deletions | additions       diff --git a/Complex DFT.tex b/Complex DFT.tex  index d9b7a14..99ffd52 100644  --- a/Complex DFT.tex  +++ b/Complex DFT.tex 
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The defining characteristic of a resonant state, often called a Siegert  state\cite{PhysRev.56.750}, state~\cite{PhysRev.56.750},  is that it has an outgoing component but not an incoming one.  They can be determined by solving the  time-independent Schrödinger 
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of every term by $\theta$ in the complex plane.  The DFT energy functional becomes  %  \newcommand{\rprime}[0]{\vec r'}  \begin{align} \newcommand{\rprime}[0]{\vec{r}'}  \begin{multline}  E_\theta &= =  \ee^{-\ii2\theta} \sum_n \int\dee\vec r\, \varphi_{\theta n}(\vec r) \left(-\frac12 \nabla^2\right)  \varphi_{\theta n}(\vec r)\\  + \ee^{-\ii\theta} \frac12 
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\frac{n_\theta(\vec r)n_\theta(\rprime)}{\Vert\vec r - \rprime\Vert}\nonumber\\  &\quad+ E_\xc^\theta[n_\theta]  + \int\dee \vec r\, v_{\mathrm{ext}}(\vec r \ee^{\ii \theta}) n_\theta(\vec r)\ ,  \end{align} \end{multline}  %  with the, now complex, electron density  \begin{align}