\eq{\hat{A} = \hat{A}^\dagger} \eq{\hat{A} = \hat{A}^\dagger}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{measurement}
\eng{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).}{}
\ger{Messung} \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.}{}
]{measurement}
\begin{ttext}
\eng{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}
\ger{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}
\end{ttext}
\begin{formula}{name} \begin{formula}{name}
\desc{Measurement probability}{Probability to measure $\psi$ in state $\lambda$}{} \desc{Measurement probability}{Probability to measure $\psi$ in state $\lambda$}{}
\desc[german]{Messwahrscheinlichkeit}{Wahrscheinlichkeit, $\psi$ im Zustand $\lambda$ zu messen}{} \desc[german]{Messwahrscheinlichkeit}{Wahrscheinlichkeit, $\psi$ im Zustand $\lambda$ zu messen}{}
@ -73,10 +73,9 @@
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{pauli_matrices}
\eng{Pauli matrices} \desc{Pauli matrices}{}{}
\ger{Pauli-Matrizen} \desc[german]{Pauli-Matrizen}{}{}
]{pauli_matrices}
\begin{formula}{pauli_matrices} \begin{formula}{pauli_matrices}
\desc{Pauli matrices}{}{} \desc{Pauli matrices}{}{}
\desc[german]{Pauli Matrizen}{}{} \desc[german]{Pauli Matrizen}{}{}
@ -91,10 +90,10 @@
% $\sigma_y$ PHASE % $\sigma_y$ PHASE
% $\sigma_z$ Sign % $\sigma_z$ Sign
\Subsection[ \Subsection{probability}
\ger{Wahrscheinlichkeitstheorie} \desc{Wahrscheinlichkeitstheorie}{}{}
\eng{Probability theory} \desc[german]{Probability theory}{}{}
]{probability}
\begin{formula}{conservation_of_probability} \begin{formula}{conservation_of_probability}
\desc{Continuity equation}{}{$\rho$ density of a conserved quantity $q$, $j$ flux density of $q$} \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 $q$} \desc[german]{Kontinuitätsgleichung}{}{$\rho$ Dichte einer Erhaltungsgröße $q$, $j$ Fluß von $q$}
@ -102,9 +101,9 @@
\end{formula} \end{formula}
\begin{formula}{state_probability} \begin{formula}{state_probability}
\desc{State probability}{}{} \desc{State probability}{Probability to measure eigenvale $n$}{$P_n$ projector, $n$ normalized eigenvalue of measurement operator with one-dimensional eigenspace}
\desc[german]{Zustandswahrscheinlichkeit}{}{} \desc[german]{Zustandswahrscheinlichkeit}{Wahrscheinlicht, den Eigenwert $n$ zu messen}{$P_n$ Projektor, $n$ normalisierter Eigenwert des Messoperators mit ein-dimensionalem Eigenraum}
\eq{TODO} \eq{p_n = \Braket{\psi|P_n|\psi} = \Braket{\psi|n}\Braket{n|\psi} = \abs{\Braket{n|\psi}}^2 }
\end{formula} \end{formula}
\begin{formula}{dispersion} \begin{formula}{dispersion}
@ -124,10 +123,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{commutator}
\eng{Commutator} \desc{Commutator}{}{}
\ger{Kommutator} \desc[german]{Kommutator}{}{}
]{commutator}
\begin{formula}{commutator} \begin{formula}{commutator}
\desc{Commutator}{}{} \desc{Commutator}{}{}
\desc[german]{Kommutator}{}{} \desc[german]{Kommutator}{}{}
@ -174,10 +172,9 @@
} }
\end{formula} \end{formula}
\Section[ \Section{se}
\eng{Schrödinger equation} \desc{Schrödinger equation}{}{}
\ger{Schrödingergleichung} \desc[german]{Schrödingergleichung}{}{}
]{se}
\abbrLink{se}{SE} \abbrLink{se}{SE}
\begin{formula}{energy_operator} \begin{formula}{energy_operator}
\desc{Energy operator}{}{} \desc{Energy operator}{}{}
@ -228,11 +225,9 @@
}} }}
\end{formula} \end{formula}
\Subsection[ \Subsection{time}
\eng{Time evolution} \desc{Time evolution}{}{}
\ger{Zeitentwicklug} \desc[german]{Zeitentwicklug}{}{}
]{time}
The time evolution of the Hamiltonian is given by:
\begin{formula}{time_evolution_op} \begin{formula}{time_evolution_op}
\desc{Time evolution operator}{}{$U$ unitary} \desc{Time evolution operator}{}{$U$ unitary}
