diff --git a/scripts/distributions.py b/scripts/distributions.py
index bda9304..8ffff58 100644
--- a/scripts/distributions.py
+++ b/scripts/distributions.py
@@ -24,6 +24,20 @@ def gauss():
ax.legend()
return fig
+# LAPLACE
+def flaplace(x, mu, b):
+ return 1 / (2*b) * np.exp(-np.abs(x - mu) / b)
+
+def laplace():
+ fig, ax = get_fig()
+ x = np.linspace(-5, 5, 300)
+ for mu, b in [(0, 1), (0, 2), (0, 5), (-2, 2)]:
+ y = flaplace(x, mu, b)
+ label = texvar("mu", mu) + ", " + texvar("b", b)
+ ax.plot(x, y, label=label)
+ ax.legend()
+ return fig
+
# CAUCHY / LORENTZ
def fcauchy(x, x_0, gamma):
return 1 / (np.pi * gamma * (1 + ((x - x_0)/gamma)**2))
@@ -128,6 +142,7 @@ def binomial():
if __name__ == '__main__':
export(gauss(), "distribution_gauss")
+ export(laplace(), "distribution_laplace")
export(cauchy(), "distribution_cauchy")
export(maxwell(), "distribution_maxwell-boltzmann")
export(gamma(), "distribution_gamma")
diff --git a/src/ch/ch.tex b/src/ch/ch.tex
index c1fc103..942653b 100644
--- a/src/ch/ch.tex
+++ b/src/ch/ch.tex
@@ -1,9 +1,8 @@
-\Part[
- \eng{Chemistry}
- \ger{Chemie}
-]{ch}
-\Section[
- \eng{Periodic table}
- \ger{Periodensystem}
-]{ptable}
+\Part{ch}
+ \desc{Chemistry}{}{}
+ \desc[german]{Chemie}{}{}
+
+\Section{ptable}
+ \desc{Periodic table}{}{}
+ \desc[german]{Periodensystem}{}{}
\drawPeriodicTable
diff --git a/src/ch/el.tex b/src/ch/el.tex
index 8c4977f..cf88b79 100644
--- a/src/ch/el.tex
+++ b/src/ch/el.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Electrochemistry}
- \ger{Elektrochemie}
-]{el}
+\Section{el}
+ \desc{Electrochemistry}{}{}
+ \desc[german]{Elektrochemie}{}{}
+
\begin{formula}{chemical_potential}
\desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{free_enthalpy}, \QtyRef{amount}}
\desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
@@ -38,10 +38,9 @@
\end{formula}
-\Subsection[
- \eng{Electrochemical cell}
- \ger{Elektrochemische Zelle}
-]{cell}
+\Subsection{cell}
+ \desc{Electrochemical cell}{}{}
+ \desc[german]{Elektrochemische Zelle}{}{}
\eng[galvanic]{galvanic}
\ger[galvanic]{galvanisch}
\eng[electrolytic]{electrolytic}
@@ -162,10 +161,9 @@
\end{formula}
-\Subsection[
- \eng{Ionic conduction in electrolytes}
- \ger{Ionische Leitung in Elektrolyten}
-]{ion_cond}
+\Subsection{ion_cond}
+ \desc{Ionic conduction in electrolytes}{}{}
+ \desc[german]{Ionische Leitung in Elektrolyten}{}{}
\eng[z]{charge number}
\ger[z]{Ladungszahl}
\eng[of_i]{of ion $i$}
@@ -280,10 +278,9 @@
\eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
\end{formula}
-\Subsection[
- \eng{Kinetics}
- \ger{Kinetik}
-]{kin}
+\Subsection{kin}
+ \desc{Kinetics}{}{}
+ \desc[german]{Kinetik}{}{}
\begin{formula}{transfer_coefficient}
\desc{Transfer coefficient}{}{}
\desc[german]{Durchtrittsfaktor}{Transferkoeffizient\\Anteil des Potentials der sich auf die freie Reaktionsenthalpie des anodischen Prozesses auswirkt}{}
@@ -307,10 +304,9 @@
\eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
\end{formula}
- \Subsubsection[
- \eng{Mass transport}
- \ger{Massentransport}
- ]{mass}
+ \Subsubsection{mass}
+ \desc{Mass transport}{}{}
+ \desc[german]{Massentransport}{}{}
\begin{formula}{concentration_overpotential}
\desc{Concentration overpotential}{Due to concentration gradient near the electrode, the ions need to \fRef[diffuse]{ch:el:ion_cond:diffusion} to the electrode before reacting}{\ConstRef{universal_gas}, \QtyRef{temperature}, $\c_{0/\txS}$ ion concentration in the electrolyte / at the double layer, $z$ \qtyRef{charge_number}, \ConstRef{faraday}}
\desc[german]{Konzentrationsüberspannung}{Durch einen Konzentrationsgradienten an der Elektrode müssen Ionen erst zur Elektrode \fRef[diffundieren]{ch:el:ion_cond:diffusion}, bevor sie reagieren können}{}
@@ -488,15 +484,13 @@
-\Subsection[
- \eng{Techniques}
- \ger{Techniken}
-]{tech}
+\Subsection{tech}
+ \desc{Techniques}{}{}
+ \desc[german]{Techniken}{}{}
- \Subsubsection[
- \eng{Reference electrodes}
- \ger{Referenzelektroden}
- ]{ref}
+ \Subsubsection{ref}
+ \desc{Reference electrodes}{}{}
+ \desc[german]{Referenzelektroden}{}{}
\begin{ttext}
\eng{Defined as reference for measuring half-cell potententials}
\ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
@@ -522,10 +516,9 @@
- \Subsubsection[
- \eng{Cyclic voltammetry}
- \ger{Zyklische Voltammetrie}
- ]{cv}
+ \Subsubsection{cv}
+ \desc{Cyclic voltammetry}{}{}
+ \desc[german]{Zyklische Voltammetrie}{}{}
\begin{bigformula}{duck}
\desc{Cyclic voltammogram}{}{}
% \desc[german]{}{}{}
@@ -647,10 +640,9 @@
\eq{j_\infty = nFD \frac{c^0}{\delta_\text{diff}} = \frac{1}{1.61} nFD^{\frac{2}{3}} v^{\frac{-1}{6}} c^0 \sqrt{\omega}}
\end{formula}
- \Subsubsection[
- \eng{AC-Impedance}
- \ger{AC-Impedanz}
- ]{ac}
+ \Subsubsection{ac}
+ \desc{AC-Impedance}{}{}
+ \desc[german]{AC-Impedanz}{}{}
\begin{formula}{nyquist}
\desc{Nyquist diagram}{Real and imaginary parts of \qtyRef{impedance} while varying the frequency}{}
\desc[german]{Nyquist-Diagram}{Real und Imaginaärteil der \qtyRef{impedance} während die Frequenz variiert wird}{}
diff --git a/src/ch/misc.tex b/src/ch/misc.tex
index f8d83ec..4c5ce8f 100644
--- a/src/ch/misc.tex
+++ b/src/ch/misc.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Thermoelectricity}
- \ger{Thermoelektrizität}
-]{thermo}
+\Section{thermo}
+ \desc{Thermoelectricity}{}{}
+ \desc[german]{Thermoelektrizität}{}{}
+
\begin{formula}{seebeck}
\desc{Seebeck coefficient}{Thermopower}{$V$ voltage, \QtyRef{temperature}}
\desc[german]{Seebeck-Koeffizient}{}{}
@@ -35,10 +35,9 @@
\end{formula}
-\Section[
- \eng{misc}
- \ger{misc}
-]{misc}
+\Section{misc}
+ \desc{misc}{}{}
+ \desc[german]{misc}{}{}
% TODO: hide
\begin{formula}{stoichiometric_coefficient}
diff --git a/src/cm/charge_transport.tex b/src/cm/charge_transport.tex
index 1fed869..f3cf2b3 100644
--- a/src/cm/charge_transport.tex
+++ b/src/cm/charge_transport.tex
@@ -1,11 +1,10 @@
-\Section[
- \eng{Charge transport}
- \ger{Ladungstransport}
-]{charge_transport}
-\Subsection[
- \eng{Drude model}
- \ger{Drude-Modell}
-]{drude}
+\Section{charge_transport}
+ \desc{Charge transport}{}{}
+ \desc[german]{Ladungstransport}{}{}
+
+\Subsection{drude}
+ \desc{Drude model}{}{}
+ \desc[german]{Drude-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -48,10 +47,9 @@
\eq{\sigma = \frac{\vec{j}}{\vec{\E}} = \frac{n e^2 \tau}{\masse} = n e \mu}
\end{formula}
-\Subsection[
- \eng{Sommerfeld model}
- \ger{Sommerfeld-Modell}
-]{sommerfeld}
+\Subsection{sommerfeld}
+ \desc{Sommerfeld model}{}{}
+ \desc[german]{Sommerfeld-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -66,10 +64,9 @@
\eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
\end{formula}
-\Subsection[
- \eng{Boltzmann-transport}
- \ger{Boltzmann-Transport}
-]{boltzmann}
+\Subsection{boltzmann}
+ \desc{Boltzmann-transport}{}{}
+ \desc[german]{Boltzmann-Transport}{}{}
\begin{ttext}
\eng{Semiclassical description using a probability distribution (\fRef{cm:sc:fermi_dirac}) to describe the particles.}
\ger{Semiklassische Beschreibung, benutzt eine Wahrscheinlichkeitsverteilung (\fRef{cm:sc:fermi_dirac}).}
@@ -82,10 +79,9 @@
}
\end{formula}
-\Subsection[
- \eng{Magneto-transport}
- \ger{Magnetotransport}
-]{mag}
+\Subsection{mag}
+ \desc{Magneto-transport}{}{}
+ \desc[german]{Magnetotransport}{}{}
\begin{formula}{cyclotron_frequency}
\desc{Cyclotron frequency}{Moving charge carriers move in cyclic orbits under applied magnetic field}{$q$ \qtyRef{charge}, \QtyRef{magnetic_flux_density}, m \qtyRef[effective]{mass}}
\desc[german]{Zyklotronfrequenz}{Ladungstraäger bewegen sich in einem Magnetfeld auf einer Kreisbahn}{}
@@ -98,13 +94,96 @@
% \desc[german]{}{}{}
% \eq{}
% \end{formula}
- \TODO{move hall here}
+
+ \Subsubsection{hall}
+ \desc{Hall-Effect}{}{}
+ \desc[german]{Hall-Effekt}{}{}
+
+
+ \Paragraph{classic}
+ \desc{Classical Hall-Effect}{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}{}
+ \desc[german]{Klassischer Hall-Effekt}{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}{}
+ \begin{formula}{voltage}
+ \desc{Hall voltage}{}{$n$ charge carrier density}
+ \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
+ \eq{U_\text{H} = \frac{I B}{ne d}}
+ \end{formula}
+
+ \begin{formula}{coefficient}
+ \desc{Hall coefficient}{Sometimes $R_\txH$}{}
+ \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
+ \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
+ \end{formula}
+
+ \begin{formula}{resistivity}
+ \desc{Resistivity}{}{}
+ \desc[german]{Spezifischer Widerstand}{}{}
+ \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
+ \end{formula}
+
+
+ \Paragraph{quantum}
+ \desc{Quantum hall effects}{}{}
+ \desc[german]{Quantenhalleffekte}{}{}
+ \begin{formula}{types}
+ \desc{Types of quantum hall effects}{}{}
+ \desc[german]{Arten von Quantenhalleffekten}{}{}
+ \ttxt{\eng{
+ \begin{itemize}
+ \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
+ \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
+ \item \textbf{Spin} (QSHE): spin currents instead of charge currents
+ \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
+ \end{itemize}
+ }\ger{
+ \begin{itemize}
+ \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
+ \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
+ \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
+ \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
+ \end{itemize}
+ }}
+ \end{formula}
+
+
+
+ \begin{formula}{conductivity}
+ \desc{Conductivity tensor}{}{}
+ \desc[german]{Leitfähigkeitstensor}{}{}
+ \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+ \end{formula}
+
+ \begin{formula}{resistivity_tensor}
+ \desc{Resistivity tensor}{}{}
+ \desc[german]{Spezifischer Widerstands-tensor}{}{}
+ \eq{
+ \rho = \sigma^{-1}
+ % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
+ }
+ \end{formula}
+
+ \begin{formula}{resistivity}
+ \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
+ \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
+ \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
+ \end{formula}
+
+ % \begin{formula}{qhe}
+ % \desc{Integer quantum hall effect}{}{}
+ % \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
+ % \fig{img/qhe-klitzing.jpeg}
+ % \end{formula}
+
+ \begin{formula}{fqhe}
+ \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
+ \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
+ \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
+ \end{formula}
-\Subsection[
- \eng{misc}
- \ger{misc}
-]{misc}
+\Subsection{misc}
+ \desc{misc}{}{}
+ \desc[german]{misc}{}{}
\begin{formula}{tsu_esaki}
\desc{Tsu-Esaki tunneling current}{Describes the current $I_{\txL \leftrightarrow \txR}$ through a barrier}{$\mu_i$ \qtyRef{chemical_potential} at left/right side, $U_i$ voltage on left/right side. Electrons occupy region between $U_i$ and $\mu_i$}
\desc[german]{Tsu-Esaki Tunnelstrom}{Beschreibt den Strom $I_{\txL \leftrightarrow \txR}$ durch eine Barriere }{$\mu_i$ \qtyRef{chemical_potential} links/rechts, $U_i$ Spannung links/rechts. Elektronen besetzen Bereich zwischen $U_i$ und $\mu_i$}
diff --git a/src/cm/cm.tex b/src/cm/cm.tex
index 05c8aef..e74964b 100644
--- a/src/cm/cm.tex
+++ b/src/cm/cm.tex
@@ -1,8 +1,8 @@
-\Part[
- \eng{Condensed matter physics}
- \ger{Festkörperphysik}
-]{cm}
- \TODO{van hove singularities, debye frequency}
+\Part{cm}
+ \desc{Condensed matter physics}{}{}
+ \desc[german]{Festkörperphysik}{}{}
+
+ \TODO{van hove singularities}
\begin{formula}{dos}
\desc{Density of states (DOS)}{}{\QtyRef{volume}, $N$ number of energy levels, \QtyRef{energy}}
@@ -11,12 +11,9 @@
\eq{D(E) = \frac{1}{V}\sum_{i=1}^{N} \delta(E-E(\vec{k_i}))}
\end{formula}
-
-
-\Section[
- \eng{Bonds}
- \ger{Bindungen}
-]{bond}
+\Section{bond}
+ \desc{Bonds}{}{}
+ \desc[german]{Bindungen}{}{}
\begin{formula}{metallic}
\desc{Metallic bond}{}{}
\desc[german]{Metallbindung}{}{}
diff --git a/src/cm/crystal.tex b/src/cm/crystal.tex
index 64d10d3..2845502 100644
--- a/src/cm/crystal.tex
+++ b/src/cm/crystal.tex
@@ -1,11 +1,11 @@
-\Section[
- \eng{Crystals}
- \ger{Kristalle}
-]{crystal}
-\Subsection[
- \eng{Bravais lattice}
- \ger{Bravais-Gitter}
-]{bravais}
+\Section{crystal}
+ \desc{Crystals}{}{}
+ \desc[german]{Kristalle}{}{}
+
+\Subsection{bravais}
+ \desc{Bravais lattice}{}{}
+ \desc[german]{Bravais-Gitter}{}{}
+
\Eng[lattice_system]{Lattice system}
\Ger[lattice_system]{Gittersystem}
\Eng[crystal_family]{Crystal system}
@@ -197,14 +197,9 @@
\end{formula}
-\Subsection[
- \eng{Reciprocal lattice}
- \ger{Reziprokes Gitter}
-]{reci}
- \begin{ttext}
- \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
- \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
- \end{ttext}
+\Subsection{reci}
+ \desc{Reciprocal lattice}{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}{}
+ \desc[german]{Reziprokes Gitter}{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}{}
\begin{formula}{vectors}
\desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
@@ -222,10 +217,9 @@
\eq{\vec{G}_{{hkl}} = h \vec{b_1} + k \vec{b_2} + l \vec{b_3}}
\end{formula}
- \Subsection[
- \eng{Scattering processes}
- \ger{Streuprozesse}
- ]{scatter}
+ \Subsection{scatter}
+ \desc{Scattering processes}{}{}
+ \desc[german]{Streuprozesse}{}{}
\begin{formula}{matthiessen}
\desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{\QtyRef{mobility}, \QtyRef{scattering_time}}
\desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{}
@@ -235,10 +229,10 @@
}
\end{formula}
-\Subsection[
- \eng{Lattices}
- \ger{Gitter}
-]{lat}
+\Subsection{lat}
+ \desc{Lattices}{}{}
+ \desc[german]{Gitter}{}{}
+
\begin{formula}{sc}
\desc{Simple cubic (SC)}{Reciprocal: Simple cubic}{\QtyRef{lattice_constant}}
\desc[german]{Einfach kubisch (SC)}{Reziprok: Einfach kubisch}{}
diff --git a/src/cm/egas.tex b/src/cm/egas.tex
index a8096af..53fbfce 100644
--- a/src/cm/egas.tex
+++ b/src/cm/egas.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Free electron gas}
- \ger{Freies Elektronengase}
-]{egas}
+\Section{egas}
+ \desc{Free electron gas}{}{}
+ \desc[german]{Freies Elektronengase}{}{}
+
\begin{formula}{desc}
\desc{Description}{\GT{see_also}: \fRef{td:id_qgas}}{}
\desc[german]{Beschreibung}{}{}
@@ -31,20 +31,18 @@
\eq{\mu = \frac{q \tau}{m}}
\end{formula}
-\Subsection[
- \eng{3D electron gas}
- \ger{3D Elektronengas}
-]{3deg}
+\Subsection{3deg}
+ \desc{3D electron gas}{}{}
+ \desc[german]{3D Elektronengas}{}{}
\begin{formula}{dos}
\desc{Density of states}{}{}
\desc[german]{Zustandsdichte}{}{}
\eq{D_\text{3D}(E) = \frac{1}{2\pi^2} \left(\frac{2m}{\hbar^2}\right)^{3/2} \sqrt{E}}
\end{formula}
-\Subsection[
- \eng{2D electron gas}
- \ger{2D Elektronengas}
-]{2deg}
+\Subsection{2deg}
+ \desc{2D electron gas}{}{}
+ \desc[german]{2D Elektronengas}{}{}
\begin{ttext}
\eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
\ger{
@@ -71,10 +69,9 @@
\eq{D_\text{2D}(E) = \frac{m}{\pi\hbar^2}}
\end{formula}
-\Subsection[
- \eng{1D electron gas / quantum wire}
- \ger{1D Eleltronengas / Quantendraht}
-]{1deg}
+\Subsection{1deg}
+ \desc{1D electron gas / quantum wire}{}{}
+ \desc[german]{1D Eleltronengas / Quantendraht}{}{}
\begin{formula}{energy}
\desc{Energy}{}{}
@@ -90,10 +87,9 @@
\TODO{condunctance}
-\Subsection[
- \eng{0D electron gas / quantum dot}
- \ger{0D Elektronengase / Quantenpunkt}
-]{0deg}
+\Subsection{0deg}
+ \desc{0D electron gas / quantum dot}{}{}
+ \desc[german]{0D Elektronengase / Quantenpunkt}{}{}
\begin{formula}{dos}
\desc{Density of states}{}{}
\desc[german]{Zustandsdichte}{}{}
diff --git a/src/cm/mat.tex b/src/cm/mat.tex
index 66f351c..f0d2d8f 100644
--- a/src/cm/mat.tex
+++ b/src/cm/mat.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Material physics}
- \ger{Materialphysik}
-]{mat}
+\Section{mat}
+ \desc{Material physics}{}{}
+ \desc[german]{Materialphysik}{}{}
+
\begin{formula}{tortuosity}
\desc{Tortuosity}{Degree of the winding of a transport path through a porous material. \\ Multiple definitions exist}{$l$ path length, $L$ distance of the end points}
diff --git a/src/cm/misc.tex b/src/cm/misc.tex
index 2bdde1d..620dd1c 100644
--- a/src/cm/misc.tex
+++ b/src/cm/misc.tex
@@ -1,15 +1,10 @@
-\Section[
- \eng{Band theory}
- \ger{Bändermodell}
-]{band}
- \Subsection[
- \eng{Hybrid orbitals}
- \ger{Hybridorbitale}
- ]{hybrid_orbitals}
- \begin{ttext}
- \eng{Hybrid orbitals are linear combinations of other atomic orbitals.}
- \ger{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.}
- \end{ttext}
+\Section{band}
+ \desc{Band theory}{}{}
+ \desc[german]{Bändermodell}{}{}
+
+ \Subsection{hybrid_orbitals}
+ \desc{Hybrid orbitals}{Hybrid orbitals are linear combinations of other atomic orbitals.}{}
+ \desc[german]{Hybridorbitale}{Hybridorbitale werden durch Linearkombinationen von anderen atomorbitalen gebildet.}{}
% chemmacros package
\begin{formula}{sp}
@@ -51,10 +46,9 @@
-\Section[
- \eng{Diffusion}
- \ger{Diffusion}
-]{diffusion}
+\Section{diffusion}
+ \desc{Diffusion}{}{}
+ \desc[german]{Diffusion}{}{}
\begin{formula}{diffusion_coefficient}
\desc{Diffusion coefficient}{}{}
\desc[german]{Diffusionskoeffizient}{}{}
@@ -91,10 +85,10 @@
\eq{\pdv{c}{t} = D \pdv[2]{c}{x}}
\end{formula}
-\Section[
- \eng{\GT{misc}}
- \ger{\GT{misc}}
-]{misc}
+\Section{misc}
+ % \desc{\GT{misc}}{}{}
+ % \desc[german]{\GT{misc}}{}{}
+
\begin{formula}{vdw_material}
\desc{Van-der-Waals material}{2D materials}{}
diff --git a/src/cm/semiconductors.tex b/src/cm/semiconductors.tex
index 6a754ac..2f88369 100644
--- a/src/cm/semiconductors.tex
+++ b/src/cm/semiconductors.tex
@@ -1,8 +1,7 @@
\def\meff{m^{*}}
-\Section[
- \eng{Semiconductors}
- \ger{Halbleiter}
-]{sc}
+\Section{sc}
+ \desc{Semiconductors}{}{}
+ \desc[german]{Halbleiter}{}{}
\begin{formula}{description}
\desc{Description}{}{$n,p$ \fRef{cm:sc:charge_carrier_density:equilibrium}}
\desc[german]{Beschreibung}{}{}
@@ -137,10 +136,9 @@
\end{formula}
\TODO{effective mass approx}
-\Subsection[
- \eng{Doping}
- \ger{Dotierung}
-]{dope}
+\Subsection{dope}
+ \desc{Doping}{}{}
+ \desc[german]{Dotierung}{}{}
\begin{formula}{description}
\desc{Description}{}{}
@@ -183,14 +181,12 @@
\TODO{plot}
\end{formula}
-\Subsection[
- \eng{Defects}
- \ger{Defekte}
-]{defect}
- \Subsubsection[
- \eng{Point defects}
- \ger{Punktdefekte}
- ]{point}
+\Subsection{defect}
+ \desc{Defects}{}{}
+ \desc[german]{Defekte}{}{}
+ \Subsubsection{point}
+ \desc{Point defects}{}{}
+ \desc[german]{Punktdefekte}{}{}
\begin{formula}{vacancy}
\desc{Vacancy}{}{}
\desc[german]{Fehlstelle}{}{}
@@ -245,10 +241,9 @@
}}
\end{formula}
- \Subsubsection[
- \eng{Line defects}
- \ger{Liniendefekte}
- ]{line}
+ \Subsubsection{line}
+ \desc{Line defects}{}{}
+ \desc[german]{Liniendefekte}{}{}
\begin{formula}{edge}
\desc{Edge distortion}{}{}
\desc[german]{Stufenversetzung}{}{}
@@ -279,10 +274,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{Area defects}
- \ger{Flächendefekte}
- ]{area}
+ \Subsubsection{area}
+ \desc{Area defects}{}{}
+ \desc[german]{Flächendefekte}{}{}
\begin{formula}{grain_boundary}
\desc{Grain boundary}{}{}
\desc[german]{Korngrenze}{}{}
@@ -303,10 +297,9 @@
}}
\end{formula}
-\Subsection[
- \eng{Devices and junctions}
- \ger{Bauelemente und Kontakte}
-]{junctions}
+\Subsection{junctions}
+ \desc{Devices and junctions}{}{}
+ \desc[german]{Bauelemente und Kontakte}{}{}
\begin{formula}{metal-sc}
\desc{Metal-semiconductor junction}{}{}
\desc[german]{Metall-Halbleiter Kontakt}{}{}
@@ -350,10 +343,9 @@
-\Subsection[
- \eng{Excitons}
- \ger{Exzitons}
-]{exciton}
+\Subsection{exciton}
+ \desc{Excitons}{}{}
+ \desc[german]{Exzitons}{}{}
\begin{formula}{desc}
\desc{Exciton}{}{}
\desc[german]{Exziton}{}{}
diff --git a/src/cm/superconductivity.tex b/src/cm/superconductivity.tex
index 2f629a8..5f5454b 100644
--- a/src/cm/superconductivity.tex
+++ b/src/cm/superconductivity.tex
@@ -4,21 +4,15 @@
\def\Tcrit{T_\text{c}}
\def\Bcth{B_\text{c,th}}
-\Section[
- \eng{Superconductivity}
- \ger{Supraleitung}
-]{super}
- \begin{ttext}
- \eng{
+\Section{super}
+ \desc{Superconductivity}{
Materials for which the electric resistance jumps to 0 under a critical temperature $\Tcrit$.
