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Chuck-Hou Yee edited correlations.tex
over 7 years ago
Commit id: e60f83e4b603a13f8ddbeaa77deed7ac6d04dc17
deletions | additions
diff --git a/correlations.tex b/correlations.tex
index 711c85e..f57c032 100644
--- a/correlations.tex
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\begin{equation}
G(\omega) = \frac{1}{\omega + \nabla^2/2 + \mu - V_\text{ion} - V_\text{H} - \Sigma(\omega)}.
\end{equation}
We have used atomic units, included a chemical potential $\mu$, and separated the large Hartree component out from the self-energy $\Sigma$. The self-energy is generally frequency-dependent, and we have omitted the argument $\vec{r}$ from all quantities. The eigenenergies that are the result diagonalizing the Kohn-Sham hamiltonian $H_\text{KS} = -\frac{1}{2}\vec{\nabla}^2 - \mu + V_\text{KS}(\vec{r})$ does not capture the frequency-dependent effects of many-body interactions, and should not be interpreted as physical eigenvalues. Nevertheless, we often ignore
the lack of 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}