\desc[german]{Zeitentwicklungsoperator}{}{$U$ unitär} \desc[german]{Zeitentwicklungsoperator}{}{$U$ unitär}
@ -255,18 +250,15 @@
\TODO{unitary transformation of time dependent H} \TODO{unitary transformation of time dependent H}
\Subsubsection[ \Subsubsection{s_h_pictures}
\eng{Schrödinger- and Heisenberg-pictures} \desc{Schrödinger- and Heisenberg-pictures}{
\ger{Schrödinger- und Heisenberg-Bild}
]{s_h_pictures}
\eng[s_h_pictures_desc]{
In the \textbf{Schrödinger picture}, the time dependecy is in the states In the \textbf{Schrödinger picture}, the time dependecy is in the states
while in the \textbf{Heisenberg picture} the observables (operators) are time dependent. 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 sind die Observablen (Operatoren) zeitabhänig
} }{}
\gt{s_h_pictures_desc}\\
\begin{formula}{schroediner_time_evolution} \begin{formula}{schroediner_time_evolution}
\desc{Schrödinger time evolution}{}{} \desc{Schrödinger time evolution}{}{}
\desc[german]{Schrödinger Zeitentwicklug}{}{} \desc[german]{Schrödinger Zeitentwicklug}{}{}
@ -285,12 +277,11 @@
} }
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{ehrenfest_theorem}
\eng{Ehrenfest theorem} \desc{Ehrenfest theorem}{\GT{see_also} \fRef{qm:se:time:ehrenfest_theorem:correspondence_principle}}{}
\ger{Ehrenfest-Theorem} \desc[german]{Ehrenfest-Theorem}{}{}
]{ehrenfest_theorem}
\absLink{}{ehrenfest_theorem} \absLink{}{ehrenfest_theorem}
\GT{see_also} \fRef{qm:se:time:ehrenfest_theorem:correspondence_principle}
\begin{formula}{ehrenfest_theorem} \begin{formula}{ehrenfest_theorem}
\desc{Ehrenfest theorem}{applies to both pictures}{} \desc{Ehrenfest theorem}{applies to both pictures}{}
\desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{} \desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{}
@ -305,26 +296,12 @@
\end{formula} \end{formula}
% \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time} % \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{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.}{}
\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}
\begin{formula}{pertubation_hamiltonian} \begin{formula}{pertubation_hamiltonian}
\desc{Hamiltonian}{}{} \desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{} \desc[german]{Hamiltonian}{}{}
@ -368,10 +345,9 @@
\end{formula} \end{formula}
\Section[ \Section{hosc}
\eng{Harmonic oscillator} \desc{Harmonic oscillator}{}{}
\ger{Harmonischer Oszillator} \desc[german]{Harmonischer Oszillator}{}{}
]{hosc}
\begin{formula}{hamiltonian} \begin{formula}{hamiltonian}
\desc{Hamiltonian}{}{} \desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{} \desc[german]{Hamiltonian}{}{}
@ -387,10 +363,9 @@
\eq{E_n = \hbar\omega \Big(\frac{1}{2} + n\Big)} \eq{E_n = \hbar\omega \Big(\frac{1}{2} + n\Big)}
\end{formula} \end{formula}
\Subsection[ \Subsection{c_a_ops}
\ger{Erzeugungs und Vernichtungsoperatoren / Leiteroperatoren} \desc{Erzeugungs und Vernichtungsoperatoren / Leiteroperatoren}{}{}
\eng{Creation and Annihilation operators / Ladder operators} \desc[german]{Creation and Annihilation operators / Ladder operators}{}{}
]{c_a_ops}
\begin{formula}{c_a_ops_def} \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{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} \desc[german]{Teilchenzahloperator/Besetzungszahloperator}{}{$\ket{n}$ = Fock-Zustände, $\hat{a}$ = Vernichtungsoperator, $\hat{a}^\dagger$ = Erzeugungsoperator}
@ -445,10 +420,9 @@
} }
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{hosc}
\eng{Harmonischer Oszillator} \desc{Harmonischer Oszillator}{}{}
\ger{Harmonic Oscillator} \desc[german]{Harmonic Oscillator}{}{}
]{hosc}
\begin{formula}{c_a_ops} \begin{formula}{c_a_ops}
\desc{Harmonic oscillator}{}{} \desc{Harmonic oscillator}{}{}
