commands.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  NEW COMMANDS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Operators
%
\newcommand\dif{\mathrm{d}}
\newcommand\grad{\boldsymbol{\nabla}}
\newcommand\diver{\boldsymbol{\nabla} \cdot}
\newcommand\curl{\boldsymbol{\nabla} \times}
\newcommand\laplace{\boldsymbol{\nabla}^{2}}
\newcommand\levi{\epsilon_{ijk}}
\newcommand\trace{\mathrm{Tr}}
%
\newcommand{\deriv}[2]{\frac{\mathrm{d} #1}{\mathrm{d} #2}}
\newcommand{\partialderiv}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\abssquare}[1]{\mathopen{}\left|#1\right|^{2}\mathclose{}}
%
% Vector: latin
%
\newcommand\avector{\mathbf{a}}
\newcommand\bvector{\mathbf{b}}
\newcommand\cvector{\mathbf{c}}
\newcommand\dvector{\mathbf{d}}
\newcommand\evector{\mathbf{e}}
\newcommand\fvector{\mathbf{f}}
\newcommand\gvector{\mathbf{g}}
\newcommand\hvector{\mathbf{h}}
\newcommand\ivector{\mathbf{i}}
\newcommand\jvector{\mathbf{j}}
\newcommand\kvector{\mathbf{k}}
\newcommand\lvector{\mathbf{l}}
\newcommand\mvector{\mathbf{m}}
\newcommand\nvector{\mathbf{n}}
\newcommand\ovector{\mathbf{o}}
\newcommand\pvector{\mathbf{p}}
\newcommand\qvector{\mathbf{q}}
\newcommand\rvector{\mathbf{r}}
\newcommand\svector{\mathbf{s}}
\newcommand\tvector{\mathbf{t}}
\newcommand\uvector{\mathbf{u}}
\newcommand\vvector{\mathbf{v}}
\newcommand\wvector{\mathbf{w}}
\newcommand\xvector{\mathbf{x}}
\newcommand\yvector{\mathbf{y}}
\newcommand\zvector{\mathbf{z}}
%
\newcommand\Avector{\mathbf{A}}
\newcommand\Bvector{\mathbf{B}}
\newcommand\Cvector{\mathbf{C}}
\newcommand\Dvector{\mathbf{D}}
\newcommand\Evector{\mathbf{E}}
\newcommand\Fvector{\mathbf{F}}
\newcommand\Gvector{\mathbf{G}}
\newcommand\Hvector{\mathbf{H}}
\newcommand\Ivector{\mathbf{I}}
\newcommand\Jvector{\mathbf{J}}
\newcommand\Kvector{\mathbf{K}}
\newcommand\Lvector{\mathbf{L}}
\newcommand\Mvector{\mathbf{M}}
\newcommand\Nvector{\mathbf{N}}
\newcommand\Ovector{\mathbf{O}}
\newcommand\Pvector{\mathbf{P}}
\newcommand\Qvector{\mathbf{Q}}
\newcommand\Rvector{\mathbf{R}}
\newcommand\Svector{\mathbf{S}}
\newcommand\Tvector{\mathbf{T}}
\newcommand\Uvector{\mathbf{U}}
\newcommand\Vvector{\mathbf{V}}
\newcommand\Wvector{\mathbf{W}}
\newcommand\Xvector{\mathbf{X}}
\newcommand\Yvector{\mathbf{Y}}
\newcommand\Zvector{\mathbf{Z}}
%
% Vectors: greek
%
\newcommand\alfvec{\boldsymbol{\alpha}}
\newcommand\betvec{\boldsymbol{\beta}}
\newcommand\gamvec{\boldsymbol{\gamma}}
\newcommand\delvec{\boldsymbol{\delta}}
\newcommand\epsvec{\boldsymbol{\epsilon}}
\newcommand\zetvec{\boldsymbol{\zeta}}