Below $\Tcrit$ they have perfect conductivity and perfect diamagnetism, up until a critical magnetic field $\Bcth$.
- }
- \ger{
+ }{}
+ \desc[german]{Supraleitung}{
Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur $\Tcrit$ auf 0 springt.
Sie verhalten sich dann wie ideale Leiter und ideale Diamagnete, bis zu einem kritischen Feld $\Bcth$.
-
- }
- \end{ttext}
+ }{}
\begin{formula}{type1}
\desc{Type-I superconductor}{}{}
@@ -92,10 +86,9 @@
}
\end{formula}
- \Subsection[
- \eng{London Theory}
- \ger{London-Theorie}
- ]{london}
+ \Subsection{london}
+ \desc{London Theory}{}{}
+ \desc[german]{London-Theorie}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -148,10 +141,9 @@
\eq{\lambda_\txL(T) = \lambda_\txL(0) \frac{1}{\sqrt{1- \left(\frac{T}{T_\txc}\right)^4}}}
\end{formula}
- \Subsubsection[
- \eng{Macroscopic wavefunction}
- \ger{Makroskopische Wellenfunktion}
- ]{macro}
+ \Subsubsection{macro}
+ \desc{Macroscopic wavefunction}{}{}
+ \desc[german]{Makroskopische Wellenfunktion}{}{}
\begin{formula}{ansatz}
\desc{Ansatz}{}{}
\desc[german]{Ansatz}{}{}
@@ -170,10 +162,9 @@
\end{formula}
- \Subsubsection[
- \eng{Josephson Effect}
- \ger{Josephson Effekt}
- ]{josephson}
+ \Subsubsection{josephson}
+ \desc{Josephson Effect}{}{}
+ \desc[german]{Josephson Effekt}{}{}
\begin{formula}{1st_relation}
\desc{1. Josephson relation}{Dissipationless supercurrent accros junction at zero applied voltage}{$\vecj_\text{C}=\frac{2e}{\hbar}E_\text{J}$ critical current, $\phi$ phase difference accross junction}
\desc[german]{1. Josephson Gleichung}{Dissipationsloser Suprastrom durch die Kreuzung ohne angelegte Spannung}{$\vecj_\text{C}=\frac{2e}{\hbar}E_\text{J}$ kritischer Strom, $\phi$ Phasendifferenz zwischen den Supraleitern}
@@ -195,10 +186,9 @@
- \Subsection[
- \eng{\GL Theory (GLAG)}
- \ger{\GL Theorie (GLAG)}
- ]{gl}
+ \Subsection{gl}
+ \desc{\GL Theory (GLAG)}{}{}
+ \desc[german]{\GL Theorie (GLAG)}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -326,10 +316,9 @@
}}
\end{formula}
- \Subsection[
- \eng{Microscopic theory}
- \ger{Mikroskopische Theorie}
- ]{micro}
+ \Subsection{micro}
+ \desc{Microscopic theory}{}{}
+ \desc[german]{Mikroskopische Theorie}{}{}
\begin{formula}{isotop_effect}
\desc{Isotope effect}{Superconducting behaviour depends on atomic mass and thereby on the lattice \Rightarrow Microscopic origin}{$\Tcrit$ critial temperature, $M$ isotope mass, $\omega_\text{ph}$}
\desc[german]{Isotopeneffekt}{Supraleitung hängt von der Atommasse und daher von den Gittereigenschaften ab \Rightarrow Mikroskopischer Ursprung}{$\Tcrit$ kritische Temperatur, $M$ Isotopen-Masse, $\omega_\text{ph}$}
@@ -347,10 +336,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{BCS-Theory}
- \ger{BCS-Theorie}
- ]{bcs}
+ \Subsubsection{bcs}
+ \desc{BCS-Theory}{}{}
+ \desc[german]{BCS-Theorie}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -429,10 +417,9 @@
\eq{E \approx 2E_\txF - 2\hbar\omega_\txD \Exp{-\frac{4}{V_0 D(E_\txF)}}}
\end{formula}
- \Subsubsection[
- \eng{Excitations and finite temperatures}
- \ger{Anregungen und endliche Temperatur}
- ]{excite}
+ \Subsubsection{excite}
+ \desc{Excitations and finite temperatures}{}{}
+ \desc[german]{Anregungen und endliche Temperatur}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -522,10 +509,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{Flux pinning}
- \ger{Haftung von Flusslinien}
- ]{pinning}
+ \Subsubsection{pinning}
+ \desc{Flux pinning}{}{}
+ \desc[german]{Haftung von Flusslinien}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
diff --git a/src/cm/techniques.tex b/src/cm/techniques.tex
index 9255374..d633e83 100644
--- a/src/cm/techniques.tex
+++ b/src/cm/techniques.tex
@@ -1,22 +1,20 @@
-\Section[
- \eng{Techniques}
- \ger{Techniken}
-]{tech}
+\Section{tech}
+ \desc{Techniques}{}{}
+ \desc[german]{Techniken}{}{}
-\Subsection[
- \eng{Measurement techniques}
- \ger{Messtechniken}
-]{meas}
+
+\Subsection{meas}
+ \desc{Measurement techniques}{}{}
+ \desc[german]{Messtechniken}{}{}
\Eng[name]{Name}
\Ger[name]{Name}
\Eng[application]{Application}
\Ger[application]{Anwendung}
- \Subsubsection[
- \eng{Raman spectroscopy}
- \ger{Raman Spektroskopie}
- ]{raman}
+ \Subsubsection{raman}
+ \desc{Raman spectroscopy}{}{}
+ \desc[german]{Raman Spektroskopie}{}{}
% TODO remove fqname from minipagetable?
@@ -66,19 +64,17 @@
\end{bigformula}
- \Subsubsection[
- \eng{ARPES}
- \ger{ARPES}
- ]{arpes}
+ \Subsubsection{arpes}
+ \desc{ARPES}{}{}
+ \desc[german]{ARPES}{}{}
what?
in?
how?
plot
- \Subsubsection[
- \eng{Scanning probe microscopy SPM}
- \ger{Rastersondenmikroskopie (SPM)}
- ]{spm}
+ \Subsubsection{spm}
+ \desc{Scanning probe microscopy SPM}{}{}
+ \desc[german]{Rastersondenmikroskopie (SPM)}{}{}
\begin{ttext}
\eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
\ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
@@ -132,10 +128,9 @@
\end{minipage}
\end{bigformula}
-\Subsection[
- \eng{Fabrication techniques}
- \ger{Herstellungsmethoden}
-]{fab}
+\Subsection{fab}
+ \desc{Fabrication techniques}{}{}
+ \desc[german]{Herstellungsmethoden}{}{}
\begin{bigformula}{cvd}
\desc{Chemical vapor deposition (CVD)}{}{}
@@ -177,10 +172,9 @@
\end{bigformula}
- \Subsubsection[
- \eng{Epitaxy}
- \ger{Epitaxie}
- ]{epitaxy}
+ \Subsubsection{epitaxy}
+ \desc{Epitaxy}{}{}
+ \desc[german]{Epitaxie}{}{}
\begin{ttext}
\eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
\ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
diff --git a/src/cm/topo.tex b/src/cm/topo.tex
index f51b19d..61ed2f2 100644
--- a/src/cm/topo.tex
+++ b/src/cm/topo.tex
@@ -1,26 +1,20 @@
-\Section[
- \eng{Topological Materials}
- \ger{Topologische Materialien}
-]{topo}
-\Subsection[
- \eng{Berry phase / Geometric phase}
- \ger{Berry-Phase / Geometrische Phase}
-]{berry_phase}
+\Section{topo}
+ \desc{Topological Materials}{}{}
+ \desc[german]{Topologische Materialien}{}{}
- \begin{ttext}[desc]
- \eng{
+\Subsection{berry_phase}
+ \desc{Berry phase / Geometric phase}{
While adiabatically traversing a closed through the parameter space $R(t)$, the wave function of a systems
may pick up an additional phase $\gamma$.\\
If $\vec{R}(t)$ varies adiabatically (slowly) and the system is initially in eigenstate $\ket{n}$,
it will stay in an Eigenstate throughout the process (quantum adiabtic theorem).
- }
- \ger{
+ }{}
+ \desc[german]{Berry-Phase / Geometrische Phase}{
Beim adiabatischem Durchlauf eines geschlossenen Weges durch den Parameterraum $R(t)$ kann die Wellenfunktion eines Systems
eine zusätzliche Phase $\gamma$ erhalten.\\
Wenn $\vec{R}(t)$ adiabatisch (langsam) variiert und das System anfangs im Eigenzustand $\ket{n}$ ist,
bleibt das System während dem Prozess in einem Eigenzustand (Adiabatisches Theorem der Quantenmechanik).
- }
- \end{ttext}
+ }{}
\Eng[dynamic_phase]{Dynamical Phase}
\Eng[berry_phase]{Berry Phase}
\Ger[dynamic_phase]{Dynamische Phase}
diff --git a/src/cm/vib.tex b/src/cm/vib.tex
index db96e39..c6e4cc6 100644
--- a/src/cm/vib.tex
+++ b/src/cm/vib.tex
@@ -1,7 +1,12 @@
-\Section[
- \eng{Lattice vibrations}
- \ger{Gitterschwingungen}
-]{vib}
+\Section{vib}
+ \desc{Lattice vibrations}{}{}
+ \desc[german]{Gitterschwingungen}{}{}
+
+ \begin{formula}{speed_of_sound}
+ \desc{Speed of sound}{Speed with which vibrations propagate through an elastic medium}{}
+ \desc[german]{Schallgeschwindigkeit}{Geschwindigkeit, mit der sich Vibrationen in einem elastischem Medium ausbreiten}{}
+ \quantity{v}{\m\per\s}{s}
+ \end{formula}
\begin{formula}{dispersion_1atom_basis}
\desc{Phonon dispersion of a lattice with a one-atom basis}{same as the dispersion of a linear chain}{$C_n$ force constants between layer $s$ and $s+n$, $M$ \qtyRef{mass} of the reference atom, $a$ \qtyRef{lattice_constant}, $q$ phonon \qtyRef{wavevector}, $u$ Ansatz for the atom displacement}
@@ -46,10 +51,9 @@
\eq{C_\txm = 3\NA \kB = 3R \approx \SI{25}{\joule\per\mol\kelvin}}
\end{formula}
- \Subsection[
- \eng{Einstein model}
- \ger{Einstein-Modell}
- ]{einstein}
+ \Subsection{einstein}
+ \desc{Einstein model}{}{}
+ \desc[german]{Einstein-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -72,10 +76,9 @@
\eq{C_V^\txE = 3N\kB \left( \frac{\hbar\omega_\txE}{\kB T}\right)^2 \frac{\e^{\frac{\hbar\omega_\txE}{\kB T}}}{ \left(\e^{\frac{\hbar\omega_\txE}{\kB T}} - 1\right)^2}}
\end{formula}
- \Subsection[
- \eng{Debye model}
- \ger{Debye-Modell}
- ]{debye}
+ \Subsection{debye}
+ \desc{Debye model}{}{}
+ \desc[german]{Debye-Modell}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
diff --git a/src/comp/ad.tex b/src/comp/ad.tex
index 31a8050..739b106 100644
--- a/src/comp/ad.tex
+++ b/src/comp/ad.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Atomic dynamics}
- % \ger{}
-]{ad}
+\Section{ad}
+ \desc{Atomic dynamics}{}{}
+ % \desc[german]{}{}{}
+
\begin{formula}{hamiltonian}
\desc{Electron Hamiltonian}{}{$\hat{T}$ \fRef{comp:est:kinetic_energy}, $\hat{V}$ \fRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
\desc[german]{Hamiltonian der Elektronen}{}{}
@@ -29,10 +29,9 @@
\end{multline}
\end{formula}
-\Subsection[
- \eng{Born-Oppenheimer Approximation}
- \ger{Born-Oppenheimer Näherung}
-]{bo}
+\Subsection{bo}
+ \desc{Born-Oppenheimer Approximation}{}{}
+ \desc[german]{Born-Oppenheimer Näherung}{}{}
\begin{formula}{adiabatic_approx}
\desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move (\absRef{adiabatic_theorem})}{$\Lambda_{ij}$ \fRef{comp:ad:coupling_operator}}
\desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{}
@@ -81,10 +80,9 @@
}
\end{formula}
-\Subsection[
- \eng{Structure optimization}
- \ger{Strukturoptimierung}
-]{opt}
+\Subsection{opt}
+ \desc{Structure optimization}{}{}
+ \desc[german]{Strukturoptimierung}{}{}
\begin{formula}{forces}
\desc{Forces}{}{}
\desc[german]{Kräfte}{}{}
@@ -139,10 +137,9 @@
}}
\end{formula}
-\Subsection[
- \eng{Lattice vibrations}
- \ger{Gitterschwingungen}
-]{latvib}
+\Subsection{latvib}
+ \desc{Lattice vibrations}{}{}
+ \desc[german]{Gitterschwingungen}{}{}
\begin{formula}{force_constant_matrix}
\desc{Force constant matrix}{}{}
% \desc[german]{}{}{}
@@ -159,10 +156,9 @@
% -> DFPT
% finite-difference method
- \Subsubsection[
- \eng{Finite difference method}
- % \ger{}
- ]{fin_diff}
+ \Subsubsection{fin_diff}
+ \desc{Finite difference method}{}{}
+ % \desc[german]{}{}{}
\begin{formula}{approx}
\desc{Approximation}{Assume forces in equilibrium structure vanish}{$\Delta s$ displacement of atom $J$}
@@ -181,10 +177,9 @@
\eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) }
\end{formula}
- \Subsubsection[
- \eng{Anharmonic approaches}
- \ger{Anharmonische Ansätze}
- ]{anharmonic}
+ \Subsubsection{anharmonic}
+ \desc{Anharmonic approaches}{}{}
+ \desc[german]{Anharmonische Ansätze}{}{}
\begin{formula}{qha}
\desc{Quasi-harmonic approximation}{}{}
@@ -205,10 +200,9 @@
-\Subsection[
- \eng{Molecular Dynamics}
- \ger{Molekulardynamik}
-]{md} \abbrLink{md}{MD}
+\Subsection{md}
+ \desc{Molecular Dynamics}{}{}
+ \desc[german]{Molekulardynamik}{}{} \abbrLink{md}{MD}
\begin{formula}{desc}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -236,10 +230,9 @@
}}
\end{formula}
- \Subsubsection[
- \eng{Ab-initio molecular dynamics}
- \ger{Ab-initio molecular dynamics}
- ]{ab-initio}
+ \Subsubsection{ab-initio}
+ \desc{Ab-initio molecular dynamics}{}{}
+ \desc[german]{Ab-initio molecular dynamics}{}{}
\begin{formula}{bomd}
\abbrLabel{BOMD}
\desc{Born-Oppenheimer MD (BOMD)}{}{}
@@ -271,10 +264,9 @@
\end{gather}
\end{formula}
- \Subsubsection[
- \eng{Force-field MD}
- \ger{Force-field MD}
- ]{ff}
+ \Subsubsection{ff}
+ \desc{Force-field MD}{}{}
+ \desc[german]{Force-field MD}{}{}
\begin{formula}{ffmd}
\desc{Force field MD (FFMD)}{}{}
@@ -291,13 +283,9 @@
- \Subsubsection[
- \eng{Integration schemes}
- % \ger{}
- ]{scheme}
- \begin{ttext}
- \eng{Procedures for updating positions and velocities to obey the equations of motion.}
- \end{ttext}
+ \Subsubsection{scheme}
+ \desc{Integration schemes}{Procedures for updating positions and velocities to obey the equations of motion.}{}
+ \desc[german]{Integrationsmethoden}{Prozeduren zum stückweisen numerischen Lösung der Bewegungsgleichungen}{}
\begin{formula}{euler}
\desc{Euler method}{First-order procedure for solving \abbrRef{ode}s with a given initial value.\\Taylor expansion of $\vecR/\vecv (t+\Delta t)$}{}
@@ -337,10 +325,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{Thermostats and barostats}
- \ger{Thermostate und Barostate}
- ]{stats}
+ \Subsubsection{stats}
+ \desc{Thermostats and barostats}{}{}
+ \desc[german]{Thermostate und Barostate}{}{}
\begin{formula}{velocity_rescaling}
\desc{Velocity rescaling}{Thermostat, keep temperature at $T_0$ by rescaling velocities. Does not allow temperature fluctuations and thus does not obey the \absRef{c_ensemble}}{$T$ target \qtyRef{temperature}, $M$ \qtyRef{mass} of nucleon $I$, $\vecv$ \qtyRef{velocity}, $f$ number of degrees of freedom, $\lambda$ velocity scaling parameter, \ConstRef{boltzmann}}
% \desc[german]{}{}{}
@@ -367,10 +354,9 @@
\end{gather}
\end{formula}
- \Subsubsection[
- \eng{Calculating observables}
- \ger{Berechnung von Observablen}
- ]{obs}
+ \Subsubsection{obs}
+ \desc{Calculating observables}{}{}
+ \desc[german]{Berechnung von Observablen}{}{}
\begin{formula}{spectral_density}
\desc{Spectral density}{Wiener-Khinchin theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{$C$ \absRef{autocorrelation}}
\desc[german]{Spektraldichte}{Wiener-Khinchin Theorem\\\absRef{fourier_transform} of \absRef{autocorrelation}}{}
diff --git a/src/comp/comp.tex b/src/comp/comp.tex
index d8416b6..ab6f321 100644
--- a/src/comp/comp.tex
+++ b/src/comp/comp.tex
@@ -1,4 +1,4 @@
-\Part[
- \eng{Computational Physics}
- \ger{Computergestützte Physik}
-]{comp}
+\Part{comp}
+ \desc{Computational Physics}{}{}
+ \desc[german]{Computergestützte Physik}{}{}
+
diff --git a/src/comp/est.tex b/src/comp/est.tex
index b91aef9..3134f9b 100644
--- a/src/comp/est.tex
+++ b/src/comp/est.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Electronic structure theory}
- % \ger{}
-]{est}
+\Section{est}
+ \desc{Electronic structure theory}{}{}
+ % \desc[german]{}{}{}
+
\begin{formula}{kinetic_energy}
\desc{Kinetic energy}{of species $i$}{$i$ = nucleons/electrons, $N$ number of particles, $m$ \qtyRef{mass}}
@@ -26,10 +26,9 @@
\end{formula}
-\Subsection[
- \eng{Tight-binding}
- \ger{Modell der stark gebundenen Elektronen / Tight-binding}
-]{tb}
+\Subsection{tb}
+ \desc{Tight-binding}{}{}
+ \desc[german]{Modell der stark gebundenen Elektronen / Tight-binding}{}{}
\begin{formula}{assumptions}
\desc{Assumptions}{}{}
\desc[german]{Annahmen}{}{}
@@ -49,15 +48,13 @@
-\Subsection[
- \eng{Density functional theory (DFT)}
- \ger{Dichtefunktionaltheorie (DFT)}
-]{dft}
+\Subsection{dft}
+ \desc{Density functional theory (DFT)}{}{}
+ \desc[german]{Dichtefunktionaltheorie (DFT)}{}{}
\abbrLink{dft}{DFT}
- \Subsubsection[
- \eng{Hartree-Fock}
- \ger{Hartree-Fock}
- ]{hf}
+ \Subsubsection{hf}
+ \desc{Hartree-Fock}{}{}
+ \desc[german]{Hartree-Fock}{}{}
\begin{formula}{description}
\desc{Description}{}{}
\desc[german]{Beschreibung}{}{}
@@ -117,10 +114,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{Hohenberg-Kohn Theorems}
- \ger{Hohenberg-Kohn Theoreme}
- ]{hk}
+ \Subsubsection{hk}
+ \desc{Hohenberg-Kohn Theorems}{}{}
+ \desc[german]{Hohenberg-Kohn Theoreme}{}{}
\begin{formula}{hk1}
\desc{Hohenberg-Kohn theorem (HK1)}{}{}
\desc[german]{Hohenberg-Kohn Theorem (HK1)}{}{}
@@ -144,10 +140,9 @@
\eq{n(\vecr) = \Braket{\psi_0|\sum_{i=1}^N \delta(\vecr-\vecr_i)|\psi_0}}
\end{formula}
- \Subsubsection[
- \eng{Kohn-Sham DFT}
- \ger{Kohn-Sham DFT}
- ]{ks}
+ \Subsubsection{ks}
+ \desc{Kohn-Sham DFT}{}{}
+ \desc[german]{Kohn-Sham DFT}{}{}
\abbrLink{ksdft}{KS-DFT}