\desc[german]{Harmonischer Oszillator}{}{} \desc[german]{Harmonischer Oszillator}{}{}
@ -475,24 +449,21 @@
% E_n=( \frac{1}{2} +n)\hbar\omega % E_n=( \frac{1}{2} +n)\hbar\omega
% \end{equation} % \end{equation}
\Section[ \Section{angular_momentum}
\eng{Angular momentum} \desc{Angular momentum}{}{}
\ger{Drehmoment} \desc[german]{Drehmoment}{}{}
]{angular_momentum}
\Subsection[ \Subsection{aharanov_bohm}
\eng{Aharanov-Bohm effect} \desc{Aharanov-Bohm effect}{}{}
\ger{Aharanov-Bohm Effekt} \desc[german]{Aharanov-Bohm Effekt}{}{}
]{aharanov_bohm}
\begin{formula}{phase} \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{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}{} \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} \eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
\end{formula} \end{formula}
\Section[ \Section{periodic}
\eng{Periodic potentials} \desc{Periodic potentials}{}{}
\ger{Periodische Potentiale} \desc[german]{Periodische Potentiale}{}{}
]{periodic}
\begin{formula}{bloch_waves} \begin{formula}{bloch_waves}
\desc{Bloch waves}{ \desc{Bloch waves}{
Solve the stat. SG in periodic potential with period Solve the stat. SG in periodic potential with period
@ -519,24 +490,18 @@
\end{formula} \end{formula}
\Section[ \Section{symmetry}
\eng{Symmetries} \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.}{}
\ger{Symmetrien} \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.}{}
]{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}
\begin{formula}{invariance} \begin{formula}{invariance}
\desc{Invariance}{$\hat{H}$ is invariant under a symmetrie described by $\hat{U}$ if this holds}{} \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:}{} \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} \eq{\hat{U}\hat{H}\hat{U}^\dagger = \hat{H} \Leftrightarrow [\hat{U}, \hat{H}] = 0}
\end{formula} \end{formula}
\Subsection[ \Subsection{time_reversal}
\eng{Time-reversal symmetry} \desc{Time-reversal symmetry}{}{}
\ger{Zeitumkehrungssymmetrie} \desc[german]{Zeitumkehrungssymmetrie}{}{}
]{time_reversal}
\begin{formula}{time} \begin{formula}{time}
\desc{Time-reversal symmetry}{}{} \desc{Time-reversal symmetry}{}{}
@ -550,10 +515,9 @@
\eq{T^2 = -1} \eq{T^2 = -1}
\end{formula} \end{formula}
\Section[ \Section{tls}
\eng{Two-level systems (TLS)} \desc{Two-level systems (TLS)}{}{}
\ger{Zwei-Niveau System (TLS)} \desc[german]{Zwei-Niveau System (TLS)}{}{}
]{tls}
\begin{formula}{james_cummings} \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{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} \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

@ -3,15 +3,13 @@
% Put quantites here that are referenced often, even if they are not exciting themselves. % 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 % This could later allow making a list of all links to this quantity, creating a list of releveant formulas
\Section[ \Section{quantities}
\eng{Physical quantities} \desc{Physical quantities}{}{}
\ger{Physikalische Größen} \desc[german]{Physikalische Größen}{}{}
]{quantities}
\Subsection[ \Subsection{si}
\eng{SI quantities} \desc{SI quantities}{}{}
\ger{SI-Basisgrößen} \desc[german]{SI-Basisgrößen}{}{}
]{si}
\begin{formula}{time} \begin{formula}{time}
\desc{Time}{}{} \desc{Time}{}{}
\desc[german]{Zeit}{}{} \desc[german]{Zeit}{}{}
@ -54,10 +52,9 @@
\quantity{I_\text{V}}{\candela}{s} \quantity{I_\text{V}}{\candela}{s}
\end{formula} \end{formula}
\Subsection[ \Subsection{mech}
\eng{Mechanics} \desc{Mechanics}{}{}
\ger{Mechanik} \desc[german]{Mechanik}{}{}
]{mech}
\begin{formula}{force} \begin{formula}{force}
\desc{Force}{}{} \desc{Force}{}{}
\desc[german]{Kraft}{}{} \desc[german]{Kraft}{}{}