\newcommand\etavec{\boldsymbol{\eta}}
\newcommand\thetvec{\boldsymbol{\theta}}
\newcommand\iotvec{\boldsymbol{\iota}}
\newcommand\kapvec{\boldsymbol{\kappa}}
\newcommand\lamvec{\boldsymbol{\lambda}}
\newcommand\muvec{\boldsymbol{\mu}}
\newcommand\nuvec{\boldsymbol{\nu}}
\newcommand\xivec{\boldsymbol{\xi}}
\newcommand\pivec{\boldsymbol{\pi}}
\newcommand\rhovec{\boldsymbol{\rho}}
\newcommand\sigvec{\boldsymbol{\sigma}}
\newcommand\tauvec{\boldsymbol{\tau}}
\newcommand\upsvec{\boldsymbol{\upsilon}}
\newcommand\phivec{\boldsymbol{\phi}}
\newcommand\chivec{\boldsymbol{\chi}}
\newcommand\psivec{\boldsymbol{\psi}}
\newcommand\omvec{\boldsymbol{\omega}}
%
\newcommand\Gamvec{\boldsymbol{\Gamma}}
\newcommand\Delvec{\boldsymbol{\Delta}}
\newcommand\Thetvec{\boldsymbol{\Theta}}
\newcommand\Lamvec{\boldsymbol{\Lambda}}
\newcommand\Xivec{\boldsymbol{\Xi}}
\newcommand\Pivec{\boldsymbol{\Pi}}
\newcommand\Sigvec{\boldsymbol{\Sigma}}
\newcommand\Upsvec{\boldsymbol{\Upsilon}}
\newcommand\Phivec{\boldsymbol{\Phi}}
\newcommand\Psivec{\boldsymbol{\Psi}}
\newcommand\Omvec{\boldsymbol{\Omega}}
%
% Unit vectors: latin
%
\newcommand\aunit{\widehat{\mathbf{a}}}
\newcommand\bunit{\widehat{\mathbf{b}}}
\newcommand\cunit{\widehat{\mathbf{c}}}
\newcommand\dunit{\widehat{\mathbf{d}}}
\newcommand\eunit{\widehat{\mathbf{e}}}
\newcommand\funit{\widehat{\mathbf{f}}}
\newcommand\gunit{\widehat{\mathbf{g}}}
\newcommand\hunit{\widehat{\mathbf{h}}}
\newcommand\iunit{\widehat{\mathbf{i}}}
\newcommand\junit{\widehat{\mathbf{j}}}
\newcommand\kunit{\widehat{\mathbf{k}}}
\newcommand\lunit{\widehat{\mathbf{l}}}
\newcommand\munit{\widehat{\mathbf{m}}}
\newcommand\nunit{\widehat{\mathbf{n}}}
\newcommand\ounit{\widehat{\mathbf{o}}}
\newcommand\punit{\widehat{\mathbf{p}}}
\newcommand\qunit{\widehat{\mathbf{q}}}
\newcommand\runit{\widehat{\mathbf{r}}}
\newcommand\sunit{\widehat{\mathbf{s}}}
\newcommand\tunit{\widehat{\mathbf{t}}}
\newcommand\uunit{\widehat{\mathbf{u}}}
\newcommand\vunit{\widehat{\mathbf{v}}}
\newcommand\wunit{\widehat{\mathbf{w}}}
\newcommand\xunit{\widehat{\mathbf{x}}}
\newcommand\yunit{\widehat{\mathbf{y}}}
\newcommand\zunit{\widehat{\mathbf{z}}}
%
\newcommand\Aunit{\widehat{\mathbf{A}}}
\newcommand\Bunit{\widehat{\mathbf{B}}}
\newcommand\Cunit{\widehat{\mathbf{C}}}
\newcommand\Dunit{\widehat{\mathbf{D}}}
\newcommand\Eunit{\widehat{\mathbf{E}}}
\newcommand\Funit{\widehat{\mathbf{F}}}
\newcommand\Gunit{\widehat{\mathbf{G}}}
\newcommand\Hunit{\widehat{\mathbf{H}}}
\newcommand\Iunit{\widehat{\mathbf{I}}}
\newcommand\Junit{\widehat{\mathbf{J}}}
