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Lecture 2 done

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Pierre-Francois Loos 2021-06-08 21:19:11 +02:00
parent 2fda251630
commit 159f5d0759
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2021/Lecture_2/ISTPC_Loos_2.tex
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@ -314,6 +314,7 @@ decoration={snake,
\item $i,j,k,l$ are \green{occupied orbitals} \item $i,j,k,l$ are \green{occupied orbitals}
\item $a,b,c,d$ are \alert{vacant orbitals} \item $a,b,c,d$ are \alert{vacant orbitals}
\item $p,q,r,s$ are \violet{arbitrary (occupied or vacant) orbitals} \item $p,q,r,s$ are \violet{arbitrary (occupied or vacant) orbitals}
\item $\mu,\nu,\lambda,\sigma$ are \purple{basis function indexes}
\bigskip \bigskip
\item $m$ indexes \purple{the $OV$ single excitations} ($i \to a$) \item $m$ indexes \purple{the $OV$ single excitations} ($i \to a$)
\end{itemize} \end{itemize}
@ -529,15 +530,15 @@ decoration={snake,
\end{block} \end{block}
\begin{block}{Polarizability} \begin{block}{Polarizability}
\begin{equation} \begin{equation}
P(\br_1,\br_2;\omega) = - \frac{i}{\pi} \int \blue{G}(\br_1,\br_2;\omega+\omega') \blue{G}(\br_1,\br_2;\omega') d\omega' P(\br_1,\br_2;\yo) = - \frac{i}{\pi} \int \blue{G}(\br_1,\br_2;\yo+\omega') \blue{G}(\br_1,\br_2;\omega') d\omega'
\end{equation} \end{equation}
\end{block} \end{block}
\begin{block}{Dielectric function and dynamically-screened Coulomb potential} \begin{block}{Dielectric function and dynamically-screened Coulomb potential}
\begin{equation} \begin{equation}
\epsilon(\br_1,\br_2;\omega) = \delta(\br_1 - \br_2) - \int \frac{P(\br_1,\br_3;\omega) }{\abs{\br_2 - \br_3}} d\br_3 \epsilon(\br_1,\br_2;\yo) = \delta(\br_1 - \br_2) - \int \frac{P(\br_1,\br_3;\yo) }{\abs{\br_2 - \br_3}} d\br_3
\end{equation} \end{equation}
\begin{equation} \begin{equation}
\highlight{W}(\br_1,\br_2;\omega) = \int \frac{\epsilon^{-1}(\br_1,\br_3;\omega) }{\abs{\br_2 - \br_3}} d\br_3 \highlight{W}(\br_1,\br_2;\yo) = \int \frac{\epsilon^{-1}(\br_1,\br_3;\yo) }{\abs{\br_2 - \br_3}} d\br_3
\end{equation} \end{equation}
\end{block} \end{block}
\end{frame} \end{frame}