@ -89,10 +86,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{td}
\eng{Thermodynamics} \desc{Thermodynamics}{}{}
\ger{Thermodynamik} \desc[german]{Thermodynamik}{}{}
]{td}
\begin{formula}{volume} \begin{formula}{volume}
\desc{Volume}{$d$ dimensional Volume}{} \desc{Volume}{$d$ dimensional Volume}{}
\desc[german]{Volumen}{$d$ dimensionales Volumen}{} \desc[german]{Volumen}{$d$ dimensionales Volumen}{}
@ -110,10 +106,9 @@
\quantity{\rho}{\kg\per\m^3}{s} \quantity{\rho}{\kg\per\m^3}{s}
\end{formula} \end{formula}
\Subsection[ \Subsection{el}
\eng{Electrodynamics} \desc{Electrodynamics}{}{}
\ger{Elektrodynamik} \desc[german]{Elektrodynamik}{}{}
]{el}
\begin{formula}{charge} \begin{formula}{charge}
\desc{Charge}{}{} \desc{Charge}{}{}
\desc[german]{Ladung}{}{} \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} \quantity{L}{\henry=\kg\m^2\per\s^2\ampere^2=\weber\per\ampere=\volt\s\per\ampere=\ohm\s}{s}
\end{formula} \end{formula}
\Subsection[ \Subsection{other}
\eng{Others} \desc{Others}{}{}
\ger{Sonstige} \desc[german]{Sonstige}{}{}
]{other}
\begin{formula}{area} \begin{formula}{area}
\desc{Area}{}{} \desc{Area}{}{}
\desc[german]{Fläche}{}{} \desc[german]{Fläche}{}{}

131
src/quantum_computing.tex

@ -1,12 +1,11 @@
\Part[ \Part{qc}
\eng{Quantum Computing} \desc{Quantum Computing}{}{}
\ger{Quantencomputing} \desc[german]{Quantencomputing}{}{}
]{qc}
\Section[
\eng{Qubits} \Section{qubit}
\ger{Qubits} \desc{Qubits}{}{}
]{qubit} \desc[german]{Qubits}{}{}
\begin{formula}{bloch_sphere} \begin{formula}{bloch_sphere}
\desc{Bloch sphere}{}{} \desc{Bloch sphere}{}{}
\desc[german]{Bloch-Sphäre}{}{} \desc[german]{Bloch-Sphäre}{}{}
@ -17,10 +16,9 @@
} }
\end{formula} \end{formula}
\Section[ \Section{gates}
\eng{Gates} \desc{Gates}{}{}
\ger{Gates} \desc[german]{Gates}{}{}
]{gates}
\begin{formula}{gates} \begin{formula}{gates}
\desc{Gates}{}{} \desc{Gates}{}{}
\desc[german]{Gates}{}{} \desc[german]{Gates}{}{}
@ -40,23 +38,16 @@
% \item \gt{bitphaseflip}: $\hat{Y} = \sigma_y = \sigmaymatrix$ % \item \gt{bitphaseflip}: $\hat{Y} = \sigma_y = \sigmaymatrix$
% \item \gt{phaseflip}: $\hat{Z} = \sigma_z = \sigmazmatrix$ \item \gt{hadamard}: $\hat{H} = \frac{1}{\sqrt{2}}(\hat{X}-\hat{Z}) = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$ % \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} % \end{itemize}
\Section[ \Section{scq}
\eng{Superconducting qubits} \desc{Superconducting qubits}{}{}
\ger{Supraleitende qubits} \desc[german]{Supraleitende qubits}{}{}
]{scq}
\Subsection[ \Subsection{elements}
\eng{Building blocks} \desc{Building blocks}{}{}
\ger{Bauelemente} \desc[german]{Bauelemente}{}{}
]{elements} \Subsubsection{josephson_junction}
\Subsubsection[ \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.}{}
\eng{Josephson Junction} \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.}{}
\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}
\begin{formula}{hamiltonian} \begin{formula}{hamiltonian}
\desc{Josephson-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} \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} \end{formula}
\Subsubsection[ \Subsubsection{squid}
\eng{SQUID} \desc{SQUID}{}{}
\ger{SQUID} \desc[german]{SQUID}{}{}
]{squid}
\ctikzsubcircuitdef{squidloop}{n, s, nw, ne, se, sw}{ \ctikzsubcircuitdef{squidloop}{n, s, nw, ne, se, sw}{
% start at top % start at top
coordinate(#1-n) 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}} \eq{\hat{H} &= -E_{\text{J}1} \cos\hat{\phi}_{1} - E_{\text{J}2} \cos\hat{\phi}_{2}}
\end{formula} \end{formula}
\Subsection[ \Subsection{josephson_qubit}
\eng{Josephson junction based qubits} \desc{Josephson junction based qubits}{}{}
\ger{Qubits mit Josephson-Junctions} \desc[german]{Qubits mit Josephson-Junctions}{}{}