\begin{formula}{map}
\desc{Kohn-Sham map}{}{}
@@ -194,10 +189,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{Exchange-Correlation functionals}
- \ger{Exchange-Correlation Funktionale}
- ]{xc}
+ \Subsubsection{xc}
+ \desc{Exchange-Correlation functionals}{}{}
+ \desc[german]{Exchange-Correlation Funktionale}{}{}
\begin{formula}{xc}
\desc{Exchange-Correlation functional}{}{}
\desc[german]{Exchange-Correlation Funktional}{}{}
@@ -250,10 +244,9 @@
\end{formula}
- \Subsubsection[
- \eng{Basis sets}
- \ger{Basis-Sets}
- ]{basis}
+ \Subsubsection{basis}
+ \desc{Basis sets}{}{}
+ \desc[german]{Basis-Sets}{}{}
\begin{formula}{plane_wave}
\desc{Plane wave basis}{Plane wave ansatz in \fRef{comp:est:dft:ks:equation}\\Good for periodic structures, allows computation parallelization over a sample points in the \abbrRef{brillouin_zone}}{}
\desc[german]{Ebene Wellen als Basis}{}{}
@@ -265,10 +258,9 @@
\eq{E_\text{cutoff} = \frac{\hbar^2 \abs{\veck+\vecG}^2}{2m}}
\end{formula}
- \Subsubsection[
- \eng{Pseudo-Potential method}
- \ger{Pseudopotentialmethode}
- ]{pseudo}
+ \Subsubsection{pseudo}
+ \desc{Pseudo-Potential method}{}{}
+ \desc[german]{Pseudopotentialmethode}{}{}
\begin{formula}{ansatz}
\desc{Ansatz}{}{}
\desc[german]{Ansatz}{}{}
diff --git a/src/comp/ml.tex b/src/comp/ml.tex
index 300a708..bcf7779 100644
--- a/src/comp/ml.tex
+++ b/src/comp/ml.tex
@@ -1,11 +1,11 @@
-\Section[
- \eng{Machine-Learning}
- \ger{Maschinelles Lernen}
-]{ml}
- \Subsection[
- \eng{Performance metrics}
- \ger{Metriken zur Leistungsmessung}
- ]{performance}
+\Section{ml}
+ \desc{Machine-Learning}{}{}
+ \desc[german]{Maschinelles Lernen}{}{}
+
+ \Subsection{performance}
+ \desc{Performance metrics}{}{}
+ \desc[german]{Metriken zur Leistungsmessung}{}{}
+
\eng[cp]{correct predictions}
\ger[cp]{richtige Vorhersagen}
\eng[fp]{false predictions}
@@ -16,13 +16,14 @@
\ger[y]{Wahrheit}
\ger[yhat]{Vorhersage}
+ \eng[n_desc]{Number of data points}
+ \ger[n_desc]{Anzahl der Datenpunkte}
+
\begin{formula}{accuracy}
\desc{Accuracy}{}{}
\desc[german]{Genauigkeit}{}{}
\eq{a = \frac{\tGT{::cp}}{\tGT{::fp} + \tGT{::cp}}}
\end{formula}
- \eng{n_desc}{Number of data points}
- \ger{n_desc}{Anzahl der Datenpunkte}
\begin{formula}{mean_abs_error}
\desc{Mean absolute error (MAE)}{}{$y$ \GT{::y}, $\hat{y}$ \GT{::yhat}, $n$ \GT{::n_desc}}
\desc[german]{Mittlerer absoluter Fehler (MAE)}{}{}
@@ -39,14 +40,12 @@
\eq{\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \left(y_i - \hat{y}_i\right)^2}}
\end{formula}
- \Subsection[
- \eng{Regression}
- \ger{Regression}
- ]{reg}
- \Subsubsection[
- \eng{Linear Regression}
- \ger{Lineare Regression}
- ]{linear}
+ \Subsection{reg}
+ \desc{Regression}{}{}
+ \desc[german]{Regression}{}{}
+ \Subsubsection{linear}
+ \desc{Linear Regression}{}{}
+ \desc[german]{Lineare Regression}{}{}
\begin{formula}{eq}
\desc{Linear regression}{Fits the data under the assumption of \fRef[normally distributed errors]{math:pt:distributions:cont:normal}}{$\mat{x}\in\R^{N\times M}$ input data, $\mat{y}\in\R^{N\times L}$ output data, $\mat{b}$ bias, $\vec{\beta}$ weights, $N$ samples, $M$ features, $L$ output variables}
\desc[german]{Lineare Regression}{Fitted Daten unter der Annahme \fRef[normalverteilter Fehler]{math:pt:distributions:cont:normal}}{}
@@ -70,10 +69,9 @@
\eq{\vec{\beta} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}}
\end{formula}
- \Subsubsection[
- \eng{Kernel method}
- \ger{Kernelmethode}
- ]{kernel}
+ \Subsubsection{kernel}
+ \desc{Kernel method}{}{}
+ \desc[german]{Kernelmethode}{}{}
\begin{formula}{kernel_trick}
\desc{Kernel trick}{}{$\vecx_i \in \R^{M_1}$ input vectors, $M_1$ dimension of data vector space, $M_2$ dimension of feature space}
% \desc[german]{}{}{}
@@ -103,10 +101,9 @@
\eq{k(\vecx_i, \vecx_j) = \Exp{-\frac{\norm{\vecx_i - \vecx_j}_2^2}{\sigma}}}
\end{formula}
- \Subsubsection[
- \eng{Bayesian regression}
- \ger{Bayes'sche Regression}
- ]{bayes}
+ \Subsubsection{bayes}
+ \desc{Bayesian regression}{}{}
+ \desc[german]{Bayes'sche Regression}{}{}
\begin{formula}{linear_regression}
\desc{Bayesian linear regression}{}{}
@@ -185,9 +182,8 @@
\eq{V_\text{BondOrder}(\vecR_M, \vecR_N) = V_\text{rep}(\vecR_M, \vecR_N) + b_{MNK} V_\text{attr}(\vecR_M, \vecR_N)}
\end{formula}
- \Subsection[
- \eng{Gradient descent}
- \ger{Gradientenverfahren}
- ]{gd}
+ \Subsection{gd}
+ \desc{Gradient descent}{}{}
+ \desc[german]{Gradientenverfahren}{}{}
\TODO{in lecture 30 CMP}
diff --git a/src/comp/qmb.tex b/src/comp/qmb.tex
index 7093924..dbcf35b 100644
--- a/src/comp/qmb.tex
+++ b/src/comp/qmb.tex
@@ -1,11 +1,10 @@
-\Section[
- \eng{Quantum many-body physics}
- \ger{Quanten-Vielteilchenphysik}
-]{qmb}
- \Subsection[
- \eng{Quantum many-body models}
- \ger{Quanten-Vielteilchenmodelle}
- ]{models}
+\Section{qmb}
+ \desc{Quantum many-body physics}{}{}
+ \desc[german]{Quanten-Vielteilchenphysik}{}{}
+
+ \Subsection{models}
+ \desc{Quantum many-body models}{}{}
+ \desc[german]{Quanten-Vielteilchenmodelle}{}{}
\begin{formula}{heg}
\desc{Homogeneous electron gas (HEG)}{Also "Jellium"}{}
% \desc[german]{}{}{}
@@ -14,26 +13,22 @@
}
\end{formula}
- \Subsection[
- \eng{Methods}
- \ger{Methoden}
- ]{methods}
- \Subsubsection[
- \eng{Quantum Monte-Carlo}
- \ger{Quantum Monte-Carlo}
- ]{qmonte-carlo}
+ \Subsection{methods}
+ \desc{Methods}{}{}
+ \desc[german]{Methoden}{}{}
+ \Subsubsection{qmonte-carlo}
+ \desc{Quantum Monte-Carlo}{}{}
+ \desc[german]{Quantum Monte-Carlo}{}{}
\TODO{TODO}
- \Subsection[
- \eng{Importance sampling}
- \ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
- ]{importance_sampling}
+ \Subsection{importance_sampling}
+ \desc{Importance sampling}{}{}
+ \desc[german]{Importance sampling / Stichprobenentnahme nach Wichtigkeit}{}{}
\TODO{Monte Carlo}
- \Subsection[
- \eng{Matrix product states}
- \ger{Matrix Produktzustände}
- ]{mps}
+ \Subsection{mps}
+ \desc{Matrix product states}{}{}
+ \desc[german]{Matrix Produktzustände}{}{}
diff --git a/src/constants.tex b/src/constants.tex
index a1197cd..df3d730 100644
--- a/src/constants.tex
+++ b/src/constants.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Constants}
- \ger{Konstanten}
-]{constants}
+\Section{constants}
+ \desc{Constants}{}{}
+ \desc[german]{Konstanten}{}{}
+
\begin{formula}{planck}
\desc{Planck Constant}{}{}
\desc[german]{Plancksches Wirkumsquantum}{}{}
diff --git a/src/ed/ed.tex b/src/ed/ed.tex
index e3a0b30..1ac7942 100644
--- a/src/ed/ed.tex
+++ b/src/ed/ed.tex
@@ -1,7 +1,7 @@
-\Part[
- \eng{Electrodynamics}
- \ger{Elektrodynamik}
-]{ed}
+\Part{ed}
+ \desc{Electrodynamics}{}{}
+ \desc[german]{Elektrodynamik}{}{}
+
% pure electronic stuff in el
% pure magnetic stuff in mag
diff --git a/src/ed/el.tex b/src/ed/el.tex
index 5ef694a..e0dea07 100644
--- a/src/ed/el.tex
+++ b/src/ed/el.tex
@@ -1,8 +1,7 @@
-\Section[
- \eng{Electric field}
- \ger{Elektrisches Feld}
-]{el}
+\Section{el}
+ \desc{Electric field}{}{}
+ \desc[german]{Elektrisches Feld}{}{}
\begin{formula}{electric_field}
\desc{Electric field}{Surrounds charged particles}{}
\desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{}
@@ -29,8 +28,8 @@
\quantity{\epsilon}{\ampere\s\per\volt\m=\farad\per\m=\coulomb\per\volt\m=C^2\per\newton\m^2=\ampere^2\s^4\per\kg\m^3}{}
\end{formula}
\begin{formula}{relative_permittivity}
- \desc{Relative permittivity / Dielectric constant}{}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}}
- \desc[german]{Relative Permittivität / Dielectric constant}{}{}
+ \desc{Relative permittivity}{Dielectric constant}{\QtyRef{permittivity}, \ConstRef{vacuum_permittivity}}
+ \desc[german]{Relative Permittivität}{Dielectric constant}{}
\eq{
\epsilon(\omega)_\txr = \frac{\epsilon(\omega)}{\epsilon_0}
}
@@ -62,7 +61,7 @@
\begin{formula}{electric_displacement_field}
\desc{Electric displacement field}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_field}, \QtyRef{dielectric_polarization_density}}
- \desc[german]{Elektrische Flussdichte / dielektrische Verschiebung}{}{}
+ \desc[german]{Elektrische Flussdichte}{Dielektrische Verschiebung}{}
\quantity{\vec{D}}{\coulomb\per\m^2=\ampere\s\per\m^2}{v}
\eq{\vec{D} = \epsilon_0 \vec{\E} + \vec{P}}
\end{formula}
diff --git a/src/ed/em.tex b/src/ed/em.tex
index d7e8ebc..1e27c42 100644
--- a/src/ed/em.tex
+++ b/src/ed/em.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Electromagnetism}
- \ger{Elektromagnetismus}
-]{em}
+\Section{em}
+ \desc{Electromagnetism}{}{}
+ \desc[german]{Elektromagnetismus}{}{}
+
\begin{formula}{vacuum_speed_of_light}
\desc{Speed of light}{in the vacuum}{}
\desc[german]{Lightgeschwindigkeit}{in the vacuum}{}
@@ -46,10 +46,9 @@
\end{formula}
- \Subsection[
- \eng{Maxwell-Equations}
- \ger{Maxwell-Gleichungen}
- ]{maxwell}
+ \Subsection{maxwell}
+ \desc{Maxwell-Equations}{}{}
+ \desc[german]{Maxwell-Gleichungen}{}{}
\begin{formula}{vacuum}
\desc{Vacuum}{microscopic formulation}{}
\desc[german]{Vakuum}{Mikroskopische Formulierung}{}
@@ -73,10 +72,9 @@
\end{formula}
- \Subsubsection[
- \eng{Gauges}
- \ger{Eichungen}
- ]{gauge}
+ \Subsubsection{gauge}
+ \desc{Gauges}{}{}
+ \desc[german]{Eichungen}{}{}
\begin{formula}{coulomb}
\desc{Coulomb gauge}{}{\QtyRef{magnetic_vector_potential}}
\desc[german]{Coulomb-Eichung}{}{}
@@ -88,10 +86,9 @@
\TODO{Polarization}
- \Subsection[
- \eng{Induction}
- \ger{Induktion}
- ]{induction}
+ \Subsection{induction}
+ \desc{Induction}{}{}
+ \desc[german]{Induktion}{}{}
\begin{formula}{farady_law}
\desc{Faraday's law of induction}{}{}
\desc[german]{Faradaysche Induktionsgesetz}{}{}
diff --git a/src/ed/mag.tex b/src/ed/mag.tex
index fc0d1ef..a7e3f8a 100644
--- a/src/ed/mag.tex
+++ b/src/ed/mag.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Magnetic field}
- \ger{Magnetfeld}
-]{mag}
+\Section{mag}
+ \desc{Magnetic field}{}{}
+ \desc[german]{Magnetfeld}{}{}
+
\begin{formula}{magnetic_flux}
\desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
@@ -98,10 +98,9 @@
- \Subsection[
- \eng{Magnetic materials}
- \ger{Magnetische Materialien}
- ]{materials}
+ \Subsection{materials}
+ \desc{Magnetic materials}{}{}
+ \desc[german]{Magnetische Materialien}{}{}
\begin{formula}{paramagnetism}
\desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
\desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
diff --git a/src/ed/misc.tex b/src/ed/misc.tex
index dbe894d..349167a 100644
--- a/src/ed/misc.tex
+++ b/src/ed/misc.tex
@@ -1,108 +1,6 @@
-% TODO move
-\Section[
- \eng{Hall-Effect}
- \ger{Hall-Effekt}
- ]{hall}
-
- \begin{formula}{cyclotron}
- \desc{Cyclontron frequency}{}{}
- \desc[german]{Zyklotronfrequenz}{}{}
- \eq{\omega_\text{c} = \frac{e B}{\masse}}
- \end{formula}
- \TODO{Move}
-
-
- \Subsection[
- \eng{Classical Hall-Effect}
- \ger{Klassischer Hall-Effekt}
- ]{classic}
- \begin{ttext}
- \eng{Current flowing in $x$ direction in a conductor ($l \times b \times d$) with a magnetic field $B$ in $z$ direction leads to a hall voltage $U_\text{H}$ in $y$ direction.}
- \ger{Fließt in einem Leiter ($l \times b \times d$) ein Strom in $x$ Richtung, während der Leiter von einem Magnetfeld $B$ in $z$-Richtung durchdrungen, wird eine Hallspannung $U_\text{H}$ in $y$-Richtung induziert.}
- \end{ttext}
- \begin{formula}{voltage}
- \desc{Hall voltage}{}{$n$ charge carrier density}
- \desc[german]{Hallspannung}{}{$n$ Ladungsträgerdichte}
- \eq{U_\text{H} = \frac{I B}{ne d}}
- \end{formula}
-
- \begin{formula}{coefficient}
- \desc{Hall coefficient}{Sometimes $R_\txH$}{}
- \desc[german]{Hall-Koeffizient}{Manchmal $R_\txH$}{}
- \eq{A_\text{H} := -\frac{E_y}{j_x B_z} \explOverEq{\GT{metals}} \frac{1}{ne} = \frac{\rho_{xy}}{B_z}}
- \end{formula}
-
- \begin{formula}{resistivity}
- \desc{Resistivity}{}{}
- \desc[german]{Spezifischer Widerstand}{}{}
- \eq{\rho_{xx} &= \frac{\masse}{ne^2\tau} \\ \rho_{xy} &= \frac{B}{ne}}
- \end{formula}
-
-
- \Subsection[
- \eng{Quantum hall effects}
- \ger{Quantenhalleffekte}
- ]{quantum}
- \begin{formula}{types}
- \desc{Types of quantum hall effects}{}{}
- \desc[german]{Arten von Quantenhalleffekten}{}{}
- \ttxt{\eng{
- \begin{itemize}
- \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
- \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
- \item \textbf{Spin} (QSHE): spin currents instead of charge currents
- \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
- \end{itemize}
- }\ger{
- \begin{itemize}
- \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
- \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
- \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
- \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
- \end{itemize}
- }}
- \end{formula}
-
-
-
- \begin{formula}{conductivity}
- \desc{Conductivity tensor}{}{}
- \desc[german]{Leitfähigkeitstensor}{}{}
- \eq{\sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
- \end{formula}
-
- \begin{formula}{resistivity_tensor}
- \desc{Resistivity tensor}{}{}
- \desc[german]{Spezifischer Widerstands-tensor}{}{}
- \eq{
- \rho = \sigma^{-1}
- % \sigma = \begin{pmatrix} \sigma_{xy} & \sigma_{xy} \\ \sigma_{yx} & \sigma_{yy} \end{pmatrix} }
- }
- \end{formula}
-
- \begin{formula}{resistivity}
- \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
- \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
- \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
- \end{formula}
-
- % \begin{formula}{qhe}
- % \desc{Integer quantum hall effect}{}{}
- % \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{}
- % \fig{img/qhe-klitzing.jpeg}
- % \end{formula}
-
- \begin{formula}{fqhe}
- \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
- \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
- \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
- \end{formula}
-
-
-\Section[
- \eng{Dipole-stuff}
- \ger{Dipol-zeug}
-]{dipole}
+\Section{dipole}
+ \desc{Dipoles}{}{}
+ \desc[german]{Dipole}{}{}
\begin{formula}{poynting}
\desc{Dipole radiation Poynting vector}{}{}
@@ -116,10 +14,9 @@
\eq{P = \frac{\mu_0\omega^4 p_0^2}{12\pi c}}
\end{formula}
-\Section[
- \eng{misc}
- \ger{misc}
-]{misc}
+\Section{misc}
+ \desc{misc}{}{}
+ \desc[german]{misc}{}{}
\begin{formula}{impedance_r}
\desc{Impedance of an ohmic resistor}{}{\QtyRef{resistance}}
\desc[german]{Impedanz eines Ohmschen Widerstands}{}{}
diff --git a/src/ed/optics.tex b/src/ed/optics.tex
index 0ccc4a7..ee1c375 100644
--- a/src/ed/optics.tex
+++ b/src/ed/optics.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Optics}
- \ger{Optik}
-]{optics}
+\Section{optics}
+ \desc{Optics}{}{}
+ \desc[german]{Optik}{}{}
+
\begin{ttext}
\eng{Properties of light and its interactions with matter}
\ger{Ausbreitung von Licht und die Interaktion mit Materie}
diff --git a/src/main.tex b/src/main.tex
index ac9ade8..c39aca0 100644
--- a/src/main.tex
+++ b/src/main.tex
@@ -122,7 +122,7 @@
\input{util/translations.tex}
-% \InputOnly{cm}
+% \InputOnly{test}
\Input{math/math}
\Input{math/linalg}
@@ -171,10 +171,9 @@
\Input{ch/misc}
\newpage
-\Part[
- \eng{Appendix}
- \ger{Anhang}
-]{appendix}
+\Part{appendix}
+ \desc{Appendix}{}{}
+ \desc[german]{Anhang}{}{}
\begin{formula}{world}
\desc{World formula}{}{}
\desc[german]{Weltformel}{}{}
@@ -186,10 +185,9 @@
% \listofquantities
\listoffigures
\listoftables
-\Section[
- \eng{List of elements}
- \ger{Liste der Elemente}
-]{elements}
+\Section{elements}
+ \desc{List of elements}{}{}
+ \desc[german]{Liste der Elemente}{}{}
\printAllElements
\newpage
\Input{test}
diff --git a/src/math/calculus.tex b/src/math/calculus.tex
index ff36b94..6ff25f4 100644
--- a/src/math/calculus.tex
+++ b/src/math/calculus.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Calculus}
- \ger{Analysis}
-]{cal}
+\Section{cal}
+ \desc{Calculus}{}{}
+ \desc[german]{Analysis}{}{}
+
% \begin{formula}{shark}
% \desc{Shark-midnight formula}{\emoji{shark}-s}{}
@@ -12,14 +12,12 @@
