% if this causes a compilation error, check that none of the units have been redefined

% 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{quantities}
    \desc{Physical quantities}{}{}
    \desc[german]{Physikalische Größen}{}{}

\Subsection{si}
    \desc{SI quantities}{}{}
    \desc[german]{SI-Basisgrößen}{}{}
    \begin{formula}{time}
        \desc{Time}{}{}
        \desc[german]{Zeit}{}{}
        \quantity{t}{\second}{}
    \end{formula}

    \begin{formula}{length}
        \desc{Length}{}{}
        \desc[german]{Länge}{}{}
        \quantity{l}{\m}{e}
    \end{formula}

    \begin{formula}{mass}
        \desc{Mass}{}{}
        \desc[german]{Masse}{}{}
        \quantity{m}{\kg}{es}
    \end{formula}

    \begin{formula}{temperature}
        \desc{Temperature}{}{}
        \desc[german]{Temperatur}{}{}
        \quantity{T}{\kelvin}{is}
    \end{formula}

    \begin{formula}{current}
        \desc{Electric current}{}{}
        \desc[german]{Elektrischer Strom}{}{}
        \quantity{I}{\ampere}{es}
    \end{formula}

    \begin{formula}{amount}
        \desc{Amount of substance}{}{}
        \desc[german]{Stoffmenge}{}{}
        \quantity{n}{\mol}{es}
    \end{formula}

    \begin{formula}{luminous_intensity}
        \desc{Luminous intensity}{}{}
        \desc[german]{Lichtstärke}{}{}
        \quantity{I_\text{V}}{\candela}{s}
    \end{formula}

\Subsection{mech}
    \desc{Mechanics}{}{}
    \desc[german]{Mechanik}{}{}
    \begin{formula}{force}
        \desc{Force}{}{}
        \desc[german]{Kraft}{}{}
        \quantity{\vec{F}}{\newton=\kg\m\per\second^2}{ev}
    \end{formula}

    \begin{formula}{spring_constant}
        \desc{Spring constant}{}{}
        \desc[german]{Federkonstante}{}{}
        \quantity{k}{\newton\per\m=\kg\per\second^2}{s}
    \end{formula}

    \begin{formula}{velocity}
        \desc{Velocity}{}{}
        \desc[german]{Geschwindigkeit}{}{}
        \quantity{\vec{v}}{\m\per\s}{v}
    \end{formula}

    \begin{formula}{torque}
        \desc{Torque}{}{}
        \desc[german]{Drehmoment}{}{}
        \quantity{\tau}{\newton\m=\kg\m^2\per\s^2}{v}
    \end{formula}

    \begin{formula}{pressure}
        \desc{Pressure}{}{}
        \desc[german]{Druck}{}{}
        \quantity{p}{\newton\per\m^2}{}
    \end{formula}
    

\Subsection{td}
    \desc{Thermodynamics}{}{}
    \desc[german]{Thermodynamik}{}{}
    \begin{formula}{volume}
        \desc{Volume}{$d$ dimensional Volume}{}
        \desc[german]{Volumen}{$d$ dimensionales Volumen}{}
        \quantity{V}{\m^d}{}
    \end{formula}
    \begin{formula}{heat}
        \desc{Heat}{}{}
        \desc[german]{Wärme}{}{}
        \quantity{Q}{\joule}{}
    \end{formula}

    \begin{formula}{density}
        \desc{Density}{}{}
        \desc[german]{Dichte}{}{}
        \quantity{\rho}{\kg\per\m^3}{s}
    \end{formula}

\Subsection{el}
    \desc{Electrodynamics}{}{}
    \desc[german]{Elektrodynamik}{}{}
    \begin{formula}{charge}
        \desc{Charge}{}{}
        \desc[german]{Ladung}{}{}
        \quantity{q}{\coulomb=\ampere\s}{}
    \end{formula}

    \begin{formula}{charge_number}
        \desc{Charge number}{}{}
        \desc[german]{Ladungszahl}{Anzahl der Elementarladungen}{}
        \quantity{Z}{}{}
    \end{formula}
    \begin{formula}{charge_density}
        \desc{Charge density}{}{}
        \desc[german]{Ladungsdichte}{}{}
        \quantity{\rho}{\coulomb\per\m^3}{s}
    \end{formula}

    \begin{formula}{charge_carrier_density}
        \desc{Charge carrier density}{Number of charge carriers per volume}{}
        \desc[german]{Ladungsträgerdichte}{Anzahl der Ladungsträger pro Volumen}{}
        \quantity{n}{\per\m^3}{s}
    \end{formula}

    \begin{formula}{frequency}
        \desc{Frequency}{}{}
        \desc[german]{Frequenz}{}{}
        \quantity{f}{\hertz=\per\s}{s}
    \end{formula}
    \begin{formula}{angular_frequency}
        \desc{Angular frequency}{}{\QtyRef{time_period}, \QtyRef{frequency}}
        \desc[german]{Kreisfrequenz}{}{}
        \quantity{\omega}{\radian\per\s}{s}
        \eq{\omega = \frac{2\pi/T}{2\pi f}}
    \end{formula}
    \begin{formula}{angular_velocity}
        \desc{Angular velocity}{}{\QtyRef{time_period}, \QtyRef{frequency}}
        \desc[german]{Kreisgeschwindigkeit}{}{}
        \quantity{\vec{\omega}}{\radian\per\s}{v}
        \eq{\vec{\omega} = \frac{\vecr \times \vecv}{r^2}}
    \end{formula}

    \begin{formula}{time_period}
        \desc{Time period}{}{\QtyRef{frequency}}
        \desc[german]{Periodendauer}{}{}
        \quantity{T}{\s}{s}
        \eq{T = \frac{1}{f}}
    \end{formula}

    \begin{formula}{wavelength}
        \desc{Wavelength}{}{}
        \desc[german]{Wellenlänge}{}{}
        \quantity{\lambda}{\per\m}{s}
    \end{formula}

    \begin{formula}{angular_wavenumber}
        \desc{Wavenumber}{Angular wavenumber}{\QtyRef{wavelength}}
        \desc[german]{Wellenzahl}{}{}
        \eq{k = \frac{2\pi}{\lambda}}
        \quantity{k}{\radian\per\m}{s}
    \end{formula}
    \begin{formula}{wavevector}
        \desc{Wavevector}{Vector perpendicular to the wavefront}{}
        \desc[german]{Wellenvektor}{Vektor senkrecht zur Wellenfront}{}
        \eq{\abs{k} = \frac{2\pi}{\lambda}}
        \quantity{\vec{k}}{1\per\m}{v}
    \end{formula}

    \begin{formula}{impedance}
        \desc{Impedance}{}{}
        \desc[german]{Impedanz}{}{}
        \quantity{Z}{\ohm}{s}
    \end{formula}
    \begin{formula}{resistance}
        \desc{Resistance}{}{}
        \desc[german]{Widerstand}{}{}
        \quantity{R}{\ohm}{s}
    \end{formula}
    \begin{formula}{inductance}
        \desc{Inductance}{}{}
        \desc[german]{Induktivität}{}{}
        \quantity{L}{\henry=\kg\m^2\per\s^2\ampere^2=\weber\per\ampere=\volt\s\per\ampere=\ohm\s}{s}
    \end{formula}

\Subsection{other}
    \desc{Others}{}{}
    \desc[german]{Sonstige}{}{}
    \begin{formula}{area}
        \desc{Area}{}{}
        \desc[german]{Fläche}{}{}
        \quantity{A}{m^2}{v}
    \end{formula}