]{josephson_qubit}
\begin{formula}{circuit} \begin{formula}{circuit}
\desc{General circuit}{}{} \desc{General circuit}{}{}
@ -194,20 +183,18 @@
\end{bigformula} \end{bigformula}
\Subsection[ \Subsection{charge}
\eng{Charge based qubits} \desc{Charge based qubits}{}{}
\ger{Ladungsbasierte Qubits} \desc[german]{Ladungsbasierte Qubits}{}{}
]{charge}
\begin{bigformula}{comparison} \begin{bigformula}{comparison}
\desc{Comparison of charge qubit states}{}{} \desc{Comparison of charge qubit states}{}{}
\desc[german]{Vergleich der Zustände von Ladungsbasierten Qubits}{}{} \desc[german]{Vergleich der Zustände von Ladungsbasierten Qubits}{}{}
\fig{img/qubit_transmon.pdf} \fig{img/qubit_transmon.pdf}
\end{bigformula} \end{bigformula}
\Subsubsection[ \Subsubsection{cpb}
\eng{Cooper Pair Box (CPB) qubit} \desc{Cooper Pair Box (CPB) qubit}{}{}
\ger{Cooper Paar Box (QPB) Qubit} \desc[german]{Cooper Paar Box (QPB) Qubit}{}{}
]{cpb}
\begin{ttext} \begin{ttext}
\eng{ \eng{
= voltage bias junction\\= charge qubit? = 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] } &=\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} \end{formula}
\Subsubsection[ \Subsubsection{transmon}
\eng{Transmon qubit} \desc{Transmon qubit}{}{}
\ger{Transmon Qubit} \desc[german]{Transmon Qubit}{}{}
]{transmon}
\begin{formula}{circuit} \begin{formula}{circuit}
\desc{Transmon qubit}{ \desc{Transmon qubit}{
Josephson junction with a shunt \textbf{capacitance}. 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}} \eq{\hat{H} &= 4 E_C\hat{n}^2 - E_\text{J} \cos\hat{\phi}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{tunable}
\eng{Tunable Transmon qubit} \desc{Tunable Transmon qubit}{}{}
\ger{Tunable Transmon Qubit} \desc[german]{Tunable Transmon Qubit}{}{}
]{tunable}
\begin{formula}{circuit} \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{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}{} \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[ \Subsection{inductive}
\eng{Inductive qubits} \desc{Inductive qubits}{}{}
\ger{Induktive Qubits} \desc[german]{Induktive Qubits}{}{}
]{inductive}
\begin{bigformula}{comparison} \begin{bigformula}{comparison}
\desc{Comparison of other qubit states}{}{} \desc{Comparison of other qubit states}{}{}
\desc[german]{Vergleich der Zustände von anderen Qubits}{}{} \desc[german]{Vergleich der Zustände von anderen Qubits}{}{}
\fig{img/qubit_flux_onium.pdf} \fig{img/qubit_flux_onium.pdf}
\end{bigformula} \end{bigformula}
\Subsubsection[ \Subsubsection{phase}
\eng{Phase qubit} \desc{Phase qubit}{}{}
\ger{Phase Qubit} \desc[german]{Phase Qubit}{}{}
]{phase}
\begin{formula}{circuit} \begin{formula}{circuit}
\desc{Phase qubit}{}{} \desc{Phase qubit}{}{}
\desc[german]{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} \eq{\hat{H} = E_C \hat{n}^2 - E_J \cos \hat{\delta} + E_L(\hat{\delta} - \delta_s)^2}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{flux}
\eng{Flux qubit} \desc{Flux qubit}{}{}
\ger{Flux Qubit} \desc[german]{Flux Qubit}{}{}
]{flux}
\begin{formula}{circuit} \begin{formula}{circuit}
\desc{Flux qubit / Persistent current qubit}{}{} \desc{Flux qubit / Persistent current qubit}{}{}
\desc[german]{Flux Qubit / Persistent current qubit}{}{} \desc[german]{Flux Qubit / Persistent current qubit}{}{}
@ -384,10 +366,9 @@
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{fluxonium}
\eng{Fluxonium qubit} \desc{Fluxonium qubit}{}{}
\ger{Fluxonium Qubit} \desc[german]{Fluxonium Qubit}{}{}
]{fluxonium}
\begin{formula}{circuit} \begin{formula}{circuit}
\desc{Fluxonium qubit}{ \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. 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[ \Section{stuff}
\eng{Two-level system} \desc{Two-level system}{}{}