% \end{formula}
- \Subsection[
- \eng{Fourier analysis}
- \ger{Fourieranalyse}
- ]{fourier}
- \Subsubsection[
- \eng{Fourier series}
- \ger{Fourierreihe}
- ]{series}
+ \Subsection{fourier}
+ \desc{Fourier analysis}{}{}
+ \desc[german]{Fourieranalyse}{}{}
+ \Subsubsection{series}
+ \desc{Fourier series}{}{}
+ \desc[german]{Fourierreihe}{}{}
\begin{formula}{series} \absLabel[fourier_series]
\desc{Fourier series}{Complex representation}{$f\in \Lebesgue^2(\R,\C)$ $T$-\GT{periodic}}
\desc[german]{Fourierreihe}{Komplexe Darstellung}{}
@@ -53,35 +51,33 @@
\end{formula}
- \Subsubsection[
- \eng{Fourier transformation}
- \ger{Fouriertransformation}
- ]{trafo}
+ \Subsubsection{trafo}
+ \desc{Fourier transformation}{}{}
+ \desc[german]{Fouriertransformation}{}{}
\begin{formula}{transform} \absLabel[fourier_transform]
\desc{Fourier transform}{}{$\hat{f}:\R^n \mapsto \C$, $\forall f\in L^1(\R^n)$}
\desc[german]{Fouriertransformierte}{}{}
\eq{\hat{f}(k) \coloneq \frac{1}{\sqrt{2\pi}^n} \int_{\R^n} \e^{-\I kx}f(x)\d x}
\end{formula}
- \Eng[linear_in]{linear in}
- \Ger[linear_in]{linear in}
- \GT{for} $f\in L^1(\R^n)$:
- \begin{enumerate}[i)]
- \item $f \mapsto \hat{f}$ \GT{linear_in} $f$
- \item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
- \item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
- \item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
- \end{enumerate}
+ \begin{formula}{properties}
+ \desc{Properties}{}{\GT{for} $f\in L^1(\R^n)$}
+ \desc[german]{Eigenschaften}{}{}
+ \Eng[linear_in]{linear in}
+ \Ger[linear_in]{linear in}
+ \begin{enumerate}[i)]
+ \item $f \mapsto \hat{f}$ \GT{linear_in} $f$
+ \item $g(x) = f(x-h) \qRarrow \hat{g}(k) = \e^{-\I kn}\hat{f}(k)$
+ \item $g(x) = \e^{ih\cdot x}f(x) \qRarrow \hat{g}(k) = \hat{f}(k-h)$
+ \item $g(\lambda) = f\left(\frac{x}{\lambda}\right) \qRarrow \hat{g}(k)\lambda^n \hat{f}(\lambda k)$
+ \end{enumerate}
+ \end{formula}
- \Subsubsection[
- \eng{Convolution}
- \ger{Faltung / Konvolution}
- ]{conv}
- \begin{ttext}
- \eng{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}
- \ger{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}
- \end{ttext}
+
+ \Subsubsection{conv}
+ \desc{Convolution}{Convolution is \textbf{commutative}, \textbf{associative} and \textbf{distributive}.}{}
+ \desc[german]{Faltung / Konvolution}{Die Faltung ist \textbf{kommutativ}, \textbf{assoziativ} und \textbf{distributiv}}{}
\begin{formula}{def}
\desc{Definition}{}{}
\desc[german]{Definition}{}{}
@@ -120,10 +116,9 @@
\end{formula}
- \Subsection[
- \eng{Misc}
- \ger{Verschiedenes}
- ]{misc}
+ \Subsection{misc}
+ \desc{Misc}{}{}
+ \desc[german]{Verschiedenes}{}{}
\begin{formula}{stirling-approx}
\desc{Stirling approximation}{}{}
@@ -154,10 +149,9 @@
\end{formula}
- \Subsection[
- \eng{Logarithm}
- \ger{Logarithmus}
- ]{log}
+ \Subsection{log}
+ \desc{Logarithm}{}{}
+ \desc[german]{Logarithmus}{}{}
\begin{formula}{identities}
\desc{Logarithm identities}{}{}
\desc[german]{Logarithmus Identitäten}{Logarithmus Rechenregeln}{}
@@ -178,19 +172,17 @@
}
\end{formula}
- \Subsection[
- \eng{Vector calculus}
- \ger{Vektor Analysis}
- ]{vec}
+ \Subsection{vec}
+ \desc{Vector calculus}{}{}
+ \desc[german]{Vektor Analysis}{}{}
\begin{formula}{laplace}
\desc{Laplace operator}{}{}
\desc[german]{Laplace-Operator}{}{}
\eq{\laplace = \Grad^2 = \pdv[2]{}{x} + \pdv[2]{}{y} + \pdv[2]{}{z}}
\end{formula}
- \Subsubsection[
- \eng{Spherical symmetry}
- \ger{Kugelsymmetrie}
- ]{sphere}
+ \Subsubsection{sphere}
+ \desc{Spherical symmetry}{}{}
+ \desc[german]{Kugelsymmetrie}{}{}
\begin{formula}{coordinates}
\desc{Spherical coordinates}{}{}
\desc[german]{Kugelkoordinaten}{}{}
@@ -214,10 +206,9 @@
\end{formula}
- \Subsection[
- \eng{Integrals}
- \ger{Integralrechnung}
- ]{integral}
+ \Subsection{integral}
+ \desc{Integrals}{}{}
+ \desc[german]{Integralrechnung}{}{}
\begin{formula}{partial}
\desc{Partial integration}{}{}
\desc[german]{Partielle integration}{}{}
@@ -247,10 +238,9 @@
\desc[german]{Klassischer Satz von Stokes}{}{}
\eq{\int_A (\Rot{\vec{F}}) \cdot \d\vec{S} = \oint_{S} \vec{F} \cdot \d \vec{r}}
\end{formula}
- \Subsubsection[
- \eng{List of common integrals}
- \ger{Liste nützlicher Integrale}
- ]{list}
+ \Subsubsection{list}
+ \desc{List of common integrals}{}{}
+ \desc[german]{Liste nützlicher Integrale}{}{}
% Put links to other integrals here
\fRef{math:cal:log:integral}
diff --git a/src/math/geometry.tex b/src/math/geometry.tex
index f8646c3..05666f8 100644
--- a/src/math/geometry.tex
+++ b/src/math/geometry.tex
@@ -1,12 +1,11 @@
-\Section[
- \eng{Geometry}
- \ger{Geometrie}
- ]{geo}
+\Section{geo}
+ \desc{Geometry}{}{}
+ \desc[german]{Geometrie}{}{}
-\Subsection[
- \eng{Trigonometry}
- \ger{Trigonometrie}
-]{trig}
+
+\Subsection{trig}
+ \desc{Trigonometry}{}{}
+ \desc[german]{Trigonometrie}{}{}
\begin{formula}{exponential_function}
\desc{Exponential function}{}{}
@@ -41,10 +40,9 @@
\eq{\cosh(x) &= \cos{ix} \\ &= \frac{e^{x}+e^{-x}}{2}}
\end{formula}
-\Subsection[
- \eng{Various theorems}
- \ger{Verschiedene Theoreme}
-]{theorems}
+\Subsection{theorems}
+ \desc{Various theorems}{}{}
+ \desc[german]{Verschiedene Theoreme}{}{}
\begin{formula}{sum}
\desc{Hypthenuse in the unit circle}{}{}
\desc[german]{Hypothenuse im Einheitskreis}{}{}
@@ -78,10 +76,9 @@
\end{formula}
- \Subsubsection[
- \eng{Table of values}
- \ger{Wertetabelle}
- ]{value_table}
+ \Subsubsection{value_table}
+ \desc{Table of values}{}{}
+ \desc[german]{Wertetabelle}{}{}
\begingroup
\setlength{\tabcolsep}{0.9em} % horizontal
\renewcommand{\arraystretch}{2} % vertical
diff --git a/src/math/linalg.tex b/src/math/linalg.tex
index cfa3a6f..b6fc5a3 100644
--- a/src/math/linalg.tex
+++ b/src/math/linalg.tex
@@ -1,12 +1,11 @@
-\Section[
- \eng{Linear algebra}
- \ger{Lineare Algebra}
-]{linalg}
+\Section{linalg}
+ \desc{Linear algebra}{}{}
+ \desc[german]{Lineare Algebra}{}{}
- \Subsection[
- \eng{Matrix basics}
- \ger{Matrizen Basics}
- ]{matrix}
+
+ \Subsection{matrix}
+ \desc{Matrix basics}{}{}
+ \desc[german]{Matrizen Basics}{}{}
\begin{formula}{matrix_matrix_product}
\desc{Matrix-matrix product as sum}{}{}
@@ -31,10 +30,9 @@
\eq{U ^\dagger U = \id}
\end{formula}
- \Subsubsection[
- \eng{Transposed matrix}
- \ger{Transponierte Matrix}
- ]{transposed}
+ \Subsubsection{transposed}
+ \desc{Transposed matrix}{}{}
+ \desc[german]{Transponierte Matrix}{}{}
\begin{formula}{sum}
\desc{Sum}{}{}
\desc[german]{Summe}{}{}
@@ -57,10 +55,9 @@
\end{formula}
- \Subsection[
- \eng{Determinant}
- \ger{Determinante}
- ]{determinant}
+ \Subsection{determinant}
+ \desc{Determinant}{}{}
+ \desc[german]{Determinante}{}{}
\begin{formula}{2x2}
\desc{2x2 matrix}{}{}
\desc[german]{2x2 Matrix}{}{}
@@ -95,10 +92,9 @@
\end{formula}
- \Subsection[
- \eng{Misc}
- \ger{Misc}
- ]{misc}
+ \Subsection{misc}
+ \desc{Misc}{}{}
+ \desc[german]{Misc}{}{}
\begin{formula}{normal_equation}
\desc{Normal equation}{Solves a linear regression problem}{\mat{\theta} hypothesis / weight matrix, \mat{X} design matrix, \vec{y} output vector}
@@ -157,10 +153,9 @@
\end{formula}
- \Subsection[
- \eng{Eigenvalues}
- \ger{Eigenwerte}
- ]{eigen}
+ \Subsection{eigen}
+ \desc{Eigenvalues}{}{}
+ \desc[german]{Eigenwerte}{}{}
\begin{formula}{values}
\desc{Eigenvalue equation}{}{$\lambda$ eigenvalue, $v$ eigenvector}
\desc[german]{Eigenwert-Gleichung}{}{$\lambda$ Eigenwert, $v$ Eigenvektor}
diff --git a/src/math/math.tex b/src/math/math.tex
index 97ada42..b005adc 100644
--- a/src/math/math.tex
+++ b/src/math/math.tex
@@ -1,5 +1,5 @@
-\Part[
- \eng{Mathematics}
- \ger{Mathematik}
-]{math}
+\Part{math}
+ \desc{Mathematics}{}{}
+ \desc[german]{Mathematik}{}{}
+
diff --git a/src/math/probability_theory.tex b/src/math/probability_theory.tex
index aa1a24d..d55d7f7 100644
--- a/src/math/probability_theory.tex
+++ b/src/math/probability_theory.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Probability theory}
- \ger{Wahrscheinlichkeitstheorie}
-]{pt}
+\Section{pt}
+ \desc{Probability theory}{}{}
+ \desc[german]{Wahrscheinlichkeitstheorie}{}{}
+
\begin{formula}{mean}
\absLabel
@@ -70,33 +70,30 @@
\eq{\binom{n}{k} = \frac{n!}{k!(n-k)!}}
\end{formula}
- \Subsection[
- \eng{Distributions}
- \ger{Verteilungen}
- ]{distributions}
- \Subsubsection[
- \eng{Continuous probability distributions}
- \ger{Kontinuierliche Wahrscheinlichkeitsverteilungen}
- ]{cont}
+ \Subsection{distributions}
+ \desc{Distributions}{}{}
+ \desc[german]{Verteilungen}{}{}
+ \Subsubsection{cont}
+ \desc{Continuous probability distributions}{}{}
+ \desc[german]{Kontinuierliche Wahrscheinlichkeitsverteilungen}{}{}
\begin{bigformula}{normal}
\absLabel[normal_distribution]
\desc{Gauß/Normal distribution}{}{}
\desc[german]{Gauß/Normal-Verteilung}{}{}
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_gauss.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
- \disteq{support}{x \in \R}
- \disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
- \disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
- \disteq{mean}{\mu}
- \disteq{median}{\mu}
- \disteq{variance}{\sigma^2}
- \end{distribution}
+ \includegraphics{img/distribution_gauss.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
+ \disteq{support}{x \in \R}
+ \disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
+ \disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
+ \disteq{mean}{\mu}
+ \disteq{median}{\mu}
+ \disteq{variance}{\sigma^2}
+ \end{distribution}
+ }
\end{bigformula}
\begin{formula}{standard_normal}
@@ -110,63 +107,77 @@
\absLabel[multivariate_normal_distribution]
\desc{Multivariate normal distribution}{Multivariate Gaussian distribution}{$\vec{\mu}$ \absRef{mean}, $\mat{\Sigma}$ \absRef{covariance}}
\desc[german]{Mehrdimensionale Normalverteilung}{Multivariate Normalverteilung}{}
- \TODO{k-variate normal plot}
- \begin{distribution}
- \disteq{parameters}{\vec{\mu} \in \R^k,+\quad \mat{\Sigma} \in \R^{k\times k}}
- \disteq{support}{\vec{x} \in \vec{\mu} + \text{span}(\mat{\Sigma})}
- \disteq{pdf}{\mathcal{N}(\vec{\mu}, \mat{\Sigma}) = \frac{1}{(2\pi)^{k/2}} \frac{1}{\sqrt{\det{\Sigma}}} \Exp{-\frac{1}{2} \left(\vecx-\vec{\mu}\right)^\T \mat{\Sigma}^{-1} \left(\vecx-\vec{\mu}\right)}}
- \disteq{mean}{\vec{\mu}}
- \disteq{variance}{\mat{\Sigma}}
- \end{distribution}
+ \fsplit[0.3]{
+ \TODO{k-variate normal plot}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{\vec{\mu} \in \R^k,+\quad \mat{\Sigma} \in \R^{k\times k}}
+ \disteq{support}{\vec{x} \in \vec{\mu} + \text{span}(\mat{\Sigma})}
+ \disteq{pdf}{\mathcal{N}(\vec{\mu}, \mat{\Sigma}) = \frac{1}{(2\pi)^{k/2}} \frac{1}{\sqrt{\det{\Sigma}}} \Exp{-\frac{1}{2} \left(\vecx-\vec{\mu}\right)^\T \mat{\Sigma}^{-1} \left(\vecx-\vec{\mu}\right)}}
+ \disteq{mean}{\vec{\mu}}
+ \disteq{variance}{\mat{\Sigma}}
+ \end{distribution}
+ }
\end{bigformula}
- \begin{formula}{laplace}
+ \begin{bigformula}{laplace}
\absLabel[laplace_distribution]
- \desc{Laplace-distribution}{}{}
- \desc[german]{Laplace-Verteilung}{}{}
- \TODO{TODO}
- \end{formula}
+ \desc{Laplace-distribution}{Double exponential distribution}{}
+ \desc[german]{Laplace-Verteilung}{Doppelexponentialverteilung}{}
+ \fsplit[\distleftwidth]{
+ \centering
+ \includegraphics{img/distribution_laplace.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{\mu \in \R,\quad b > 0 \in \R}
+ \disteq{support}{x \in \R}
+ \disteq{pdf}{\frac{1}{\sqrt{2b}}\Exp{-\frac{\abs{x-\mu}}{b}}}
+ % \disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
+ \disteq{mean}{\mu}
+ \disteq{median}{\mu}
+ \disteq{variance}{2b^2}
+ \end{distribution}
+ }
+ \end{bigformula}
\begin{bigformula}{cauchy}
\absLabel[lorentz_distribution]
\desc{Cauchys / Lorentz distribution}{Also known as Cauchy-Lorentz distribution, Lorentz(ian) function, Breit-Wigner distribution.}{}
\desc[german]{Cauchy / Lorentz-Verteilung}{Auch bekannt als Cauchy-Lorentz Verteilung, Lorentz Funktion, Breit-Wigner Verteilung.}{}
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_cauchy.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
- \disteq{support}{x \in \R}
- \disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
- \disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
- \disteq{mean}{\text{\GT{undefined}}}
- \disteq{median}{x_0}
- \disteq{variance}{\text{\GT{undefined}}}
- \end{distribution}
+ \includegraphics{img/distribution_cauchy.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
+ \disteq{support}{x \in \R}
+ \disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
+ \disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
+ \disteq{mean}{\text{\GT{undefined}}}
+ \disteq{median}{x_0}
+ \disteq{variance}{\text{\GT{undefined}}}
+ \end{distribution}
+ }
\end{bigformula}
\begin{bigformula}{maxwell-boltzmann}
\absLabel[maxwell-boltzmann_distribution]
\desc{Maxwell-Boltzmann distribution}{}{}
\desc[german]{Maxwell-Boltzmann Verteilung}{}{}
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{a > 0}
- \disteq{support}{x \in (0, \infty)}
- \disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
- \disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
- \disteq{mean}{2a \frac{2}{\pi}}
- \disteq{median}{}
- \disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
- \end{distribution}
+ \includegraphics{img/distribution_maxwell-boltzmann.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{a > 0}
+ \disteq{support}{x \in (0, \infty)}
+ \disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
+ \disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
+ \disteq{mean}{2a \frac{2}{\pi}}
+ % \disteq{median}{}
+ \disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
+ \end{distribution}
+ }
\end{bigformula}
@@ -174,48 +185,45 @@
\absLabel[gamma_distribution]
\desc{Gamma Distribution}{with $\lambda$ parameter}{$\Gamma$ \fRef{math:cal:integral:list:gamma_function}, $\gamma$ \fRef{math:cal:integral:list:lower_incomplete_gamma_function}}
\desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{}
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_gamma.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{\alpha > 0, \lambda > 0}
- \disteq{support}{x\in(0,1)}
- \disteq{pdf}{\frac{\lambda^\alpha}{\Gamma(\alpha) x^{\alpha-1} \e^{-\lambda x}}}
- \disteq{cdf}{\frac{1}{\Gamma(\alpha) \gamma(\alpha, \lambda x)}}
- \disteq{mean}{\frac{\alpha}{\lambda}}
- \disteq{variance}{\frac{\alpha}{\lambda^2}}
- \end{distribution}
+ \includegraphics{img/distribution_gamma.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{\alpha > 0, \lambda > 0}
+ \disteq{support}{x\in(0,1)}
+ \disteq{pdf}{\frac{\lambda^\alpha}{\Gamma(\alpha) x^{\alpha-1} \e^{-\lambda x}}}
+ \disteq{cdf}{\frac{1}{\Gamma(\alpha) \gamma(\alpha, \lambda x)}}
+ \disteq{mean}{\frac{\alpha}{\lambda}}
+ \disteq{variance}{\frac{\alpha}{\lambda^2}}
+ \end{distribution}
+ }
\end{bigformula}
\begin{bigformula}{beta}
\absLabel[beta_distribution]
\desc{Beta Distribution}{}{$\txB$ \fRef{math:cal:integral:list:beta_function} / \fRef{math:cal:integral:list:incomplete_beta_function}}
\desc[german]{Beta Verteilung}{}{}
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_beta.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{\alpha \in \R, \beta \in \R}
- \disteq{support}{x\in[0,1]}
- \disteq{pdf}{\frac{x^{\alpha-1} (1-x)^{\beta-1}}{\txB(\alpha,\beta)}}
- \disteq{cdf}{\frac{\txB(x;\alpha,\beta)}{\txB(\alpha,\beta)}}
- \disteq{mean}{\frac{\alpha}{\alpha+\beta}}
- % \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
- \disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
- \end{distribution}
+ \includegraphics{img/distribution_beta.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{\alpha \in \R, \beta \in \R}
+ \disteq{support}{x\in[0,1]}
+ \disteq{pdf}{\frac{x^{\alpha-1} (1-x)^{\beta-1}}{\txB(\alpha,\beta)}}
+ \disteq{cdf}{\frac{\txB(x;\alpha,\beta)}{\txB(\alpha,\beta)}}
