deletions | additions       diff --git a/correlations.tex b/correlations.tex  index 575ad3f..912946d 100644  --- a/correlations.tex  +++ b/correlations.tex 
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\begin{equation}  G(\omega) = \frac{1}{\omega + \nabla^2/2 - V_\text{ion} - \Sigma(\omega)}.  \end{equation}  We have written the definition of $G(\omega)$ in atomic units for electrons in the lattice potential of the nuclear ions. The self-energy $\Sigma(\omega)$ is generally frequency-dependent, and we have omitted arguments the argument  $\vec{r}$ from all quantities. The eigenenergies that are the result diagonalizing the Kohn-Sham hamiltonian $H_\text{KS} = -\frac{1}{2}\vec{\nabla}^2 + V_\text{KS}(\vec{r})$ lack the ability to capture the frequency-dependent effects of many-body interactions, and should not be interpreted as physical eigenvalues. Nevertheless, we often ignore formal justification and compute the Green's function using the Kohn-Sham solution anyway: \begin{equation}  G_\text{KS}(\omega) = \frac{1}{\omega - H_\text{KS}}.  \end{equation}