From 702fc1eb33a60a876fe4bf55e5005ad012c2d51c Mon Sep 17 00:00:00 2001 From: "matthias@quintern.xyz" Date: Fri, 21 Mar 2025 22:48:38 +0100 Subject: [PATCH] refactor sectioning --- scripts/distributions.py | 15 ++ src/ch/ch.tex | 15 +- src/ch/el.tex | 64 ++++--- src/ch/misc.tex | 15 +- src/cm/charge_transport.tex | 129 +++++++++++--- src/cm/cm.tex | 19 +-- src/cm/crystal.tex | 42 ++--- src/cm/egas.tex | 36 ++-- src/cm/mat.tex | 8 +- src/cm/misc.tex | 34 ++-- src/cm/semiconductors.tex | 56 +++---- src/cm/superconductivity.tex | 72 ++++---- src/cm/techniques.tex | 50 +++--- src/cm/topo.tex | 22 +-- src/cm/vib.tex | 27 +-- src/comp/ad.tex | 88 +++++----- src/comp/comp.tex | 8 +- src/comp/est.tex | 64 ++++--- src/comp/ml.tex | 56 +++---- src/comp/qmb.tex | 43 +++-- src/constants.tex | 8 +- src/ed/ed.tex | 8 +- src/ed/el.tex | 13 +- src/ed/em.tex | 29 ++-- src/ed/mag.tex | 15 +- src/ed/misc.tex | 115 +------------ src/ed/optics.tex | 8 +- src/main.tex | 16 +- src/math/calculus.tex | 104 ++++++------ src/math/geometry.tex | 29 ++-- src/math/linalg.tex | 43 +++-- src/math/math.tex | 8 +- src/math/probability_theory.tex | 286 ++++++++++++++++---------------- src/mechanics.tex | 72 ++++---- src/particle.tex | 8 +- src/pkg/mqformula.sty | 26 +-- src/pkg/mqfqname.sty | 64 ++++--- src/pkg/mqperiodictable.sty | 19 ++- src/qm/atom.tex | 241 +++++++++++++-------------- src/qm/misc.tex | 8 +- src/qm/qm.tex | 196 +++++++++------------- src/quantities.tex | 42 ++--- src/quantum_computing.tex | 131 ++++++--------- src/spv.tex | 8 +- src/statistical_mechanics.tex | 169 ++++++++----------- src/test.tex | 30 ++++ src/util/environments.tex | 20 +-- 47 files changed, 1196 insertions(+), 1383 deletions(-) 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{} @@ -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
, 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: where 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