deletions | additions       diff --git a/Sternheimer.tex b/Sternheimer.tex  index c2edccc..39e023c 100644  --- a/Sternheimer.tex  +++ b/Sternheimer.tex 
...
\begin{equation}  \label{eq:psi}  \bar{\varphi}_{k}(\vec r, t) =  e^{-{\mathrm{i}}\left(\epsilon_k+\lambda\delta\epsilon_{k}\right){t}}\Big[ \mathrm{e}^{-{\mathrm{i}}\left(\epsilon_k+\lambda\delta\epsilon_{k}\right){t}}\Big[  \varphi_k(\vec r) + \frac\lambda2e^{{\mathrm{i}}\omega{t}} \frac\lambda2\mathrm{e}^{{\mathrm{i}}\omega{t}}  \delta\varphi_{k}(\vec r, \omega) +\frac\lambda2{e^{-\mathrm{i}\omega{t}}} +\frac\lambda2{\mathrm{e}^{-\mathrm{i}\omega{t}}}  \delta\varphi_{k}(\vec r, -\omega)\Big] \,,  \end{equation}  %\end{multline}