+ \disteq{mean}{\frac{\alpha}{\alpha+\beta}}
+ % \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
+ \disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
+ \end{distribution}
+ }
\end{bigformula}
- \Subsubsection[
- \eng{Discrete probability distributions}
- \ger{Diskrete Wahrscheinlichkeitsverteilungen}
- ]{discrete}
+ \Subsubsection{discrete}
+ \desc{Discrete probability distributions}{}{}
+ \desc[german]{Diskrete Wahrscheinlichkeitsverteilungen}{}{}
\begin{bigformula}{binomial}
\absLabel[binomial_distribution]
\desc{Binomial distribution}{}{}
@@ -224,42 +232,40 @@
\eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \absRef[poisson distribution]{poisson_distribution}}
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \absRef[Poissonverteilung]{poisson_distribution}}
\end{ttext}\\
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_binomial.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
- \disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
- \disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
- % \disteq{cdf}{\text{regularized incomplete beta function}}
- \disteq{mean}{np}
- \disteq{median}{\floor{np} \text{ or } \ceil{np}}
- \disteq{variance}{npq = np(1-p)}
- \end{distribution}
+ \includegraphics{img/distribution_binomial.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
+ \disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
+ \disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
+ % \disteq{cdf}{\text{regularized incomplete beta function}}
+ \disteq{mean}{np}
+ \disteq{median}{\floor{np} \text{ or } \ceil{np}}
+ \disteq{variance}{npq = np(1-p)}
+ \end{distribution}
+ }
\end{bigformula}
\begin{bigformula}{poisson}
\absLabel[poisson_distribution]
\desc{Poisson distribution}{}{}
\desc[german]{Poissonverteilung}{}{}
- \begin{minipage}{\distleftwidth}
- \begin{figure}[H]
+ \fsplit[\distleftwidth]{
\centering
- \includegraphics[width=\textwidth]{img/distribution_poisson.pdf}
- \end{figure}
- \end{minipage}
- \begin{distribution}
- \disteq{parameters}{\lambda \in (0,\infty)}
- \disteq{support}{k \in \N}
- \disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
- \disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
- \disteq{mean}{\lambda}
- \disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
- \disteq{variance}{\lambda}
- \end{distribution}
+ \includegraphics{img/distribution_poisson.pdf}
+ }{
+ \begin{distribution}
+ \disteq{parameters}{\lambda \in (0,\infty)}
+ \disteq{support}{k \in \N}
+ \disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
+ \disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
+ \disteq{mean}{\lambda}
+ \disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
+ \disteq{variance}{\lambda}
+ \end{distribution}
+ }
\end{bigformula}
@@ -277,10 +283,9 @@
% \end{distribution}
- \Subsection[
- \eng{Central limit theorem}
- \ger{Zentraler Grenzwertsatz}
- ]{cls}
+ \Subsection{cls}
+ \desc{Central limit theorem}{}{}
+ \desc[german]{Zentraler Grenzwertsatz}{}{}
\begin{ttext}
\eng{
Suppose $X_1, X_2, \dots$ is a sequence of independent and identically distributed random variables with $\braket{X_i} = \mu$ and $(\Delta X_i)^2 = \sigma^2 < \infty$.
@@ -294,10 +299,9 @@
}
\end{ttext}
- \Subsection[
- \eng{Propagation of uncertainty / error}
- \ger{Fehlerfortpflanzung}
- ]{error}
+ \Subsection{error}
+ \desc{Propagation of uncertainty / error}{}{}
+ \desc[german]{Fehlerfortpflanzung}{}{}
\begin{formula}{generalised}
\desc{Generalized error propagation}{}{$V$ \fRef{math:pt:covariance} matrix, $J$ \fRef{math:cal:jacobi-matrix}}
\desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fRef{math:pt:covariance} Matrix, $J$ \fRef{cal:jacobi-matrix}}{}
@@ -328,10 +332,9 @@
\eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
\end{formula}
- \Subsection[
- \eng{Maximum likelihood estimation}
- \ger{Maximum likelihood Methode}
- ]{mle}
+ \Subsection{mle}
+ \desc{Maximum likelihood estimation}{}{}
+ \desc[german]{Maximum likelihood Methode}{}{}
\begin{formula}{likelihood}
\desc{Likelihood function}{Likelihood of observing $x$ when parameter is $\theta$\\in general not normalized!}{$\rho$ \fRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ depending on parameter $\theta$, $\Theta$ parameter space}
\desc[german]{Likelihood Funktion}{"Plausibilität" $x$ zu messen, wenn der Parameter $\theta$ ist\\nicht normalisiert!}{$\rho$ \fRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ hängt ab von Parameter $\theta$, $\Theta$ Parameterraum}
@@ -348,10 +351,9 @@
\eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)}
\end{formula}
- \Subsection[
- \eng{Bayesian probability theory}
- \ger{Bayessche Wahrscheinlichkeitstheorie}
- ]{bayesian}
+ \Subsection{bayesian}
+ \desc{Bayesian probability theory}{}{}
+ \desc[german]{Bayessche Wahrscheinlichkeitstheorie}{}{}
\begin{formula}{prior}
\desc{Prior distribution}{Expected distribution before conducting the experiment}{$\theta$ parameter}
\desc[german]{Prior Verteilung}{}{}
diff --git a/src/mechanics.tex b/src/mechanics.tex
index 5176aa5..0f8a58f 100644
--- a/src/mechanics.tex
+++ b/src/mechanics.tex
@@ -1,12 +1,11 @@
-\Part[
- \eng{Mechanics}
- \ger{Mechanik}
-]{mech}
+\Part{mech}
+ \desc{Mechanics}{}{}
+ \desc[german]{Mechanik}{}{}
-\Section[
- \eng{Newton}
- \ger{Newton}
-]{newton}
+
+\Section{newton}
+ \desc{Newton}{}{}
+ \desc[german]{Newton}{}{}
\begin{formula}{newton_laws}
\desc{Newton's laws}{}{}
\desc[german]{Newtonsche Gesetze}{}{}
@@ -31,10 +30,9 @@
}
\end{formula}
-\Section[
- \eng{Misc}
- \ger{Verschiedenes}
-]{misc}
+\Section{misc}
+ \desc{Misc}{}{}
+ \desc[german]{Verschiedenes}{}{}
\begin{formula}{hook}
\desc{Hooke's law}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ spring length}
\desc[german]{Hookesches Gesetz}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ Federlänge}
@@ -50,28 +48,36 @@
\end{formula}
\def\lagrange{\mathcal{L}}
-\Section[
- \eng{Lagrange formalism}
- \ger{Lagrange Formalismus}
-]{lagrange}
- \begin{ttext}[desc]
- \eng{The Lagrange formalism is often the most simple approach the get the equations of motion,
- because with suitable generalied coordinates obtaining the Lagrange function is often relatively easy.
+\Section{lagrange}
+ \desc{Lagrange formalism}{}{}
+ \desc[german]{Lagrange Formalismus}{}{}
+ \begin{formula}{description}
+ \desc{Description}{}{}
+ \desc[german]{Beschreibung}{}{}
+ \ttxt{
+ \eng{The Lagrange formalism is often the most simple approach the get the equations of motion,
+ because with suitable generalied coordinates obtaining the Lagrange function is often relatively easy.
+ }
+ \ger{Der Lagrange-Formalsismus ist oft der einfachste Weg die Bewegungsgleichungen zu erhalten,
+ da das Aufstellen der Lagrange-Funktion mit geeigneten generalisierten Koordinaten oft relativ einfach ist.
+ }
}
- \ger{Der Lagrange-Formalsismus ist oft der einfachste Weg die Bewegungsgleichungen zu erhalten,
- da das Aufstellen der Lagrange-Funktion mit geeigneten generalisierten Koordinaten oft relativ einfach ist.
- }
- \end{ttext}
- \begin{ttext}[generalized_coords]
- \eng{
- The generalized coordinates are choosen so that the cronstraints are automatically fullfilled.
- For example, the generalized coordinate for a 2D pendelum is $q=\varphi$, with $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
- }
- \ger{
- Die generalisierten Koordinaten werden so gewählt, dass die Zwangsbedingungen automatisch erfüllt sind.
- Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
- }
- \end{ttext}
+ \end{formula}
+ \begin{formula}{generalized_coordinates}
+ \desc{Generalized coordinates}{}{}
+ \desc[german]{Generalisierte Koordinaten}{}{}
+ \absLabel
+ \begin{ttext}[generalized_coords]
+ \eng{
+ The generalized coordinates are choosen so that the cronstraints are automatically fullfilled.
+ For example, the generalized coordinate for a 2D pendelum is $q=\varphi$, with $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
+ }
+ \ger{
+ Die generalisierten Koordinaten werden so gewählt, dass die Zwangsbedingungen automatisch erfüllt sind.
+ Zum Beispiel findet man für ein 2D Pendel die generalisierte Koordinate $q=\varphi$, mit $\vec{x} = \begin{pmatrix} \cos\varphi \\ \sin\varphi \end{pmatrix}$.
+ }
+ \end{ttext}
+ \end{formula}
\begin{formula}{lagrangian} \absLabel
\desc{Lagrange function}{}{$T$ kinetic energy, $V$ potential energy }
\desc[german]{Lagrange-Funktion}{}{$T$ kinetische Energie, $V$ potentielle Energie}
diff --git a/src/particle.tex b/src/particle.tex
index 5b33a9c..e079ae0 100644
--- a/src/particle.tex
+++ b/src/particle.tex
@@ -1,7 +1,7 @@
-\Part[
- \eng{Particle physics}
- \ger{Teilchenphysik}
-]{particle}
+\Part{particle}
+ \desc{Particle physics}{}{}
+ \desc[german]{Teilchenphysik}{}{}
+
\begin{formula}{electron_mass}
\desc{Electron mass}{}{}
diff --git a/src/pkg/mqformula.sty b/src/pkg/mqformula.sty
index a9fe99c..f37d927 100644
--- a/src/pkg/mqformula.sty
+++ b/src/pkg/mqformula.sty
@@ -54,16 +54,6 @@
% 1: key
\newenvironment{formulainternal}[1]{
\mqfqname@enter{#1}
- % [1]: language
- % 2: name
- % 3: description
- % 4: definitions/links
- \newcommand{\desc}[4][english]{
- % language, name, description, definitions
- \ifblank{##2}{}{\dt{##1}{##2}}
- \ifblank{##3}{}{\dt[desc]{##1}{##3}}
- \ifblank{##4}{}{\dt[defs]{##1}{##4}}
- }
\directlua{n_formulaEntries = 0}
% makes this formula referencable with \abbrRef{<name>}
@@ -196,11 +186,10 @@
\par\noindent\ignorespaces
% \textcolor{gray}{\hrule}
% \vspace{0.5\baselineskip}
- \textbf{
- \raggedright
- \GT{\fqname}
- }
- \IfTranslationExists{\fqname:desc}{
+ \textbf{%
+ \raggedright\GT{\fqname}\ignorespaces%
+ }%
+ \IfTranslationExists{\fqname:desc}{\ignorespaces%
: {\color{fg1} \GT{\fqname:desc}}
}{}
\hfill
@@ -228,13 +217,6 @@
\newenvironment{formulagroup}[1]{
\mqfqname@enter{#1}
- \newcommand{\desc}[4][english]{
- % language, name, description, definitions
- \ifblank{##2}{}{\dt{##1}{##2}}
- \ifblank{##3}{}{\dt[desc]{##1}{##3}}
- \ifblank{##4}{}{\dt[defs]{##1}{##4}}
- }
-
\par\noindent
\begin{minipage}{\textwidth} % using a minipage to now allow line breaks within the bigformula
\mqfqname@label
diff --git a/src/pkg/mqfqname.sty b/src/pkg/mqfqname.sty
index fe182ce..7082d46 100644
--- a/src/pkg/mqfqname.sty
+++ b/src/pkg/mqfqname.sty
@@ -93,45 +93,57 @@
\directlua{fqnameLeaveOnlyFirstN(#1)}%
}
+
+% Define translations for the current fqname
+% [1]: language
+% 2: name
+% 3: description -> :desc
+% 4: definitions/links -> :defs
+\newcommand{\desc}[4][english]{
+ % language, name, description, definitions
+ \ifblank{#2}{}{\dt{#1}{#2}}
+ \ifblank{#3}{}{\dt[desc]{#1}{#3}}
+ \ifblank{#4}{}{\dt[defs]{#1}{#4}}
+}
+
% SECTIONING
% start <section>, get heading from translation, set label
% fqname is the fully qualified name of all sections and formulas, the keys of all previous sections joined with a ':'
% fqname is secFqname:<key> where <key> is the key/id of some environment, like formula
% [1]: code to run after setting \fqname, but before the \part, \section etc
% 2: key
-\newcommand{\Part}[2][desc]{
- \newpage
- \mqfqname@leaveOnlyFirstN{0}
+
+% 1: depth
+% 2: key
+% 3: Latex section command
+\newcommand\mqfqname@section[3]{
+ \mqfqname@leaveOnlyFirstN{#1}
\mqfqname@enter{#2}
- #1
% this is necessary so that \part/\section... takes the fully expanded string. Otherwise the pdf toc will have just the fqname
\edef\fqnameText{\GT{\fqname}}
- \part{\fqnameText}
+ #3{\fqnameText}
\mqfqname@label
+ \IfTranslationExists{\fqname:desc}{
+ {\color{fg1} \GT{\fqname:desc}}
+ }{}
}
-\newcommand{\Section}[2][]{
- \mqfqname@leaveOnlyFirstN{1}
- \mqfqname@enter{#2}
- #1
- \edef\fqnameText{\GT{\fqname}}
- \section{\fqnameText}
- \mqfqname@label
+
+
+\newcommand{\Part}[1]{
+ \newpage
+ \mqfqname@section{0}{#1}{\part}
}
-\newcommand{\Subsection}[2][]{
- \mqfqname@leaveOnlyFirstN{2}
- \mqfqname@enter{#2}
- #1
- \edef\fqnameText{\GT{\fqname}}
- \subsection{\fqnameText}
- \mqfqname@label
+\newcommand{\Section}[1]{
+ \mqfqname@section{1}{#1}{\section}
}
-\newcommand{\Subsubsection}[2][]{
- \mqfqname@leaveOnlyFirstN{3}
- \mqfqname@enter{#2}
- #1
- \edef\fqnameText{\GT{\fqname}}
- \subsubsection{\fqnameText}
- \mqfqname@label
+\newcommand{\Subsection}[1]{
+ \mqfqname@section{2}{#1}{\subsection}
+}
+\newcommand{\Subsubsection}[1]{
+ \mqfqname@section{3}{#1}{\subsubsection}
+}
+\newcommand{\Paragraph}[1]{
+ \mqfqname@section{4}{#1}{\paragraph}
}
\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
diff --git a/src/pkg/mqperiodictable.sty b/src/pkg/mqperiodictable.sty
index c7d949b..93f17df 100644
--- a/src/pkg/mqperiodictable.sty
+++ b/src/pkg/mqperiodictable.sty
@@ -33,15 +33,13 @@ end
% 3: period
% 4: column
\newenvironment{element}[4]{
- % [1]: language
- % 2: name
- % 3: description
- % 4: definitions/links
- \newcommand{\desc}[4][english]{
- \ifblank{##2}{}{\DT[el:#1]{##1}{##2}}
- \ifblank{##3}{}{\DT[el:#1_desc]{##1}{##3}}
- \ifblank{##4}{}{\DT[el:#1_defs]{##1}{##4}}
+ % force the fqname to el
+ \directlua{
+ old_sections = sections
+ sections = {}
+ table.insert(sections, "el")
}
+ \mqfqname@update
\directLuaAuxExpand{
elementAdd(\luastring{#1}, \luastring{#2}, \luastring{#3}, \luastring{#4})
}
@@ -55,6 +53,11 @@ end
\edef\lastElementName{#1}
}{
\ignorespacesafterend
+ % restore fqname
+ \directlua{
+ sections = old_sections
+ }
+ \mqfqname@update
}
% LIST
diff --git a/src/qm/atom.tex b/src/qm/atom.tex
index 09643b7..3ddf88a 100644
--- a/src/qm/atom.tex
+++ b/src/qm/atom.tex
@@ -1,100 +1,114 @@
\def\vecr{{\vec{r}}}
\def\abohr{a_\textrm{B}}
-\Section[
- \eng{Hydrogen Atom}
- \ger{Wasserstoffatom}
-]{h}
+\Section{h}
+ \desc{Hydrogen Atom}{}{}
+ \desc[german]{Wasserstoffatom}{}{}
- \begin{formula}{reduced_mass}
- \desc{Reduced mass}{}{}
- \desc[german]{Reduzierte Masse}{}{}
- \eq{\mu = \frac{\masse m_\textrm{K}}{\masse + m_\textrm{K}} \explOverEq[\approx]{$\masse \ll m_\textrm{K}$} \masse}
- \end{formula}
+\begin{formula}{reduced_mass}
+ \desc{Reduced mass}{}{}
+ \desc[german]{Reduzierte Masse}{}{}
+ \eq{\mu = \frac{\masse m_\textrm{K}}{\masse + m_\textrm{K}} \explOverEq[\approx]{$\masse \ll m_\textrm{K}$} \masse}
+\end{formula}
- \begin{formula}{potential}
- \desc{Coulumb potential}{For a single electron atom}{$Z$ atomic number}
- \desc[german]{Coulumb potential}{Für ein Einelektronenatom}{$Z$ Ordnungszahl/Kernladungszahl}
- \eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
- \end{formula}
- \begin{formula}{hamiltonian}
- \desc{Hamiltonian}{}{}
- \desc[german]{Hamiltonian}{}{}
- % \eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
- \eq{
- \hat{H} &= -\frac{\hbar^2}{2\mu} {\Grad_\vecr}^2 - V(\vecr) \\
- &= \frac{\hat{p}_r^2}{2\mu} + \frac{\hat{L}^2}{2\mu r} + V(r)
- }
- \end{formula}
+\begin{formula}{potential}
+ \desc{Coulumb potential}{For a single electron atom}{$Z$ atomic number}
+ \desc[german]{Coulumb potential}{Für ein Einelektronenatom}{$Z$ Ordnungszahl/Kernladungszahl}
+ \eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
+\end{formula}
+\begin{formula}{hamiltonian}
+ \desc{Hamiltonian}{}{}
+ \desc[german]{Hamiltonian}{}{}
+ % \eq{V(\vecr) = \frac{Z\,e^2}{4\pi\epsilon_0 r}}
+ \eq{
+ \hat{H} &= -\frac{\hbar^2}{2\mu} {\Grad_\vecr}^2 - V(\vecr) \\
+ &= \frac{\hat{p}_r^2}{2\mu} + \frac{\hat{L}^2}{2\mu r} + V(r)
+ }
+\end{formula}
- \begin{formula}{wave_function}
- \desc{Wave function}{}{$R_{nl}(r)$ \fRef{qm:h:radial}, $Y_{lm}$ \fRef{qm:spherical_harmonics}}
- \desc[german]{Wellenfunktion}{}{}
- \eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
- \end{formula}
+\begin{formula}{wave_function}
+ \desc{Wave function}{}{$R_{nl}(r)$ \fRef{qm:h:radial}, $Y_{lm}$ \fRef{qm:spherical_harmonics}}
+ \desc[german]{Wellenfunktion}{}{}
+ \eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
+\end{formula}