\newcommand\Kunit{\widehat{\mathbf{K}}}
\newcommand\Lunit{\widehat{\mathbf{L}}}
\newcommand\Munit{\widehat{\mathbf{M}}}
\newcommand\Nunit{\widehat{\mathbf{N}}}
\newcommand\Ounit{\widehat{\mathbf{O}}}
\newcommand\Punit{\widehat{\mathbf{P}}}
\newcommand\Qunit{\widehat{\mathbf{Q}}}
\newcommand\Runit{\widehat{\mathbf{R}}}
\newcommand\Sunit{\widehat{\mathbf{S}}}
\newcommand\Tunit{\widehat{\mathbf{T}}}
\newcommand\Uunit{\widehat{\mathbf{U}}}
\newcommand\Vunit{\widehat{\mathbf{V}}}
\newcommand\Wunit{\widehat{\mathbf{W}}}
\newcommand\Xunit{\widehat{\mathbf{X}}}
\newcommand\Yunit{\widehat{\mathbf{Y}}}
\newcommand\Zunit{\widehat{\mathbf{Z}}}
%
% Unit vectors: greek
%
\newcommand\alfunit{\widehat{\boldsymbol{\alpha}}}
\newcommand\betunit{\widehat{\boldsymbol{\beta}}}
\newcommand\gamunit{\widehat{}\boldsymbol{\gamma}}
\newcommand\delunit{\widehat{\boldsymbol{\delta}}}
\newcommand\epsunit{\widehat{\boldsymbol{\epsilon}}}
\newcommand\zetunit{\widehat{\boldsymbol{\zeta}}}
\newcommand\etaunit{\widehat{\boldsymbol{\eta}}}
\newcommand\thetunit{\widehat{\boldsymbol{\theta}}}
\newcommand\iotunit{\widehat{\boldsymbol{\iota}}}
\newcommand\kapunit{\widehat{\boldsymbol{\kappa}}}
\newcommand\lamunit{\widehat{\boldsymbol{\lambda}}}
\newcommand\muunit{\widehat{\boldsymbol{\mu}}}
\newcommand\nuunit{\widehat{\boldsymbol{\nu}}}
\newcommand\xiunit{\widehat{\boldsymbol{\xi}}}
\newcommand\piunit{\widehat{\boldsymbol{\pi}}}
\newcommand\rhounit{\widehat{\boldsymbol{\rho}}}
\newcommand\sigunit{\widehat{\boldsymbol{\sigma}}}
\newcommand\tauunit{\widehat{\boldsymbol{\tau}}}
\newcommand\upsunit{\widehat{\boldsymbol{\upsilon}}}
\newcommand\phiunit{\widehat{\boldsymbol{\phi}}}
\newcommand\chiunit{\widehat{\boldsymbol{\chi}}}
\newcommand\psiunit{\widehat{\boldsymbol{\psi}}}
\newcommand\omunit{\widehat{\boldsymbol{\omega}}}
%
\newcommand\Gamunit{\widehat{\boldsymbol{\Gamma}}}
\newcommand\Delunit{\widehat{\boldsymbol{\Delta}}}
\newcommand\Thetunit{\widehat{\boldsymbol{\Theta}}}
\newcommand\Lamunit{\widehat{\boldsymbol{\Lambda}}}
\newcommand\Xiunit{\widehat{\boldsymbol{\Xi}}}
\newcommand\Piunit{\widehat{\boldsymbol{\Pi}}}
\newcommand\Sigunit{\widehat{\boldsymbol{\Sigma}}}
\newcommand\Upsunit{\widehat{\boldsymbol{\Upsilon}}}
\newcommand\Phiunit{\widehat{\boldsymbol{\Phi}}}
\newcommand\Psiunit{\widehat{\boldsymbol{\Psi}}}
\newcommand\Omunit{\widehat{\boldsymbol{\Omega}}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Roman fonts
%
\newcommand\arm{\mathrm{a}}
\newcommand\brm{\mathrm{b}}
\newcommand\crm{\mathrm{c}}
\newcommand\drm{\mathrm{d}}