\ger{Zwei-Niveau System} \desc[german]{Zwei-Niveau System}{}{}
]{stuff}
\begin{formula}{resonance_frequency} \begin{formula}{resonance_frequency}
\desc{Resonance frequency}{}{} \desc{Resonance frequency}{}{}
@ -444,10 +424,9 @@
\end{ttext} \end{ttext}
\end{formula} \end{formula}
\Section[ \Section{noise}
\eng{Noise and decoherence} \desc{Noise and decoherence}{}{}
\ger{Noise und Dekohärenz} \desc[german]{Noise und Dekohärenz}{}{}
]{noise}
\begin{formula}{long} \begin{formula}{long}
\desc{Longitudinal relaxation rate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{} \desc{Longitudinal relaxation rate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{}
\desc[german]{Longitudinale Relaxationsrate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{} \desc[german]{Longitudinale Relaxationsrate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{}

8
src/spv.tex

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

169
src/statistical_mechanics.tex

@ -1,7 +1,7 @@
\Part[ \Part{stat}
\eng{Statistichal Mechanics} \desc{Statistichal Mechanics}{}{}
\ger{Statistische Mechanik} \desc[german]{Statistische Mechanik}{}{}
]{stat}
\begin{ttext} \begin{ttext}
\eng{ \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\}} \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} \end{formula}
\Section[ \Section{entropy}
\eng{Entropy} \desc{Entropy}{}{}
\ger{Entropie} \desc[german]{Entropie}{}{}
]{entropy}
\begin{formula}{properties} \begin{formula}{properties}
\desc{Positive-definite and additive}{}{} \desc{Positive-definite and additive}{}{}
@ -64,10 +63,9 @@
\eq{p = T \pdv{S}{V}_E} \eq{p = T \pdv{S}{V}_E}
\end{formula} \end{formula}
\Part[ \Part{td}
\eng{Thermodynamics} \desc{Thermodynamics}{}{}
\ger{Thermodynamik} \desc[german]{Thermodynamik}{}{}
]{td}
\begin{formula}{therm_wavelength} \begin{formula}{therm_wavelength}
\desc{Thermal wavelength}{}{} \desc{Thermal wavelength}{}{}
@ -75,10 +73,9 @@
\eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}} \eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
\end{formula} \end{formula}
\Section[ \Section{process}
\eng{Processes} \desc{Processes}{}{}
\ger{Prozesse} \desc[german]{Prozesse}{}{}
]{process}
\begin{ttext} \begin{ttext}
\eng{ \eng{
\begin{itemize} \begin{itemize}
@ -106,10 +103,9 @@
} }
\end{ttext} \end{ttext}
\Subsection[ \Subsection{gay}
\eng{Irreversible gas expansion (Gay-Lussac experiment)} \desc{Irreversible gas expansion (Gay-Lussac experiment)}{}{}
\ger{Irreversible Gasexpansion (Gay-Lussac-Versuch)} \desc[german]{Irreversible Gasexpansion (Gay-Lussac-Versuch)}{}{}
]{gay}
\begin{bigformula}{experiment} \begin{bigformula}{experiment}
\desc{Gay-Lussac experiment}{}{} \desc{Gay-Lussac experiment}{}{}
@ -151,10 +147,9 @@
\TODO{Joule-Thompson Prozess} \TODO{Joule-Thompson Prozess}
\Section[ \Section{phases}
\eng{Phase transitions} \desc{Phase transitions}{}{}
\ger{Phasenübergänge} \desc[german]{Phasenübergänge}{}{}
]{phases}
\begin{ttext} \begin{ttext}
\eng{ \eng{
@ -189,10 +184,9 @@
\eq{f = c - p + 2} \eq{f = c - p + 2}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{osmosis}
\eng{Osmosis} \desc{Osmosis}{}{}
\ger{Osmose} \desc[german]{Osmose}{}{}
]{osmosis}
\begin{ttext} \begin{ttext}
\eng{ \eng{
Osmosis is the spontaneous net movement or diffusion of solvent molecules Osmosis is the spontaneous net movement or diffusion of solvent molecules
@ -215,10 +209,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{props}
\eng{Material properties} \desc{Material properties}{}{}
\ger{Materialeigenschaften} \desc[german]{Materialeigenschaften}{}{}
]{props}
\begin{formula}{heat_capacity} \begin{formula}{heat_capacity}
\desc{Heat capacity}{}{\QtyRef{heat}} \desc{Heat capacity}{}{\QtyRef{heat}}
