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final versions for 2021

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This commit is contained in:
Pierre-Francois Loos 2021-06-09 09:01:13 +02:00
parent 159f5d0759
commit 29e346772e
1 changed files with 7 additions and 7 deletions
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14
2021/Lecture_2/ISTPC_Loos_2.tex
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@ -550,7 +550,7 @@ decoration={snake,
\begin{equation} \begin{equation}
\begin{split} \begin{split}
\highlight{W}_{pq,rs}(\yo) \highlight{W}_{pq,rs}(\yo)
& = \iint \MO{p}(\br_1) \MO{q}(\br_1) \highlight{W}_{pq,rs}(\br_1,\br_2;\yo) \MO{r}(\br_2) \MO{s}(\br_2) d\br_1 d\br_2 & = \iint \MO{p}(\br_1) \MO{q}(\br_1) \highlight{W}(\br_1,\br_2;\yo) \MO{r}(\br_2) \MO{s}(\br_2) d\br_1 d\br_2
\\ \\
& = \underbrace{\ERI{pq}{rs}}_{\text{(static) exchange part}} & = \underbrace{\ERI{pq}{rs}}_{\text{(static) exchange part}}
+ \underbrace{2 \sum_m \violet{\ERI{pq}{m}} \violet{\ERI{rs}{m}} + \underbrace{2 \sum_m \violet{\ERI{pq}{m}} \violet{\ERI{rs}{m}}
@ -585,7 +585,7 @@ decoration={snake,
\orange{\bY{m}{\RPA}} \\ \orange{\bY{m}{\RPA}} \\
\end{pmatrix} \end{pmatrix}
= =
\orange{\Om{m}{}} \orange{\Om{m}{\RPA}}
\begin{pmatrix} \begin{pmatrix}
\orange{\bX{m}{\RPA}} \\ \orange{\bX{m}{\RPA}} \\
\orange{\bY{m}{\RPA}} \\ \orange{\bY{m}{\RPA}} \\
@ -609,7 +609,7 @@ decoration={snake,
\end{block} \end{block}
\begin{block}{Tamm-Dancoff approximation (TDA)} \begin{block}{Tamm-Dancoff approximation (TDA)}
\begin{equation} \begin{equation}
\bB{}{} = \bO \quad \Rightarrow \quad \bA{}{} \cdot \bX{m}{} = \Om{m}{\TDA} \bX{m}{} \bB{}{} = \bO \quad \Rightarrow \quad \bA{}{} \cdot \orange{\bX{m}{}} = \orange{\Om{m}{\TDA} \bX{m}{}}
\end{equation} \end{equation}
\end{block} \end{block}
\end{frame} \end{frame}
@ -1013,7 +1013,7 @@ decoration={snake,
\boxed{\begin{pmatrix} \boxed{\begin{pmatrix}
\red{\bA{}{}} & \orange{\bB{}{}} \red{\bA{}{}} & \orange{\bB{}{}}
\\ \\
\orange{-\bA{}{}} & \red{-\bB{}{}} \orange{-\bB{}{}} & \red{-\bA{}{}}
\end{pmatrix} \end{pmatrix}
\cdot \cdot
\begin{pmatrix} \begin{pmatrix}
@ -1109,7 +1109,7 @@ decoration={snake,
\boxed{\begin{pmatrix} \boxed{\begin{pmatrix}
\red{\bA{}{}} & \orange{\bB{}{}} \red{\bA{}{}} & \orange{\bB{}{}}
\\ \\
\orange{-\bA{}{}} & \red{-\bB{}{}} \orange{-\bB{}{}} & \red{-\bA{}{}}
\end{pmatrix} \end{pmatrix}
\cdot \cdot
\begin{pmatrix} \begin{pmatrix}
@ -1339,9 +1339,9 @@ decoration={snake,
\btB{}{} & \btA{}{} \btB{}{} & \btA{}{}
\end{pmatrix} \end{pmatrix}
\qquad \qquad
\tA{ia,jb}{} = 2\la\ERI{ia}{bj} \tA{ia,jb}{} = 2\ERI{ia}{bj}
\qquad \qquad
\tB{ia,jb}{} = 2\la\ERI{ia}{jb} \tB{ia,jb}{} = 2\ERI{ia}{jb}
\end{equation} \end{equation}
\end{block} \end{block}
\begin{block}{Correlation part of the two-particle density matrix} \begin{block}{Correlation part of the two-particle density matrix}