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final versions for 2021

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{split}
\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{2 \sum_m \violet{\ERI{pq}{m}} \violet{\ERI{rs}{m}}
@ -585,7 +585,7 @@ decoration={snake,
\orange{\bY{m}{\RPA}} \\
\end{pmatrix}
=
\orange{\Om{m}{}}
\orange{\Om{m}{\RPA}}
\begin{pmatrix}
\orange{\bX{m}{\RPA}} \\
\orange{\bY{m}{\RPA}} \\
@ -609,7 +609,7 @@ decoration={snake,
\end{block}
\begin{block}{Tamm-Dancoff approximation (TDA)}
\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{block}
\end{frame}
@ -1013,7 +1013,7 @@ decoration={snake,
\boxed{\begin{pmatrix}
\red{\bA{}{}} & \orange{\bB{}{}}
\\
\orange{-\bA{}{}} & \red{-\bB{}{}}
\orange{-\bB{}{}} & \red{-\bA{}{}}
\end{pmatrix}
\cdot
\begin{pmatrix}
@ -1109,7 +1109,7 @@ decoration={snake,
\boxed{\begin{pmatrix}
\red{\bA{}{}} & \orange{\bB{}{}}
\\
\orange{-\bA{}{}} & \red{-\bB{}{}}
\orange{-\bB{}{}} & \red{-\bA{}{}}
\end{pmatrix}
\cdot
\begin{pmatrix}
@ -1339,9 +1339,9 @@ decoration={snake,
\btB{}{} & \btA{}{}
\end{pmatrix}
\qquad
\tA{ia,jb}{} = 2\la\ERI{ia}{bj}
\tA{ia,jb}{} = 2\ERI{ia}{bj}
\qquad
\tB{ia,jb}{} = 2\la\ERI{ia}{jb}
\tB{ia,jb}{} = 2\ERI{ia}{jb}
\end{equation}
\end{block}
\begin{block}{Correlation part of the two-particle density matrix}