- \begin{formula}{radial}
- \desc{Radial part}{}{$L_r^s(x)$ Laguerre-polynomials}
- \desc[german]{Radialanteil}{}{$L_r^s(x)$ Laguerre-Polynome}
- \eq{
- R_{nl} &= - \sqrt{\frac{(n-l-1)!(2\kappa)^3}{2n[(n+l)!]^3}} (2\kappa r)^l \e^{-\kappa r} L_{n+1}^{2l+1}(2\kappa r)
- \shortintertext{\GT{with}}
- \kappa &= \frac{\sqrt{2\mu\abs{E}}}{\hbar} = \frac{Z}{n \abohr}
- }
- \end{formula}
+\begin{formula}{radial}
+ \desc{Radial part}{}{$L_r^s(x)$ Laguerre-polynomials}
+ \desc[german]{Radialanteil}{}{$L_r^s(x)$ Laguerre-Polynome}
+ \eq{
+ R_{nl} &= - \sqrt{\frac{(n-l-1)!(2\kappa)^3}{2n[(n+l)!]^3}} (2\kappa r)^l \e^{-\kappa r} L_{n+1}^{2l+1}(2\kappa r)
+ \shortintertext{\GT{with}}
+ \kappa &= \frac{\sqrt{2\mu\abs{E}}}{\hbar} = \frac{Z}{n \abohr}
+ }
+\end{formula}
- \begin{formula}{energy}
- \desc{Energy eigenvalues}{}{}
- \desc[german]{Energieeigenwerte}{}{}
- \eq{E_n &= \frac{Z^2\mu e^4}{n^2(4\pi\epsilon_0)^2 2\hbar^2} = -E_\textrm{H}\frac{Z^2}{n^2}}
- \end{formula}
+\begin{formula}{energy}
+ \desc{Energy eigenvalues}{}{}
+ \desc[german]{Energieeigenwerte}{}{}
+ \eq{E_n &= \frac{Z^2\mu e^4}{n^2(4\pi\epsilon_0)^2 2\hbar^2} = -E_\textrm{H}\frac{Z^2}{n^2}}
+\end{formula}
- \begin{formula}{rydberg_constant_heavy}
- \desc{Rydberg constant}{for heavy atoms}{\ConstRef{electron_mass}, \ConstRef{charge}, \ConstRef{vacuum_permittivity}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
- \desc[german]{Rydberg-Konstante}{für schwere Atome}{}
- \constant{R_\infty}{exp}{
- \val{10973731.568157(12)}{\per\m}
- }
- \eq{
- R_\infty = \frac{m_e e^4}{8\epsilon_0^2 h^3 c}
- }
- \end{formula}
+\begin{formula}{rydberg_constant_heavy}
+ \desc{Rydberg constant}{for heavy atoms}{\ConstRef{electron_mass}, \ConstRef{charge}, \ConstRef{vacuum_permittivity}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
+ \desc[german]{Rydberg-Konstante}{für schwere Atome}{}
+ \constant{R_\infty}{exp}{
+ \val{10973731.568157(12)}{\per\m}
+ }
+ \eq{
+ R_\infty = \frac{m_e e^4}{8\epsilon_0^2 h^3 c}
+ }
+\end{formula}
- \begin{formula}{rydberg_constant_corrected}
- \desc{Rydberg constant}{corrected for nucleus mass $M$}{\ConstRef{rydberg_constant_heavy}, $\mu = \left(\frac{1}{m_\txe} + \frac{1}{M}\right)^{-1}$ \GT{reduced_mass}, \ConstRef{electron_mass}}
- \desc[german]{Rydberg Konstante}{korrigiert für Kernmasse $M$}{}
- \eq{R_\txM = \frac{\mu}{m_\txe} R_\infty}
- \end{formula}
+\begin{formula}{rydberg_constant_corrected}
+ \desc{Rydberg constant}{corrected for nucleus mass $M$}{\ConstRef{rydberg_constant_heavy}, $\mu = \left(\frac{1}{m_\txe} + \frac{1}{M}\right)^{-1}$ \GT{reduced_mass}, \ConstRef{electron_mass}}
+ \desc[german]{Rydberg Konstante}{korrigiert für Kernmasse $M$}{}
+ \eq{R_\txM = \frac{\mu}{m_\txe} R_\infty}
+\end{formula}
- \begin{formula}{rydberg_energy}
- \desc{Rydberg energy}{Energy unit}{\ConstRef{rydberg_constant_heavy}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
- \desc[german]{Rydberg-Energy}{Energie Einheit}{}
- \eq{1\,\text{Ry} = hc\,R_\infty}
- \end{formula}
+\begin{formula}{rydberg_energy}
+ \desc{Rydberg energy}{Energy unit}{\ConstRef{rydberg_constant_heavy}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
+ \desc[german]{Rydberg-Energy}{Energie Einheit}{}
+ \eq{1\,\text{Ry} = hc\,R_\infty}
+\end{formula}
- \begin{formula}{bohr_radius}
- \desc{Bohr radius}{}{\ConstRef{vacuum_permittivity}, \ConstRef{electron_mass}}
- \desc[german]{Bohrscher Radius}{}{}
- \constant{a_0}{exp}{
- \val{5.29177210544(82) \xE{-11}}{\m}
- }
- \eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
- \end{formula}
+\begin{formula}{bohr_radius}
+ \desc{Bohr radius}{}{\ConstRef{vacuum_permittivity}, \ConstRef{electron_mass}}
+ \desc[german]{Bohrscher Radius}{}{}
+ \constant{a_0}{exp}{
+ \val{5.29177210544(82) \xE{-11}}{\m}
+ }
+ \eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
+\end{formula}
+\begin{formula}{hunds_rules}
+ \desc{Hund's rules}{Angular momentum configuration rules for electrons in atomic orbitals in the atom's ground state}{}
+ \desc[german]{Hundsche Regeln}{Drehimpulskonfiguration für Elektronen in Atomorbitalen im Grundzustand des Atoms }{}
+ \ttxt{\eng{
+ \begin{enumerate}
+ \item Full shells: $J=0$
+ \item $S$ takes the maximum possible value
+ \item For equal $S$ configurations, the one where $L$ is maximized is taken
+ \item Outermost shell half filled or less \Rightarrow $J$ minimized: $J=\abs{L-S}$ \\
+ Outermost shell more than half filled \Rightarrow $J$ maximized $J=L+S$
+ \end{enumerate}
+ }\ger{
+ \begin{enumerate}
+ \item Volle Schalen haben Gesamtdrehimpuls 0: $J=0$
+ \item $S$ nimmt den höchstmöglichsten Wert an
+ \item Für gleiche $S$ wird $L$ maximiert
+ \item Äußerste Schale halb oder weniger gefüllt \Rightarrow $J$ minimiert: $J=\abs{L-S}$\\
+ Äußerste Schale mehr als halb gefüllt \Rightarrow $J$ maximiert: $J=L+S$
+ \end{enumerate}
+ }}
+\end{formula}
-\Subsection[
- \eng{Corrections}
- \ger{Korrekturen}
-]{corrections}
+\Subsection{corrections}
+ \desc{Corrections}{}{}
+ \desc[german]{Korrekturen}{}{}
- \Subsubsection[
- \eng{Darwin term}
- \ger{Darwin-Term}
- ]{darwin}
- \begin{ttext}[desc]
- \eng{Relativisitc correction: Accounts for interaction with nucleus (non-zero wavefunction at nucleaus position)}
- \ger{Relativistische Korrektur: Berücksichtigt die Interatkion mit dem Kern (endliche Wellenfunktion bei der Kernposition)}
- \end{ttext}
+ \Subsubsection{darwin}
+ \desc{Darwin term}{Relativisitc correction: Accounts for interaction with nucleus (non-zero wavefunction at nucleaus position)}{}
+ \desc[german]{Darwin-Term}{Relativistische Korrektur: Berücksichtigt die Interatkion mit dem Kern (endliche Wellenfunktion bei der Kernposition)}{}
\begin{formula}{energy_shift}
\desc{Energy shift}{}{}
\desc[german]{Energieverschiebung}{}{}
@@ -107,14 +121,9 @@
\eq{\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c} \approx \frac{1}{137}}
\end{formula}
- \Subsubsection[
- \eng{Spin-orbit coupling (LS-coupling)}
- \ger{Spin-Bahn-Kopplung (LS-Kopplung)}
- ]{ls_coupling}
- \begin{ttext}[desc]
- \eng{The interaction of the electron spin with the electrostatic field of the nuclei lead to energy shifts.}
- \ger{The Wechselwirkung zwischen dem Elektronenspin und dem elektrostatischen Feld des Kerns führt zu Energieverschiebungen.}
- \end{ttext}
+ \Subsubsection{ls_coupling}
+ \desc{Spin-orbit coupling (LS-coupling)}{The interaction of the electron spin with the electrostatic field of the nuclei lead to energy shifts.}{}
+ \desc[german]{Spin-Bahn-Kopplung (LS-Kopplung)}{The Wechselwirkung zwischen dem Elektronenspin und dem elektrostatischen Feld des Kerns führt zu Energieverschiebungen.}{}
\begin{formula}{energy_shift}
\desc{Energy shift}{}{}
@@ -122,20 +131,15 @@
\eq{\Delta E_\text{LS} = \frac{\mu_0 Z e^2}{8\pi \masse^2\,r^3} \braket{\vec{S} \cdot \vec{L}}}
\end{formula}
\begin{formula}{sl}
- \desc{\TODO{name}}{}{}
- \desc[german]{??}{}{}
+ \desc{Spin-orbit coupling}{}{}
+ \desc[german]{Spin-Bahn-Kopplung}{}{}
\eq{\braket{\vec{S} \cdot \vec{L}} &= \frac{1}{2} \braket{[J^2-L^2-S^2]} \nonumber \\
&= \frac{\hbar^2}{2}[j(j+1) -l(l+1) -s(s+1)]}
\end{formula}
- \Subsubsection[
- \eng{Fine-structure}
- \ger{Feinstruktur}
- ]{fine_structure}
- \begin{ttext}[desc]
- \eng{The fine-structure combines \fRef[relativistic corrections]{qm:h:corrections:darwin} and \fRef{qm:h:corrections:ls_coupling}.}
- \ger{Die Feinstruktur vereint \fRef[relativistische Korrekturen]{qm:h:corrections:darwin} und \fRef{qm:h:corrections:ls_coupling}.}
- \end{ttext}
+ \Subsubsection{fine_structure}
+ \desc{Fine-structure}{The fine-structure combines \fRef[relativistic corrections]{qm:h:corrections:darwin} and \fRef{qm:h:corrections:ls_coupling}.}{}
+ \desc[german]{Feinstruktur}{Die Feinstruktur vereint \fRef[relativistische Korrekturen]{qm:h:corrections:darwin} und \fRef{qm:h:corrections:ls_coupling}.}{}
\begin{formula}{energy_shift}
\desc{Energy shift}{}{}
\desc[german]{Energieverschiebung}{}{}
@@ -143,28 +147,18 @@
\end{formula}
- \Subsubsection[
- \eng{Lamb-shift}
- \ger{Lamb-Shift}
- ]{lamb_shift}
- \begin{ttext}[desc]
- \eng{The interaction of the electron with virtual photons emitted/absorbed by the nucleus leads to a (very small) shift in the energy level.}
- \ger{The Wechselwirkung zwischen dem Elektron und vom Kern absorbierten/emittierten virtuellen Photonen führt zu einer (sehr kleinen) Energieverschiebung.}
- \end{ttext}
+ \Subsubsection{lamb_shift}
+ \desc{Lamb-shift}{The interaction of the electron with virtual photons emitted/absorbed by the nucleus leads to a (very small) shift in the energy level.}{}
+ \desc[german]{Lamb-Shift}{The Wechselwirkung zwischen dem Elektron und vom Kern absorbierten/emittierten virtuellen Photonen führt zu einer (sehr kleinen) Energieverschiebung.}{}
\begin{formula}{energy}
\desc{Potential energy}{}{$\delta r$ pertubation of $r$}
\desc[german]{Potentielle Energy}{}{$\delta r$ Schwankung von $r$}
\eq{\braket{E_\textrm{pot}} = -\frac{Z e^2}{4\pi\epsilon_0} \Braket{\frac{1}{r+\delta r}}}
\end{formula}
- \Subsubsection[
- \eng{Hyperfine structure}
- \ger{Hyperfeinstruktur}
- ]{hyperfine_structure}
- \begin{ttext}[desc]
- \eng{Interaction of the nucleus spin with the magnetic field created by the electron leads to energy shifts. (Lifts degeneracy) }
- \ger{Wechselwirkung von Kernspin mit dem vom Elektron erzeugten Magnetfeld spaltet Energieniveaus}
- \end{ttext}
+ \Subsubsection{hyperfine_structure}
+ \desc{Hyperfine structure}{Interaction of the nucleus spin with the magnetic field created by the electron leads to energy shifts. (Lifts degeneracy) }{}
+ \desc[german]{Hyperfeinstruktur}{Wechselwirkung von Kernspin mit dem vom Elektron erzeugten Magnetfeld spaltet Energieniveaus}{}
\begin{formula}{nuclear_spin}
\desc{Nuclear spin}{}{}
\desc[german]{Kernspin}{}{}
@@ -199,17 +193,14 @@
\end{formula}
\TODO{landé factor}
-\Subsection[
- \eng{Effects in magnetic field}
- \ger{Effekte im Magnetfeld}
-]{mag_effects}
+\Subsection{mag_effects}
+ \desc{Effects in magnetic field}{}{}
+ \desc[german]{Effekte im Magnetfeld}{}{}
\TODO{all}
- \\\TODO{Hunds rules}
-\Subsection[
- \eng{misc}
- \ger{Sonstiges}
-]{other}
+\Subsection{other}
+ \desc{misc}{}{}
+ \desc[german]{Sonstiges}{}{}
\begin{formula}{auger_effect}
\desc{Auger-Meitner-Effekt}{Auger-Effect}{}
\desc[german]{Auger-Meitner-Effekt}{Auger-Effekt}{}
diff --git a/src/qm/misc.tex b/src/qm/misc.tex
index 179235c..653e0ca 100644
--- a/src/qm/misc.tex
+++ b/src/qm/misc.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Other}
- \ger{Sonstiges}
-]{misc}
+\Section{misc}
+ \desc{Other}{}{}
+ \desc[german]{Sonstiges}{}{}
+
\begin{formula}{RWA}
\desc{Rotating Wave Approximation (RWS)}{Rapidly oscilating terms are neglected}{$\omega_\text{L}$ light frequency, $\omega_0$ transition frequency}
\desc[german]{Rotating Wave Approximation / Drehwellennäherung (RWS)}{Schnell oscillierende Terme werden vernachlässigt}{$\omega_\text{L}$ Frequenz des Lichtes, $\omega_0$ Übergangsfrequenz}
diff --git a/src/qm/qm.tex b/src/qm/qm.tex
index 3c62cd2..9b9aad3 100644
--- a/src/qm/qm.tex
+++ b/src/qm/qm.tex
@@ -5,18 +5,23 @@
\def\sigmaybraket{-i \ket{0}\bra{1} + i \ket{1}\bra{0}}
\def\sigmazbraket{\ket{0}\bra{0} - \ket{1}\bra{1}}
-\Part[
- \eng{Quantum Mechanics}
- \ger{Quantenmechanik}
-]{qm}
- \Section[
- \eng{Basics}
- \ger{Basics}
- ]{basics}
- \Subsection[
- \eng{Operators}
- \ger{Operatoren}
- ]{op}
+\Part{qm}
+ \desc{Quantum Mechanics}{}{}
+ \desc[german]{Quantenmechanik}{}{}
+ \Section{basics}
+ \desc{Basics}{}{}
+ \desc[german]{Basics}{}{}
+ \begin{formula}{correspondence_principle}
+ \desc{Correspondence principle}{}{}
+ \desc[german]{Korrespondenzprinzip}{}{}
+ \ttxt{
+ \ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
+ \eng{The equations of motion of classical mechanics can be derived from quantum mechanics in the limit of large quantum numbers.}
+ }
+ \end{formula}
+ \Subsection{op}
+ \desc{Operators}{}{}
+ \desc[german]{Operatoren}{}{}
\Ger[row_vector]{Zeilenvektor}
\Ger[column_vector]{Spaltenvektor}
\Eng[column_vector]{Column vector}
@@ -53,14 +58,9 @@
\eq{\hat{A} = \hat{A}^\dagger}
\end{formula}
- \Subsubsection[
- \eng{Measurement}
- \ger{Messung}
- ]{measurement}
- \begin{ttext}
- \eng{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}
- \ger{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}
- \end{ttext}
+ \Subsubsection{measurement}
+ \desc{Measurement}{An observable is a hermition operator acting on $\hat{H}$. The measurement randomly yields one of the eigenvalues of $\hat{O}$ (all real).}{}
+ \desc[german]{Messung}{Eine Observable ist ein hermitscher Operator, der auf $\hat{H}$ wirkt. Die Messung ergibt zufällig einen der Eigenwerte von $\hat{O}$, welche alle reell sind.}{}
\begin{formula}{name}
\desc{Measurement probability}{Probability to measure $\psi$ in state $\lambda$}{}
\desc[german]{Messwahrscheinlichkeit}{Wahrscheinlichkeit, $\psi$ im Zustand $\lambda$ zu messen}{}
@@ -73,10 +73,9 @@
\end{formula}
- \Subsubsection[
- \eng{Pauli matrices}
- \ger{Pauli-Matrizen}
- ]{pauli_matrices}
+ \Subsubsection{pauli_matrices}
+ \desc{Pauli matrices}{}{}
+ \desc[german]{Pauli-Matrizen}{}{}
\begin{formula}{pauli_matrices}
\desc{Pauli matrices}{}{}
\desc[german]{Pauli Matrizen}{}{}
@@ -91,10 +90,10 @@
% $\sigma_y$ PHASE
% $\sigma_z$ Sign
- \Subsection[
- \ger{Wahrscheinlichkeitstheorie}
- \eng{Probability theory}
- ]{probability}
+ \Subsection{probability}
+ \desc{Wahrscheinlichkeitstheorie}{}{}
+ \desc[german]{Probability theory}{}{}
+
\begin{formula}{conservation_of_probability}
\desc{Continuity equation}{}{$\rho$ density of a conserved quantity $q$, $j$ flux density of $q$}
\desc[german]{Kontinuitätsgleichung}{}{$\rho$ Dichte einer Erhaltungsgröße $q$, $j$ Fluß von $q$}
@@ -102,9 +101,9 @@
\end{formula}
\begin{formula}{state_probability}
- \desc{State probability}{}{}
- \desc[german]{Zustandswahrscheinlichkeit}{}{}
- \eq{TODO}
+ \desc{State probability}{Probability to measure eigenvale $n$}{$P_n$ projector, $n$ normalized eigenvalue of measurement operator with one-dimensional eigenspace}
+ \desc[german]{Zustandswahrscheinlichkeit}{Wahrscheinlicht, den Eigenwert $n$ zu messen}{$P_n$ Projektor, $n$ normalisierter Eigenwert des Messoperators mit ein-dimensionalem Eigenraum}
+ \eq{p_n = \Braket{\psi|P_n|\psi} = \Braket{\psi|n}\Braket{n|\psi} = \abs{\Braket{n|\psi}}^2 }
\end{formula}
\begin{formula}{dispersion}
@@ -124,10 +123,9 @@
\end{formula}
- \Subsection[
- \eng{Commutator}
- \ger{Kommutator}
- ]{commutator}
+ \Subsection{commutator}
+ \desc{Commutator}{}{}
+ \desc[german]{Kommutator}{}{}
\begin{formula}{commutator}
\desc{Commutator}{}{}
\desc[german]{Kommutator}{}{}
@@ -174,10 +172,9 @@
}
\end{formula}
- \Section[
- \eng{Schrödinger equation}
- \ger{Schrödingergleichung}
- ]{se}
+ \Section{se}
+ \desc{Schrödinger equation}{}{}
+ \desc[german]{Schrödingergleichung}{}{}
\abbrLink{se}{SE}
\begin{formula}{energy_operator}
\desc{Energy operator}{}{}
@@ -228,11 +225,9 @@
}}
\end{formula}
- \Subsection[
- \eng{Time evolution}
- \ger{Zeitentwicklug}
- ]{time}
- The time evolution of the Hamiltonian is given by:
+ \Subsection{time}
+ \desc{Time evolution}{}{}
+ \desc[german]{Zeitentwicklug}{}{}
\begin{formula}{time_evolution_op}
\desc{Time evolution operator}{}{$U$ unitary}
\desc[german]{Zeitentwicklungsoperator}{}{$U$ unitär}
@@ -255,18 +250,15 @@
\TODO{unitary transformation of time dependent H}
- \Subsubsection[
- \eng{Schrödinger- and Heisenberg-pictures}
- \ger{Schrödinger- und Heisenberg-Bild}
- ]{s_h_pictures}
- \eng[s_h_pictures_desc]{
+ \Subsubsection{s_h_pictures}
+ \desc{Schrödinger- and Heisenberg-pictures}{
In the \textbf{Schrödinger picture}, the time dependecy is in the states
while in the \textbf{Heisenberg picture} the observables (operators) are time dependent.