\newcommand\erm{\mathrm{e}}
\newcommand\frm{\mathrm{f}}
\newcommand\grm{\mathrm{g}}
\newcommand\hrm{\mathrm{h}}
\newcommand\irm{\mathrm{i}}
\newcommand\jrm{\mathrm{j}}
\newcommand\krm{\mathrm{k}}
\newcommand\lrm{\mathrm{l}}
\newcommand\mrm{\mathrm{m}}
\newcommand\nrm{\mathrm{n}}
\newcommand\orm{\mathrm{o}}
\newcommand\prm{\mathrm{p}}
\newcommand\qrm{\mathrm{q}}
\newcommand\rrm{\mathrm{r}}
\newcommand\srm{\mathrm{s}}
\newcommand\trm{\mathrm{t}}
\newcommand\urm{\mathrm{u}}
\newcommand\vrm{\mathrm{v}}
\newcommand\wrm{\mathrm{w}}
\newcommand\xrm{\mathrm{x}}
\newcommand\yrm{\mathrm{y}}
\newcommand\zrm{\mathrm{z}}
%
\newcommand\Arm{\mathrm{A}}
\newcommand\Brm{\mathrm{B}}
\newcommand\Crm{\mathrm{C}}
\newcommand\Drm{\mathrm{D}}
\newcommand\Erm{\mathrm{E}}
\newcommand\Frm{\mathrm{F}}
\newcommand\Grm{\mathrm{G}}
\newcommand\Hrm{\mathrm{H}}
\newcommand\Irm{\mathrm{I}}
\newcommand\Jrm{\mathrm{J}}
\newcommand\Krm{\mathrm{K}}
\newcommand\Lrm{\mathrm{L}}
\newcommand\Mrm{\mathrm{M}}
\newcommand\Nrm{\mathrm{N}}
\newcommand\Orm{\mathrm{O}}
\newcommand\Prm{\mathrm{P}}
\newcommand\Qrm{\mathrm{Q}}
\newcommand\Rrm{\mathrm{R}}
\newcommand\Srm{\mathrm{S}}
\newcommand\Trm{\mathrm{T}}
\newcommand\Urm{\mathrm{U}}
\newcommand\Vrm{\mathrm{V}}
\newcommand\Wrm{\mathrm{W}}
\newcommand\Xrm{\mathrm{X}}
\newcommand\Yrm{\mathrm{Y}}
\newcommand\Zrm{\mathrm{Z}}
%
\newcommand\oned{\mathrm{1D}}
\newcommand\twod{\mathrm{2D}}
\newcommand\threed{\mathrm{3D}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Complex analysis
%
\newcommand\ci{\mathrm{i}}
\newcommand\real{\mathrm{Re}}
\newcommand\imag{\mathrm{Im}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Response functions etc
%
\newcommand\homega{\hbar \omega}
\newcommand\hgamma{\hbar \gamma}
\newcommand\omnought{\omega_{0}}
\newcommand\homnought{\hbar \omega_{0}}
%
\newcommand\lambdap{\lambda_{\mathrm{p}}}
\newcommand\omegap{\omega_{\mathrm{p}}}
\newcommand\homegap{\hbar \omega_{\mathrm{p}}}
\newcommand\gammap{\gamma_{\mathrm{p}}}
\newcommand\hgammap{\hbar \gamma_{\mathrm{p}}}
%
\newcommand\omegax{\omega_{\mathrm{x}}}
\newcommand\homegax{\hbar \omega_{\mathrm{x}}}
\newcommand\gammax{\gamma_{\mathrm{x}}}
\newcommand\hgammax{\hbar \gamma_{\mathrm{x}}}
%
\newcommand\omegaplus{\omega_{+}}
\newcommand\homegaplus{\hbar \omega_{+}}
\newcommand\omegamin{\omega_{-}}
\newcommand\homegamin{\hbar \omega_{-}}
\newcommand\homegadif{\hbar \Omega}
%
\newcommand\vfermi{\nu_{\mathrm{F}}}
\newcommand\vel{\nu_{\mathrm{el}}}
\newcommand\velvec{\boldsymbol{\nu}_{\mathrm{el}}}
\newcommand\mel{m_{\mathrm{e}}}