\desc[german]{Wärmekapazität}{}{} \desc[german]{Wärmekapazität}{}{}
@ -269,15 +262,13 @@
\Section[ \Section{laws}
\eng{Laws of thermodynamics} \desc{Laws of thermodynamics}{}{}
\ger{Hauptsätze der Thermodynamik} \desc[german]{Hauptsätze der Thermodynamik}{}{}
]{laws}
\Subsection[ \Subsection{law0}
\eng{Zeroeth law} \desc{Zeroeth law}{}{}
\ger{Nullter Hauptsatz} \desc[german]{Nullter Hauptsatz}{}{}
]{law0}
\begin{ttext} \begin{ttext}
\eng{If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.} \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.} \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 A \ggwarrow C \quad\wedge\quad B \ggwarrow C \quad\Rightarrow\quad A \ggwarrow B
\end{equation} \end{equation}
\Subsection[ \Subsection{law1}
\eng{First law} \desc{First law}{}{}
\ger{Erster Hauptsatz} \desc[german]{Erster Hauptsatz}{}{}
]{law1}
\begin{ttext} \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.} \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 $W$.} \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} \end{formula}
\Subsection[ \Subsection{law2}
\eng{Second law} \desc{Second law}{}{}
\ger{Zweiter Hauptsatz} \desc[german]{Zweiter Hauptsatz}{}{}
]{law2}
\begin{ttext} \begin{ttext}
\eng{ \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.\\ \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. \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} \end{ttext}
\Subsection[ \Subsection{law3}
\eng{Third law} \desc{Third law}{}{}
\ger{Dritter Hauptsatz} \desc[german]{Dritter Hauptsatz}{}{}
]{law3}
\begin{ttext} \begin{ttext}
\eng{It is impussible to cool a system to absolute zero.} \eng{It is impussible to cool a system to absolute zero.}
\ger{Es ist unmöglich, ein System bis zum absoluten Nullpunkt abzukühlen.} \ger{Es ist unmöglich, ein System bis zum absoluten Nullpunkt abzukühlen.}
@ -343,10 +331,9 @@
} }
\end{formula} \end{formula}
\Section[ \Section{ensembles}
\eng{Ensembles} \desc{Ensembles}{}{}
\ger{Ensembles} \desc[german]{Ensembles}{}{}
]{ensembles}
\Eng[const_variables]{Constant variables} \Eng[const_variables]{Constant variables}
\Ger[const_variables]{Konstante Variablen} \Ger[const_variables]{Konstante Variablen}
@ -425,10 +412,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{pots}
\eng{Potentials} \desc{Potentials}{}{}
\ger{Potentiale} \desc[german]{Potentiale}{}{}
]{pots}
\begin{formula}{internal_energy} \begin{formula}{internal_energy}
\desc{Internal energy}{}{} \desc{Internal energy}{}{}
\desc[german]{Innere Energie}{}{} \desc[german]{Innere Energie}{}{}
@ -484,10 +470,9 @@
} }
\end{formula} \end{formula}
\Section[ \Section{id_gas}
\eng{Ideal gas} \desc{Ideal gas}{}{}
\ger{Ideales Gas} \desc[german]{Ideales Gas}{}{}
]{id_gas}
\begin{ttext} \begin{ttext}
\eng{The ideal gas consists of non-interacting, undifferentiable particles.} \eng{The ideal gas consists of non-interacting, undifferentiable particles.}
\ger{Das ideale Gas besteht aus nicht-wechselwirkenden, ununterscheidbaren Teilchen.} \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}} \eq{\braket{v^2} = \int_0^\infty \d v\,v^2 w(v) = \frac{3\kB T}{m}}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{molecule_gas}
\eng{Molecule gas} \desc{Molecule gas}{}{}
\ger{Molekülgas} \desc[german]{Molekülgas}{}{}
]{molecule_gas}
\begin{formula}{desc} \begin{formula}{desc}
\desc{Molecule gas}{2 particles of mass $M$ connected by a ``spring'' with distance $L$}{} \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} \TODO{Diagram für verschiedene Temperaturen, Weiler Skript p.83}
\Section[ \Section{real_gas}
\eng{Real gas} \desc{Real gas}{}{}
\ger{Reales Gas} \desc[german]{Reales Gas}{}{}
]{real_gas}
\Subsection[ \Subsection{virial}