- }
- \ger[s_h_pictures_desc]{Im Schrödinger-Bild sind die Zustände zeitabhänig, im Heisenberg-Bild
+ }{}
+ \desc[german]{Schrödinger- und Heisenberg-Bild}{
+ Im Schrödinger-Bild sind die Zustände zeitabhänig, im Heisenberg-Bild
sind die Observablen (Operatoren) zeitabhänig
- }
- \gt{s_h_pictures_desc}\\
+ }{}
\begin{formula}{schroediner_time_evolution}
\desc{Schrödinger time evolution}{}{}
\desc[german]{Schrödinger Zeitentwicklug}{}{}
@@ -285,12 +277,11 @@
}
\end{formula}
- \Subsubsection[
- \eng{Ehrenfest theorem}
- \ger{Ehrenfest-Theorem}
- ]{ehrenfest_theorem}
+ \Subsubsection{ehrenfest_theorem}
+ \desc{Ehrenfest theorem}{\GT{see_also} \fRef{qm:se:time:ehrenfest_theorem:correspondence_principle}}{}
+ \desc[german]{Ehrenfest-Theorem}{}{}
\absLink{}{ehrenfest_theorem}
- \GT{see_also} \fRef{qm:se:time:ehrenfest_theorem:correspondence_principle}
+
\begin{formula}{ehrenfest_theorem}
\desc{Ehrenfest theorem}{applies to both pictures}{}
\desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{}
@@ -304,27 +295,13 @@
\eq{m\odv[2]{}{t}\braket{x} = -\braket{\nabla V(x)} = \braket{F(x)}}
\end{formula}
% \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time}
-
- % TODO: wo gehört das hin?
- \begin{formula}{correspondence_principle}
- \desc{Correspondence principle}{}{}
- \desc[german]{Korrespondenzprinzip}{}{}
- \ttxt{
- \ger{Die klassischen Bewegungsgleichungen lassen sich als Grenzfall (große Quantenzahlen) aus der Quantenmechanik ableiten.}
- \eng{The classical mechanics can be derived from quantum mechanics in the limit of large quantum numbers.}
- }
- \end{formula}
- \Section[
- \eng{Pertubation theory}
- \ger{Störungstheorie}
- ]{qm_pertubation}
- \begin{ttext}
- \eng{The following holds true if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}
- \ger{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}
- \end{ttext}
+ \Section{qm_pertubation}
+ \desc{Pertubation theory}{Applies if the pertubation $\hat{H_1}$ is sufficently small and the $E^{(0)}_n$ levels are not degenerate.}{}
+ \desc[german]{Störungstheorie}{Die folgenden Gleichungen gelten wenn $\hat{H_1}$ ausreichend klein ist und die $E_n^{(0)}$ Niveaus nicht entartet sind.}{}
+
\begin{formula}{pertubation_hamiltonian}
\desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{}
@@ -368,10 +345,9 @@
\end{formula}
- \Section[
- \eng{Harmonic oscillator}
- \ger{Harmonischer Oszillator}
- ]{hosc}
+ \Section{hosc}
+ \desc{Harmonic oscillator}{}{}
+ \desc[german]{Harmonischer Oszillator}{}{}
\begin{formula}{hamiltonian}
\desc{Hamiltonian}{}{}
\desc[german]{Hamiltonian}{}{}
@@ -387,10 +363,9 @@
\eq{E_n = \hbar\omega \Big(\frac{1}{2} + n\Big)}
\end{formula}
- \Subsection[
- \ger{Erzeugungs und Vernichtungsoperatoren / Leiteroperatoren}
- \eng{Creation and Annihilation operators / Ladder operators}
- ]{c_a_ops}
+ \Subsection{c_a_ops}
+ \desc{Erzeugungs und Vernichtungsoperatoren / Leiteroperatoren}{}{}
+ \desc[german]{Creation and Annihilation operators / Ladder operators}{}{}
\begin{formula}{c_a_ops_def}
\desc{Particle number operator/occupation number operator}{}{$\ket{n}$ = Fock states, $\hat{a}$ = Annihilation operator, $\hat{a}^\dagger$ = Creation operator}
\desc[german]{Teilchenzahloperator/Besetzungszahloperator}{}{$\ket{n}$ = Fock-Zustände, $\hat{a}$ = Vernichtungsoperator, $\hat{a}^\dagger$ = Erzeugungsoperator}
@@ -445,10 +420,9 @@
}
\end{formula}
- \Subsubsection[
- \eng{Harmonischer Oszillator}
- \ger{Harmonic Oscillator}
- ]{hosc}
+ \Subsubsection{hosc}
+ \desc{Harmonischer Oszillator}{}{}
+ \desc[german]{Harmonic Oscillator}{}{}
\begin{formula}{c_a_ops}
\desc{Harmonic oscillator}{}{}
\desc[german]{Harmonischer Oszillator}{}{}
@@ -475,24 +449,21 @@
% E_n=( \frac{1}{2} +n)\hbar\omega
% \end{equation}
- \Section[
- \eng{Angular momentum}
- \ger{Drehmoment}
- ]{angular_momentum}
+ \Section{angular_momentum}
+ \desc{Angular momentum}{}{}
+ \desc[german]{Drehmoment}{}{}
- \Subsection[
- \eng{Aharanov-Bohm effect}
- \ger{Aharanov-Bohm Effekt}
- ]{aharanov_bohm}
+ \Subsection{aharanov_bohm}
+ \desc{Aharanov-Bohm effect}{}{}
+ \desc[german]{Aharanov-Bohm Effekt}{}{}
\begin{formula}{phase}
\desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{\QtyRef{magnetic_vector_potential}, \QtyRef{magnetic_flux}}
\desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{}
\eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
\end{formula}
- \Section[
- \eng{Periodic potentials}
- \ger{Periodische Potentiale}
- ]{periodic}
+ \Section{periodic}
+ \desc{Periodic potentials}{}{}
+ \desc[german]{Periodische Potentiale}{}{}
\begin{formula}{bloch_waves}
\desc{Bloch waves}{
Solve the stat. SG in periodic potential with period
@@ -519,24 +490,18 @@
\end{formula}
- \Section[
- \eng{Symmetries}
- \ger{Symmetrien}
- ]{symmetry}
- \begin{ttext}[desc]
- \eng{Most symmetry operators are \fRef[unitary]{math:linalg:matrix:unitary} because the norm of a state must be invariant under transformations of space, time and spin.}
- \ger{Die meisten Symmetrieoperatoren sind \fRef[unitär]{math:linalg:matrix:unitary}, da die Norm eines Zustands invariant unter Raum-, Zeit- und Spin-Transformationen sein muss.}
- \end{ttext}
+ \Section{symmetry}
+ \desc{Symmetries}{Most symmetry operators are \fRef[unitary]{math:linalg:matrix:unitary} because the norm of a state must be invariant under transformations of space, time and spin.}{}
+ \desc[german]{Symmetrien}{Die meisten Symmetrieoperatoren sind \fRef[unitär]{math:linalg:matrix:unitary}, da die Norm eines Zustands invariant unter Raum-, Zeit- und Spin-Transformationen sein muss.}{}
\begin{formula}{invariance}
\desc{Invariance}{$\hat{H}$ is invariant under a symmetrie described by $\hat{U}$ if this holds}{}
\desc[german]{Invarianz}{$\hat{H}$ is invariant unter der von $\hat{U}$ beschriebenen Symmetrie wenn gilt:}{}
\eq{\hat{U}\hat{H}\hat{U}^\dagger = \hat{H} \Leftrightarrow [\hat{U}, \hat{H}] = 0}
\end{formula}
- \Subsection[
- \eng{Time-reversal symmetry}
- \ger{Zeitumkehrungssymmetrie}
- ]{time_reversal}
+ \Subsection{time_reversal}
+ \desc{Time-reversal symmetry}{}{}
+ \desc[german]{Zeitumkehrungssymmetrie}{}{}
\begin{formula}{time}
\desc{Time-reversal symmetry}{}{}
@@ -550,10 +515,9 @@
\eq{T^2 = -1}
\end{formula}
- \Section[
- \eng{Two-level systems (TLS)}
- \ger{Zwei-Niveau System (TLS)}
- ]{tls}
+ \Section{tls}
+ \desc{Two-level systems (TLS)}{}{}
+ \desc[german]{Zwei-Niveau System (TLS)}{}{}
\begin{formula}{james_cummings}
\desc{James-Cummings Hamiltonian}{TLS interacting with optical cavity}{$\hat{E} = E_\text{ZPF}(\hat{a} + \hat{a}^\dagger)$ field operator with bosonic ladder operators, $\hat{S} = \hat{\sigma}^\dagger + \hat{\sigma}$ polarization operator with ladder operators of the TLS}
\desc[german]{James-Cummings Hamiltonian}{TLS interagiert mit resonantem Lichtfeld}{$\hat{E} = E_\text{ZPF}(\hat{a} + \hat{a}^\dagger)$ Feldoperator mit bosonischen Leiteroperatoren, $\hat{S} = \hat{\sigma}^\dagger + \hat{\sigma}$ Polarisationsoperator mit Leiteroperatoren des TLS}
diff --git a/src/quantities.tex b/src/quantities.tex
index a444495..4c822b0 100644
--- a/src/quantities.tex
+++ b/src/quantities.tex
@@ -3,15 +3,13 @@
% Put quantites here that are referenced often, even if they are not exciting themselves.
% This could later allow making a list of all links to this quantity, creating a list of releveant formulas
-\Section[
- \eng{Physical quantities}
- \ger{Physikalische Größen}
-]{quantities}
+\Section{quantities}
+ \desc{Physical quantities}{}{}
+ \desc[german]{Physikalische Größen}{}{}
-\Subsection[
- \eng{SI quantities}
- \ger{SI-Basisgrößen}
-]{si}
+\Subsection{si}
+ \desc{SI quantities}{}{}
+ \desc[german]{SI-Basisgrößen}{}{}
\begin{formula}{time}
\desc{Time}{}{}
\desc[german]{Zeit}{}{}
@@ -54,10 +52,9 @@
\quantity{I_\text{V}}{\candela}{s}
\end{formula}
-\Subsection[
- \eng{Mechanics}
- \ger{Mechanik}
-]{mech}
+\Subsection{mech}
+ \desc{Mechanics}{}{}
+ \desc[german]{Mechanik}{}{}
\begin{formula}{force}
\desc{Force}{}{}
\desc[german]{Kraft}{}{}
@@ -89,10 +86,9 @@
\end{formula}
-\Subsection[
- \eng{Thermodynamics}
- \ger{Thermodynamik}
-]{td}
+\Subsection{td}
+ \desc{Thermodynamics}{}{}
+ \desc[german]{Thermodynamik}{}{}
\begin{formula}{volume}
\desc{Volume}{$d$ dimensional Volume}{}
\desc[german]{Volumen}{$d$ dimensionales Volumen}{}
@@ -110,10 +106,9 @@
\quantity{\rho}{\kg\per\m^3}{s}
\end{formula}
-\Subsection[
- \eng{Electrodynamics}
- \ger{Elektrodynamik}
-]{el}
+\Subsection{el}
+ \desc{Electrodynamics}{}{}
+ \desc[german]{Elektrodynamik}{}{}
\begin{formula}{charge}
\desc{Charge}{}{}
\desc[german]{Ladung}{}{}
@@ -197,10 +192,9 @@
\quantity{L}{\henry=\kg\m^2\per\s^2\ampere^2=\weber\per\ampere=\volt\s\per\ampere=\ohm\s}{s}
\end{formula}
-\Subsection[
- \eng{Others}
- \ger{Sonstige}
-]{other}
+\Subsection{other}
+ \desc{Others}{}{}
+ \desc[german]{Sonstige}{}{}
\begin{formula}{area}
\desc{Area}{}{}
\desc[german]{Fläche}{}{}
diff --git a/src/quantum_computing.tex b/src/quantum_computing.tex
index e1a06a2..a917340 100644
--- a/src/quantum_computing.tex
+++ b/src/quantum_computing.tex
@@ -1,12 +1,11 @@
-\Part[
- \eng{Quantum Computing}
- \ger{Quantencomputing}
-]{qc}
+\Part{qc}
+ \desc{Quantum Computing}{}{}
+ \desc[german]{Quantencomputing}{}{}
-\Section[
- \eng{Qubits}
- \ger{Qubits}
- ]{qubit}
+
+\Section{qubit}
+ \desc{Qubits}{}{}
+ \desc[german]{Qubits}{}{}
\begin{formula}{bloch_sphere}
\desc{Bloch sphere}{}{}
\desc[german]{Bloch-Sphäre}{}{}
@@ -17,10 +16,9 @@
}
\end{formula}
-\Section[
- \eng{Gates}
- \ger{Gates}
-]{gates}
+\Section{gates}
+ \desc{Gates}{}{}
+ \desc[german]{Gates}{}{}
\begin{formula}{gates}
\desc{Gates}{}{}
\desc[german]{Gates}{}{}
@@ -40,23 +38,16 @@
% \item \gt{bitphaseflip}: $\hat{Y} = \sigma_y = \sigmaymatrix$
% \item \gt{phaseflip}: $\hat{Z} = \sigma_z = \sigmazmatrix$ \item \gt{hadamard}: $\hat{H} = \frac{1}{\sqrt{2}}(\hat{X}-\hat{Z}) = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$
% \end{itemize}
-\Section[
- \eng{Superconducting qubits}
- \ger{Supraleitende qubits}
- ]{scq}
+\Section{scq}
+ \desc{Superconducting qubits}{}{}
+ \desc[german]{Supraleitende qubits}{}{}
- \Subsection[
- \eng{Building blocks}
- \ger{Bauelemente}
- ]{elements}
- \Subsubsection[
- \eng{Josephson Junction}
- \ger{Josephson-Kontakt}
- ]{josephson_junction}
- \begin{ttext}[desc]
- \eng{When two superconductors are separated by a thin isolator, Cooper pairs can tunnel through the insulator. The Josephson junction is a non-linear inductor.}
- \ger{Wenn zwei Supraleiter durch einen dünnen Isolator getrennt sind, können Cooper-Paare durch den Isolator tunneln. Der Josephson-Kontakt ist ein nicht-linearer Induktor.}
- \end{ttext}
+ \Subsection{elements}
+ \desc{Building blocks}{}{}
+ \desc[german]{Bauelemente}{}{}
+ \Subsubsection{josephson_junction}
+ \desc{Josephson Junction}{When two superconductors are separated by a thin isolator, Cooper pairs can tunnel through the insulator. The Josephson junction is a non-linear inductor.}{}
+ \desc[german]{Josephson-Kontakt}{Wenn zwei Supraleiter durch einen dünnen Isolator getrennt sind, können Cooper-Paare durch den Isolator tunneln. Der Josephson-Kontakt ist ein nicht-linearer Induktor.}{}
\begin{formula}{hamiltonian}
\desc{Josephson-Hamiltonian}{}{}
@@ -78,10 +69,9 @@
\eq{\odv{\hat{\delta}}{t}=\frac{1}{i\hbar}[\hat{H},\hat{\delta}] = -\frac{2eU}{i\hbar}[\hat{n},\hat{\delta}] = \frac{1}{\varphi_0} U}
\end{formula}
- \Subsubsection[
- \eng{SQUID}
- \ger{SQUID}
- ]{squid}
+ \Subsubsection{squid}
+ \desc{SQUID}{}{}
+ \desc[german]{SQUID}{}{}
\ctikzsubcircuitdef{squidloop}{n, s, nw, ne, se, sw}{
% start at top
coordinate(#1-n)
@@ -107,10 +97,9 @@
\eq{\hat{H} &= -E_{\text{J}1} \cos\hat{\phi}_{1} - E_{\text{J}2} \cos\hat{\phi}_{2}}
\end{formula}
- \Subsection[
- \eng{Josephson junction based qubits}
- \ger{Qubits mit Josephson-Junctions}
- ]{josephson_qubit}
+ \Subsection{josephson_qubit}
+ \desc{Josephson junction based qubits}{}{}
+ \desc[german]{Qubits mit Josephson-Junctions}{}{}
\begin{formula}{circuit}
\desc{General circuit}{}{}
@@ -194,20 +183,18 @@
\end{bigformula}
- \Subsection[
- \eng{Charge based qubits}
- \ger{Ladungsbasierte Qubits}
- ]{charge}
+ \Subsection{charge}
+ \desc{Charge based qubits}{}{}
+ \desc[german]{Ladungsbasierte Qubits}{}{}
\begin{bigformula}{comparison}
\desc{Comparison of charge qubit states}{}{}
\desc[german]{Vergleich der Zustände von Ladungsbasierten Qubits}{}{}
\fig{img/qubit_transmon.pdf}
\end{bigformula}
- \Subsubsection[
- \eng{Cooper Pair Box (CPB) qubit}
- \ger{Cooper Paar Box (QPB) Qubit}
- ]{cpb}
+ \Subsubsection{cpb}
+ \desc{Cooper Pair Box (CPB) qubit}{}{}
+ \desc[german]{Cooper Paar Box (QPB) Qubit}{}{}
\begin{ttext}
\eng{
= voltage bias junction\\= charge qubit?