\newcommand\rwigner{r_{\mathrm{s}}}
%
\newcommand\dperp{d_{\perp}}
\newcommand\dpar{d_{\parallel}}
%
\newcommand\eps{\varepsilon}
\newcommand\epsone{\varepsilon_{1}}
\newcommand\epstwo{\varepsilon_{2}}
\newcommand\epsnought{\varepsilon_{0}}
\newcommand\epsinf{\varepsilon_{\infty}}
\newcommand\epsinfexp{\varepsilon_{\infty,\mathrm{exp}}}
\newcommand\epseff{\varepsilon_{\mathrm{eff}}}
\newcommand\etensor{\boldsymbol{\varepsilon}}
%
\newcommand\muone{\mu_{1}}
\newcommand\mutwo{\mu_{2}}
\newcommand\munought{\mu_{0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Scattering
%
% cross sections
%
\newcommand\sigmaext{\sigma_{\mathrm{ext}}}
\newcommand\sigmascat{\sigma_{\mathrm{scat}}}
\newcommand\sigmaabs{\sigma_{\mathrm{abs}}}
\newcommand\sigmageom{\sigma_{\mathrm{geom}}}
%
% angles of incidence, reflection, refraction, dipoles
%
\newcommand\thetai{\theta_{\mathrm{i}}}
\newcommand\thetar{\theta_{\mathrm{r}}}
\newcommand\thetat{\theta_{\mathrm{t}}}
\newcommand\thetad{\theta_{\mathrm{d}}}
\newcommand\phid{\phi_{\mathrm{d}}}
%
% Bessel functions
%
\newcommand\jell{j_{\ell}}
\newcommand\jellc{j_{\ell}^{\ast}}
\newcommand\jellp{j_{\ell}^{'}}
\newcommand\nell{n_{\ell}}
\newcommand\nellp{n_{\ell}^{'}}
\newcommand\hell{h_{\ell}^{+}}
\newcommand\hellc{h_{\ell}^{+\ast}}
\newcommand\hellp{h_{\ell}^{+'}}
\newcommand\Jderiv{\mathrm{J}_{\ell}}
\newcommand\Jderivc{\mathrm{J}_{\ell}^{\ast}}
\newcommand\Hderiv{\mathrm{H}_{\ell}}
\newcommand\Hderivc{\mathrm{H}_{\ell}^{\ast}}
%
% spherical harmonics
%
\newcommand\lmax{\ell_{\mathrm{max}}}
\newcommand\lm{\ell m}
\newcommand\lmprime{\ell' m'}
\newcommand\lmprimes{\ell'' m''}
\newcommand\suml{\sum_{\ell = 1}^{+\infty}}
\newcommand\sumlm{\sum_{\ell = 1}^{+\infty} \sum_{m = -\ell}^{\ell} }
\newcommand\sumlmprime{\sum_{\ell' m'}}
\newcommand\ylm{Y_{\ell m}}
\newcommand\ylmast{Y_{\ell m}^{\ast}}
\newcommand\ylmprime{Y_{\ell' m'}}
\newcommand\ylmprimeast{Y_{\ell' m'}^{\ast}}
\newcommand\xlm{\mathbf{X}_{\ell m}}
\newcommand\xlmast{\mathbf{X}_{\ell m}^{\ast}}
\newcommand\xlmprime{\mathbf{X}_{\ell' m'}}
\newcommand\xlmprimeast{\mathbf{X}_{\ell' m'}^{\ast}}
%
% Incoming and scattering fields & amplitudes
%
\newcommand\escat{\mathbf{E}_{\mathrm{sc}}}
\newcommand\ein{\mathbf{E}_{\mathrm{in}}}
\newcommand\enought{\mathbf{E}_{0}}
%
\newcommand\aelm{a_{E\ell m}}
\newcommand\ahlm{a_{H\ell m}}
\newcommand\aelmprimeast{a_{E\ell' m'}^{\ast}}
\newcommand\ahlmprimeast{a_{H\ell' m'}^{\ast}}
\newcommand\aelmo{a_{E\ell m}^{0}}
\newcommand\ahlmo{a_{H\ell m}^{0}}
\newcommand\aelmin{a_{E\ell m}^{\mathrm{in}}}