\eng{Virial expansion} \desc{Virial expansion}{}{}
\ger{Virialentwicklung} \desc[german]{Virialentwicklung}{}{}
]{virial}
\begin{ttext} \begin{ttext}
\eng{Expansion of the pressure $p$ in a power series of the density $\rho$.} \eng{Expansion of the pressure $p$ in a power series of the density $\rho$.}
\ger{Entwicklung desw Drucks $p$ in eine Potenzreihe der Dichte $\rho$.} \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]} \eq{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
\end{formula} \end{formula}
\Subsection[ \Subsection{vdw}
\eng{Van der Waals equation} \desc{Van der Waals equation}{}{}
\ger{Van der Waals Gleichung} \desc[german]{Van der Waals Gleichung}{}{}
]{vdw}
\begin{ttext} \begin{ttext}
\eng{Assumes a hard-core potential with a weak attraction.} \eng{Assumes a hard-core potential with a weak attraction.}
\ger{Annahme eines Harte-Kugeln Potentials mit einer schwachen Anziehung} \ger{Annahme eines Harte-Kugeln Potentials mit einer schwachen Anziehung}
@ -654,10 +635,9 @@
\TODO{sometimes N is included in a, b} \TODO{sometimes N is included in a, b}
\Section[ \Section{id_qgas}
\eng{Ideal quantum gas} \desc{Ideal quantum gas}{}{}
\ger{Ideales Quantengas} \desc[german]{Ideales Quantengas}{}{}
]{id_qgas}
\def\bosfer{$\pm$: {$\text{bos} \atop \text{fer}$}} \def\bosfer{$\pm$: {$\text{bos} \atop \text{fer}$}}
\begin{formula}{fugacity} \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}} \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} \end{formula}
\Subsection[ \Subsection{bos}
\eng{Bosons} \desc{Bosons}{}{}
\ger{Bosonen} \desc[german]{Bosonen}{}{}
]{bos}
\begin{formula}{partition-sum} \begin{formula}{partition-sum}
\desc{Partition sum}{}{$p \in\N_0$} \desc{Partition sum}{}{$p \in\N_0$}
\desc[german]{Zustandssumme}{}{$p \in\N_0$} \desc[german]{Zustandssumme}{}{$p \in\N_0$}
@ -762,10 +741,9 @@
\end{formula} \end{formula}
\Subsection[ \Subsection{fer}
\eng{Fermions} \desc{Fermions}{}{}
\ger{Fermionen} \desc[german]{Fermionen}{}{}
]{fer}
\begin{formula}{partition_sum} \begin{formula}{partition_sum}
\desc{Partition sum}{}{$p = 0,\,1$} \desc{Partition sum}{}{$p = 0,\,1$}
\desc[german]{Zustandssumme}{}{$p = 0,\,1$} \desc[german]{Zustandssumme}{}{$p = 0,\,1$}
@ -815,10 +793,9 @@
\eq{v = \frac{N}{V} = \frac{g}{\lambda^3}f_{3/2}(z)} \eq{v = \frac{N}{V} = \frac{g}{\lambda^3}f_{3/2}(z)}
\end{formula} \end{formula}
\Subsubsection[ \Subsubsection{degenerate}
\eng{Strong degeneracy} \desc{Strong degeneracy}{}{}
\ger{Starke Entartung} \desc[german]{Starke Entartung}{}{}
]{degenerate}
\eng[low_temps]{for low temperatures $T \ll T_\text{F}$} \eng[low_temps]{for low temperatures $T \ll T_\text{F}$}
\ger[low_temps]{für geringe Temperaturen $T\ll T_\text{F}$} \ger[low_temps]{für geringe Temperaturen $T\ll T_\text{F}$}

30
src/test.tex

@ -103,3 +103,33 @@ Link to defined quantity: \qtyRef{mass}
\end{formula} \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}

6
src/util/environments.tex

@ -29,8 +29,8 @@
% %
% DISTRIBUTION % DISTRIBUTION
% %
\def\distrightwidth{0.45\textwidth} \def\distrightwidth{0.45}
\def\distleftwidth{0.45\textwidth} \def\distleftwidth{0.45}
% Table for distributions % Table for distributions
% create entries for parameters using \disteq % create entries for parameters using \disteq
@ -57,7 +57,6 @@
& ##2 \\ \hline & ##2 \\ \hline
} }
\hfill \hfill
\begin{minipage}{\distrightwidth}
\begingroup \begingroup
\setlength{\tabcolsep}{0.9em} % horizontal \setlength{\tabcolsep}{0.9em} % horizontal
\renewcommand{\arraystretch}{2} % vertical \renewcommand{\arraystretch}{2} % vertical
@ -66,7 +65,6 @@
}{ }{
\end{tabular} \end{tabular}
\endgroup \endgroup
\end{minipage}
} }
% A 2 column table in a minipage % A 2 column table in a minipage