deletions | additions       diff --git a/2QEnergies.tex b/2QEnergies.tex  index 76af4ff..62f9231 100644  --- a/2QEnergies.tex  +++ b/2QEnergies.tex 
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\newcommand{\kket}[1]{\ensuremath{\left|#1\right\rangle\rangle}}  \newcommand{\braket}[2]{\ensuremath{\left\langle#1 \vphantom{#2}\right| \left. #2 \vphantom{#1}\right\rangle}}  \newcommand{\ketbra}[2]{\ensuremath{\left|#1\right\rangle \left\langle#2\right|}}  \newcommand{\disp}[1]{D(#1)} \newcommand{\ddag}[1]{D^{\dagger}(#1)}  \newcommand{\Abs}[1]{\ensuremath{|#1|}}  \newcommand{\Absq}[1]{\ensuremath{|#1|^2}} 
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H_{2q}=\hbar \frac{\omega_0}{2}\adag a + \hbar \frac{\omega_1}{2}\sigma^{(1)}_z + \frac{\omega_2}{2}\sigma^{(2)}_z + \hbar(\Gamma_1\sigma^{(1)}_x + \Gamma_2\sigma^{(2)}_x)(\adag + a)    \end{equation}  $\disp{e}$ $\ddag{e}$  $D(e)$ \end{document}