\newcommand\allmin{a_{L\ell m}^{\mathrm{in}}}
\newcommand\ahlmin{a_{H\ell m}^{\mathrm{in}}}
\newcommand\aelmp{a_{E\ell m}^{+}}
\newcommand\ahlmp{a_{H\ell m}^{+}}
\newcommand\aelme{a_{E\ell m}^{e}}
\newcommand\ahlme{a_{H\ell m}^{e}}
\newcommand\aelmpast{a_{E\ell m}^{+\ast}}
\newcommand\ahlmpast{a_{H\ell m}^{+\ast}}
\newcommand\aelmpprimeast{a_{E\ell' m'}^{+\ast}}
\newcommand\ahlmpprimeast{a_{H\ell' m'}^{+\ast}}
\newcommand\aelminone{a_{E\ell m}^{1\mathrm{in}}}
\newcommand\ahlminone{a_{H\ell m}^{1\mathrm{in}}}
\newcommand\aelminoneast{a_{E\ell m}^{1\mathrm{in} \ast}}
\newcommand\ahlminoneast{a_{H\ell m}^{1\mathrm{in} \ast}}
\newcommand\aelminoneprimeast{a_{E\ell' m'}^{1\mathrm{in} \ast}}
\newcommand\ahlminoneprimeast{a_{H\ell' m'}^{1\mathrm{in} \ast}}
\newcommand\aelmintwo{a_{E\ell m}^{2\mathrm{in}}}
\newcommand\ahlmintwo{a_{H\ell m}^{2\mathrm{in}}}
\newcommand\allmintwo{a_{L\ell m}^{2\mathrm{in}}}
\newcommand\aelmptwo{a_{E\ell m}^{2+}}
\newcommand\ahlmptwo{a_{H\ell m}^{2+}}
\newcommand\allmptwo{a_{L\ell m}^{2+}}
%
\newcommand\delmo{d_{E\ell m}^{0}}
\newcommand\dhlmo{d_{H\ell m}^{0}}
\newcommand\delmoast{d_{E\ell m}^{0\ast}}
\newcommand\dhlmoast{d_{H\ell m}^{0\ast}}
\newcommand\delmoprimeast{d_{E\ell' m'}^{0\ast}}
\newcommand\dhlmoprimeast{d_{H\ell' m'}^{0\ast}}
\newcommand\delmp{d_{E\ell m}^{+}}
\newcommand\dhlmp{d_{H\ell m}^{+}}
\newcommand\delmpast{d_{E\ell m}^{+\ast}}
\newcommand\dhlmpast{d_{H\ell m}^{+\ast}}
\newcommand\delmpprimeast{d_{E\ell' m'}^{+\ast}}
\newcommand\dhlmpprimeast{d_{H\ell' m'}^{+\ast}}
%
% Dipoles
%
\newcommand\pd{\mathbf{p}_{\mathrm{d}}}
\newcommand\ppd{p_{\mathrm{d}}}
\newcommand\rd{\mathbf{r}_{\mathrm{d}}}
\newcommand\rrd{r_{\mathrm{d}}}
%
\newcommand\omegaem{\omega_{\mathrm{em}}}
\newcommand\homegaem{\hbar \omega_{\mathrm{em}}}
\newcommand\gammaem{\gamma_{\mathrm{em}}}
\newcommand\hgammaem{\habr \gamma_{\mathrm{em}}}
\newcommand\omegaexc{\omega_{\mathrm{exc}}}
\newcommand\homegaexc{\hbar \omega_{\mathrm{exc}}}
\newcommand\gammaexc{\gamma_{\mathrm{exc}}}
\newcommand\hgammaexc{\habr \gamma_{\mathrm{exc}}}
%
\newcommand\gammad{\gamma_{\mathrm{d}}}
\newcommand\gammar{\gamma_{\mathrm{r}}}
\newcommand\gammanr{\gamma_{\mathrm{nr}}}
\newcommand\gammaemnorm{\gamma_{\mathrm{em}}/\gamma_{\mathrm{em}}^{0}}
\newcommand\gammaexcnorm{\gamma_{\mathrm{exc}}/\gamma_{\mathrm{exc}}^{0}}
\newcommand\yieldnorm{q/q^{0}}
\newcommand\taur{\tau_{\mathrm{r}}}
\newcommand\taunr{\tau_{\mathrm{nr}}}
\newcommand\Prad{P_{\mathrm{r}}}
\newcommand\Pnr{P_{\mathrm{nr}}}
\newcommand\Pnought{P_{0}}
%
%
% parallel vectors