@@ -245,10 +232,9 @@
&=\sum_n \left[4 E_C (n-n_\text{g})^2 \ket{n}\bra{n} - \frac{E_\text{J}}{2}\ket{n}\bra{n+1}+\ket{n+1}\bra{n}\right] }
\end{formula}
- \Subsubsection[
- \eng{Transmon qubit}
- \ger{Transmon Qubit}
- ]{transmon}
+ \Subsubsection{transmon}
+ \desc{Transmon qubit}{}{}
+ \desc[german]{Transmon Qubit}{}{}
\begin{formula}{circuit}
\desc{Transmon qubit}{
Josephson junction with a shunt \textbf{capacitance}.
@@ -279,10 +265,9 @@
\eq{\hat{H} &= 4 E_C\hat{n}^2 - E_\text{J} \cos\hat{\phi}}
\end{formula}
- \Subsubsection[
- \eng{Tunable Transmon qubit}
- \ger{Tunable Transmon Qubit}
- ]{tunable}
+ \Subsubsection{tunable}
+ \desc{Tunable Transmon qubit}{}{}
+ \desc[german]{Tunable Transmon Qubit}{}{}
\begin{formula}{circuit}
\desc{Frequency tunable transmon}{By using a \fRef{qc:scq:elements:squid} instead of a \fRef{qc:scq:elements:josephson_junction}, the qubit is frequency tunable through an external field}{}
\desc[german]{}{Durch Nutzung eines \fRef{qc:scq:elements:squid} anstatt eines \fRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{}
@@ -309,19 +294,17 @@
- \Subsection[
- \eng{Inductive qubits}
- \ger{Induktive Qubits}
- ]{inductive}
+ \Subsection{inductive}
+ \desc{Inductive qubits}{}{}
+ \desc[german]{Induktive Qubits}{}{}
\begin{bigformula}{comparison}
\desc{Comparison of other qubit states}{}{}
\desc[german]{Vergleich der Zustände von anderen Qubits}{}{}
\fig{img/qubit_flux_onium.pdf}
\end{bigformula}
- \Subsubsection[
- \eng{Phase qubit}
- \ger{Phase Qubit}
- ]{phase}
+ \Subsubsection{phase}
+ \desc{Phase qubit}{}{}
+ \desc[german]{Phase Qubit}{}{}
\begin{formula}{circuit}
\desc{Phase qubit}{}{}
\desc[german]{Phase Qubit}{}{}
@@ -348,10 +331,9 @@
\eq{\hat{H} = E_C \hat{n}^2 - E_J \cos \hat{\delta} + E_L(\hat{\delta} - \delta_s)^2}
\end{formula}
- \Subsubsection[
- \eng{Flux qubit}
- \ger{Flux Qubit}
- ]{flux}
+ \Subsubsection{flux}
+ \desc{Flux qubit}{}{}
+ \desc[german]{Flux Qubit}{}{}
\begin{formula}{circuit}
\desc{Flux qubit / Persistent current qubit}{}{}
\desc[german]{Flux Qubit / Persistent current qubit}{}{}
@@ -384,10 +366,9 @@
\end{formula}
- \Subsubsection[
- \eng{Fluxonium qubit}
- \ger{Fluxonium Qubit}
- ]{fluxonium}
+ \Subsubsection{fluxonium}
+ \desc{Fluxonium qubit}{}{}
+ \desc[german]{Fluxonium Qubit}{}{}
\begin{formula}{circuit}
\desc{Fluxonium qubit}{
Josephson junction with a shunt \textbf{inductance}. Instead of having to tunnel, cooper pairs can move to the island via the inductance.
@@ -418,10 +399,9 @@
- \Section[
- \eng{Two-level system}
- \ger{Zwei-Niveau System}
- ]{stuff}
+ \Section{stuff}
+ \desc{Two-level system}{}{}
+ \desc[german]{Zwei-Niveau System}{}{}
\begin{formula}{resonance_frequency}
\desc{Resonance frequency}{}{}
@@ -444,10 +424,9 @@
\end{ttext}
\end{formula}
- \Section[
- \eng{Noise and decoherence}
- \ger{Noise und Dekohärenz}
- ]{noise}
+ \Section{noise}
+ \desc{Noise and decoherence}{}{}
+ \desc[german]{Noise und Dekohärenz}{}{}
\begin{formula}{long}
\desc{Longitudinal relaxation rate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{}
\desc[german]{Longitudinale Relaxationsrate}{$\Gamma_{1\downarrow}$: $\ket{1}\rightarrow \ket{0}$ \\ $\Gamma_{1\uparrow}$: $\ket{0}\rightarrow \ket{1}$}{}
diff --git a/src/spv.tex b/src/spv.tex
index 3226015..99ba613 100644
--- a/src/spv.tex
+++ b/src/spv.tex
@@ -1,7 +1,7 @@
-\Section[
- \eng{Surface-Photovoltage}
- \ger{Oberflächen-Photospannung}
-]{spv}
+\Section{spv}
+ \desc{Surface-Photovoltage}{}{}
+ \desc[german]{Oberflächen-Photospannung}{}{}
+
Mechanisms:
\begin{formula}{scr}
\desc{Space-charge regions}{}{}
diff --git a/src/statistical_mechanics.tex b/src/statistical_mechanics.tex
index 4351b15..00b2f76 100644
--- a/src/statistical_mechanics.tex
+++ b/src/statistical_mechanics.tex
@@ -1,7 +1,7 @@
-\Part[
- \eng{Statistichal Mechanics}
- \ger{Statistische Mechanik}
-]{stat}
+\Part{stat}
+ \desc{Statistichal Mechanics}{}{}
+ \desc[german]{Statistische Mechanik}{}{}
+
\begin{ttext}
\eng{
@@ -20,10 +20,9 @@
\eq{\pdv{\rho}{t} = - \sum_{i=1}^{N} \left(\pdv{\rho}{q_i} \pdv{H}{p_i} - \pdv{\rho}{p_i} \pdv{H}{q_i} \right) = \{H, \rho\}}
\end{formula}
-\Section[
- \eng{Entropy}
- \ger{Entropie}
-]{entropy}
+\Section{entropy}
+ \desc{Entropy}{}{}
+ \desc[german]{Entropie}{}{}
\begin{formula}{properties}
\desc{Positive-definite and additive}{}{}
@@ -64,10 +63,9 @@
\eq{p = T \pdv{S}{V}_E}
\end{formula}
-\Part[
- \eng{Thermodynamics}
- \ger{Thermodynamik}
-]{td}
+\Part{td}
+ \desc{Thermodynamics}{}{}
+ \desc[german]{Thermodynamik}{}{}
\begin{formula}{therm_wavelength}
\desc{Thermal wavelength}{}{}
@@ -75,10 +73,9 @@
\eq{\lambda = \frac{\hbar}{\sqrt{2\pi m \kB T}}}
\end{formula}
-\Section[
- \eng{Processes}
- \ger{Prozesse}
-]{process}
+\Section{process}
+ \desc{Processes}{}{}
+ \desc[german]{Prozesse}{}{}
\begin{ttext}
\eng{
\begin{itemize}
@@ -106,10 +103,9 @@
}
\end{ttext}
- \Subsection[
- \eng{Irreversible gas expansion (Gay-Lussac experiment)}
- \ger{Irreversible Gasexpansion (Gay-Lussac-Versuch)}
- ]{gay}
+ \Subsection{gay}
+ \desc{Irreversible gas expansion (Gay-Lussac experiment)}{}{}
+ \desc[german]{Irreversible Gasexpansion (Gay-Lussac-Versuch)}{}{}
\begin{bigformula}{experiment}
\desc{Gay-Lussac experiment}{}{}
@@ -151,10 +147,9 @@
\TODO{Joule-Thompson Prozess}
- \Section[
- \eng{Phase transitions}
- \ger{Phasenübergänge}
- ]{phases}
+ \Section{phases}
+ \desc{Phase transitions}{}{}
+ \desc[german]{Phasenübergänge}{}{}
\begin{ttext}
\eng{
@@ -189,10 +184,9 @@
\eq{f = c - p + 2}
\end{formula}
- \Subsubsection[
- \eng{Osmosis}
- \ger{Osmose}
- ]{osmosis}
+ \Subsubsection{osmosis}
+ \desc{Osmosis}{}{}
+ \desc[german]{Osmose}{}{}
\begin{ttext}
\eng{
Osmosis is the spontaneous net movement or diffusion of solvent molecules
@@ -215,10 +209,9 @@
\end{formula}
- \Subsection[
- \eng{Material properties}
- \ger{Materialeigenschaften}
- ]{props}
+ \Subsection{props}
+ \desc{Material properties}{}{}
+ \desc[german]{Materialeigenschaften}{}{}
\begin{formula}{heat_capacity}
\desc{Heat capacity}{}{\QtyRef{heat}}
\desc[german]{Wärmekapazität}{}{}
@@ -269,15 +262,13 @@
-\Section[
- \eng{Laws of thermodynamics}
- \ger{Hauptsätze der Thermodynamik}
-]{laws}
+\Section{laws}
+ \desc{Laws of thermodynamics}{}{}
+ \desc[german]{Hauptsätze der Thermodynamik}{}{}
- \Subsection[
- \eng{Zeroeth law}
- \ger{Nullter Hauptsatz}
- ]{law0}
+ \Subsection{law0}
+ \desc{Zeroeth law}{}{}
+ \desc[german]{Nullter Hauptsatz}{}{}
\begin{ttext}
\eng{If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.}
\ger{Wenn sich zwei Siesteme jeweils im thermischen Gleichgewicht mit einem dritten befinden, befinden sie sich auch untereinander im thermischen Gleichgewicht.}
@@ -291,10 +282,9 @@
A \ggwarrow C \quad\wedge\quad B \ggwarrow C \quad\Rightarrow\quad A \ggwarrow B
\end{equation}
- \Subsection[
- \eng{First law}
- \ger{Erster Hauptsatz}
- ]{law1}
+ \Subsection{law1}
+ \desc{First law}{}{}
+ \desc[german]{Erster Hauptsatz}{}{}
\begin{ttext}
\eng{In a process without transfer of matter, the change in internal energy, $\Delta U$, of a thermodynamic system is equal to the energy gained as heat, $Q$, less the thermodynamic work, W, done by the system on its surroundings.}
\ger{In einem abgeschlossenem System ist die Änderung der inneren Energie $U$ gleich der gewonnenen Wärme $Q$ minus der vom System an der Umgebung verrichteten Arbeit $W$.}
@@ -310,10 +300,9 @@
\end{formula}
- \Subsection[
- \eng{Second law}
- \ger{Zweiter Hauptsatz}
- ]{law2}
+ \Subsection{law2}
+ \desc{Second law}{}{}
+ \desc[german]{Zweiter Hauptsatz}{}{}
\begin{ttext}
\eng{
\textbf{Clausius}: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.\\
@@ -324,10 +313,9 @@
\textbf{Kelvin}: Es ist unmöglich, eine periodisch arbeitende Maschine zu konstruieren, die weiter nichts bewirkt als Hebung einer Last und Abkühlung eines Wärmereservoirs.
}
\end{ttext}
- \Subsection[
- \eng{Third law}
- \ger{Dritter Hauptsatz}
- ]{law3}
+ \Subsection{law3}
+ \desc{Third law}{}{}
+ \desc[german]{Dritter Hauptsatz}{}{}
\begin{ttext}
\eng{It is impussible to cool a system to absolute zero.}
\ger{Es ist unmöglich, ein System bis zum absoluten Nullpunkt abzukühlen.}
@@ -343,10 +331,9 @@
}
\end{formula}
-\Section[
- \eng{Ensembles}
- \ger{Ensembles}
-]{ensembles}
+\Section{ensembles}
+ \desc{Ensembles}{}{}
+ \desc[german]{Ensembles}{}{}
\Eng[const_variables]{Constant variables}
\Ger[const_variables]{Konstante Variablen}
@@ -425,10 +412,9 @@
\end{formula}
- \Subsection[
- \eng{Potentials}
- \ger{Potentiale}
- ]{pots}
+ \Subsection{pots}
+ \desc{Potentials}{}{}
+ \desc[german]{Potentiale}{}{}
\begin{formula}{internal_energy}
\desc{Internal energy}{}{}
\desc[german]{Innere Energie}{}{}
@@ -484,10 +470,9 @@
}
\end{formula}
-\Section[
- \eng{Ideal gas}
- \ger{Ideales Gas}
-]{id_gas}
+\Section{id_gas}
+ \desc{Ideal gas}{}{}
+ \desc[german]{Ideales Gas}{}{}
\begin{ttext}
\eng{The ideal gas consists of non-interacting, undifferentiable particles.}
\ger{Das ideale Gas besteht aus nicht-wechselwirkenden, ununterscheidbaren Teilchen.}
@@ -550,10 +535,9 @@
\eq{\braket{v^2} = \int_0^\infty \d v\,v^2 w(v) = \frac{3\kB T}{m}}
\end{formula}
- \Subsubsection[
- \eng{Molecule gas}
- \ger{Molekülgas}
- ]{molecule_gas}
+ \Subsubsection{molecule_gas}
+ \desc{Molecule gas}{}{}
+ \desc[german]{Molekülgas}{}{}
\begin{formula}{desc}
\desc{Molecule gas}{2 particles of mass $M$ connected by a ``spring'' with distance $L$}{}
@@ -592,15 +576,13 @@
\TODO{Diagram für verschiedene Temperaturen, Weiler Skript p.83}
-\Section[
- \eng{Real gas}
- \ger{Reales Gas}
-]{real_gas}
+\Section{real_gas}
+ \desc{Real gas}{}{}
+ \desc[german]{Reales Gas}{}{}
- \Subsection[
- \eng{Virial expansion}
- \ger{Virialentwicklung}
- ]{virial}
+ \Subsection{virial}
+ \desc{Virial expansion}{}{}
+ \desc[german]{Virialentwicklung}{}{}
\begin{ttext}
\eng{Expansion of the pressure $p$ in a power series of the density $\rho$.}
\ger{Entwicklung desw Drucks $p$ in eine Potenzreihe der Dichte $\rho$.}
@@ -633,10 +615,9 @@
\eq{V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]}
\end{formula}
- \Subsection[
- \eng{Van der Waals equation}
- \ger{Van der Waals Gleichung}
- ]{vdw}
+ \Subsection{vdw}
+ \desc{Van der Waals equation}{}{}
+ \desc[german]{Van der Waals Gleichung}{}{}
\begin{ttext}
\eng{Assumes a hard-core potential with a weak attraction.}
\ger{Annahme eines Harte-Kugeln Potentials mit einer schwachen Anziehung}
@@ -654,10 +635,9 @@
\TODO{sometimes N is included in a, b}
-\Section[
- \eng{Ideal quantum gas}
- \ger{Ideales Quantengas}
-]{id_qgas}
+\Section{id_qgas}
+ \desc{Ideal quantum gas}{}{}
+ \desc[german]{Ideales Quantengas}{}{}
\def\bosfer{$\pm$: {$\text{bos} \atop \text{fer}$}}
\begin{formula}{fugacity}
@@ -746,10 +726,9 @@
\eq{\left. \begin{array}{l}g_\nu(z)\\f_\nu(z)\end{array}\right\} \coloneq \frac{1}{\Gamma(\nu)} \int_0^\infty \d x\, \frac{x^{\nu-1}}{\e^x z^{-1} \mp 1}}
\end{formula}
- \Subsection[
- \eng{Bosons}
- \ger{Bosonen}
- ]{bos}
+ \Subsection{bos}
+ \desc{Bosons}{}{}
+ \desc[german]{Bosonen}{}{}
\begin{formula}{partition-sum}
\desc{Partition sum}{}{$p \in\N_0$}
\desc[german]{Zustandssumme}{}{$p \in\N_0$}
@@ -762,10 +741,9 @@
\end{formula}
- \Subsection[
- \eng{Fermions}
- \ger{Fermionen}
- ]{fer}
+ \Subsection{fer}
+ \desc{Fermions}{}{}
+ \desc[german]{Fermionen}{}{}
\begin{formula}{partition_sum}
\desc{Partition sum}{}{$p = 0,\,1$}
\desc[german]{Zustandssumme}{}{$p = 0,\,1$}
@@ -815,10 +793,9 @@
\eq{v = \frac{N}{V} = \frac{g}{\lambda^3}f_{3/2}(z)}
\end{formula}
- \Subsubsection[
- \eng{Strong degeneracy}
- \ger{Starke Entartung}
- ]{degenerate}
+ \Subsubsection{degenerate}
+ \desc{Strong degeneracy}{}{}
+ \desc[german]{Starke Entartung}{}{}
\eng[low_temps]{for low temperatures $T \ll T_\text{F}$}
\ger[low_temps]{für geringe Temperaturen $T\ll T_\text{F}$}
diff --git a/src/test.tex b/src/test.tex
index 7a681f5..6669d6b 100644
--- a/src/test.tex
+++ b/src/test.tex
@@ -103,3 +103,33 @@ Link to defined quantity: \qtyRef{mass}
\end{formula}
+
+\newpage
+\Section{layout}
+ \desc{Layout Test}{}{}
+ \desc[german]{}{}{}
+
+\begin{formula}{tt1}
+ \desc{Formula}{Desc}{Defs}
+ \eq{E=mc^2}
+\end{formula}
+
+\begin{bigformula}{tt2}
+ \desc{Big formula}{Desc}{Defs}
+ \eq{E=mc^3}
+\end{bigformula}
+
+
+\begin{formulagroup}{tt3}
+ \desc{Formula group}{Desc}{Defs}
+ \begin{formula}{tt1}
+ \desc{Formula}{Desc}{Defs}
+ \eq{E=mc^2}
+ \end{formula}
+
+ \begin{bigformula}{tt2}
+ \desc{Big formula}{Desc}{Defs}
+ \eq{E=mc^3}
+ \end{bigformula}
+
+\end{formulagroup}
diff --git a/src/util/environments.tex b/src/util/environments.tex
index a612ed7..7fc46e5 100644
--- a/src/util/environments.tex
+++ b/src/util/environments.tex
@@ -29,8 +29,8 @@
%
% DISTRIBUTION
%
-\def\distrightwidth{0.45\textwidth}
-\def\distleftwidth{0.45\textwidth}
+\def\distrightwidth{0.45}
+\def\distleftwidth{0.45}
% Table for distributions
% create entries for parameters using \disteq
@@ -57,16 +57,14 @@
& ##2 \\ \hline
}
\hfill
- \begin{minipage}{\distrightwidth}
- \begingroup
- \setlength{\tabcolsep}{0.9em} % horizontal
- \renewcommand{\arraystretch}{2} % vertical
- \begin{tabular}{|l|>{$\displaystyle}c<{$}|}
- \hline
+ \begingroup
+ \setlength{\tabcolsep}{0.9em} % horizontal
+ \renewcommand{\arraystretch}{2} % vertical
+ \begin{tabular}{|l|>{$\displaystyle}c<{$}|}
+ \hline
}{
- \end{tabular}
- \endgroup
- \end{minipage}
+ \end{tabular}
+ \endgroup
}
% A 2 column table in a minipage