%
\newcommand\kparallel{\mathbf{k}_{\parallel}}
\newcommand\qparallel{\mathbf{q}_{\parallel}}
\newcommand\rparallel{\mathbf{r}_{\parallel}}
%
% 
% Quantum mechanics
%
\newcommand\hbarkin{-\frac{\hbar^{2}}{2m}}
\newcommand\coulomb{\frac{e^{2}}{4 \pi \epsnought}}
\newcommand\hamilton{\mathcal{H}}
\newcommand\potential{\mathcal{V}}
\newcommand\parity{\mathcal{P}}
\newcommand\pt{\mathcal{PT}}
\newcommand\rotate{\mathcal{R}}
\newcommand\Lsq{\hat{L}^{2}}
\newcommand\Lsqdag{\hat{L}^{2\dagger}}
\newcommand\Lz{\hat{L}_{z}}
\newcommand\Li{\hat{L}_{i}}
\newcommand\Lplus{\hat{L}_{+}}
\newcommand\Lmin{\hat{L}_{-}}
\newcommand\Lpm{\hat{L}_{\pm}}
%
\newcommand\ahat{\hat{\mathbf{a}}}
\newcommand\ahatdag{\hat{\mathbf{a}}^{\dag}}
\newcommand\bhat{\hat{\mathbf{b}}}
\newcommand\bhatdag{\hat{\mathbf{b}}^{\dag}}
\newcommand\fhat{\hat{\mathbf{f}}}
\newcommand\fhatdag{\hat{\mathbf{f}}^{\dag}}
%
\newcommand\upket{\ket{\uparrow}}
\newcommand\dket{\ket{\downarrow}}
\newcommand\upbra{\bra{\uparrow}}
\newcommand\dbra{\bra{\downarrow}}
\newcommand{\upupket}{\ket{\uparrow \uparrow}}
\newcommand{\ddket}{\ket{\downarrow \downarrow}}
\newcommand{\updket}{\ket{\uparrow \downarrow}}
\newcommand{\dupket}{\ket{\downarrow \uparrow}}
\newcommand{\updbra}{\bra{\uparrow \downarrow}}
\newcommand{\dupbra}{\bra{\downarrow \uparrow}}
%
%
% Electrostatics
%
\newcommand\kel{\frac{1}{4 \pi \epsnought}}
\newcommand\fourpie{4 \pi \epsnought}
\newcommand\mufourpi{\frac{\munought}{4 \pi}}
%
% Statistical physics
%
\newcommand\kbt{k_{\mathrm{B}}T}

%My own vectors

\newcommand{\nullvector}{\mathbf{0}}

%position vector -> r in bold
\newcommand{\br}{\mathbf{r}}
\newcommand{\bk}{\mathbf{k}}
\newcommand{\bq}{\mathbf{q}}
\newcommand{\bp}{\mathbf{p}}

%Commands for tikz Feynamn diagrams
\tikzset{
    every node/.append style={font=\small},
    every edge/.append style={thick},
    arrow/.style={thick, shorten >=5pt,shorten <=5pt,->},
    photon/.style={dashed,dash phase=3pt,postaction={decorate},
        decoration={markings,mark=at position .55 with {\arrow[]{latex}}}},
    electron/.style={postaction={decorate},
        decoration={markings,mark=at position .55 with {\arrow[]{latex}}}},
    fullprop/.style={double,postaction={decorate},
        decoration={markings,mark=at position .55 with {\arrow[]{latex}}}},
    bareprop/.style={postaction={decorate},
        decoration={markings,mark=at position .55 with {\arrow[]{latex}}}},
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% END OF NEW COMMANDS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%