ab_initio:交換相関ポテンシャル
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次のリビジョン | 前のリビジョン | ||
ab_initio:交換相関ポテンシャル [2020/08/17 15:41] – 作成 kimi | ab_initio:交換相関ポテンシャル [2022/08/23 13:34] (現在) – 外部編集 127.0.0.1 | ||
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行 3: | 行 3: | ||
二つの電子に対する波動関数を | 二つの電子に対する波動関数を | ||
- | < | + | $$ |
\Psi(q_1, q_2)=\frac{1}{\sqrt{2}}\left(\phi_a(q_1)\phi_b(q_2)-\phi_a(q_2)\phi_b(q_1)\right) | \Psi(q_1, q_2)=\frac{1}{\sqrt{2}}\left(\phi_a(q_1)\phi_b(q_2)-\phi_a(q_2)\phi_b(q_1)\right) | ||
- | </ | + | $$ |
- | < | + | $$ |
q_1 = (\vec{r_1}, \sigma_1)=(x_1, | q_1 = (\vec{r_1}, \sigma_1)=(x_1, | ||
- | </ | + | $$ |
- | < | + | $$ |
V(\vec{r_1}, | V(\vec{r_1}, | ||
- | </ | + | $$ |
- | < | + | $$ |
\langle\Psi|V|\Psi\rangle | \langle\Psi|V|\Psi\rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
=\frac{1}{2} | =\frac{1}{2} | ||
- | \langle | + | $$ |
+ | |||
+ | $$ | ||
\phi_a(q_1)\phi_b(q_2)-\phi_a(q_2)\phi_b(q_1) | \phi_a(q_1)\phi_b(q_2)-\phi_a(q_2)\phi_b(q_1) | ||
|V| | |V| | ||
\phi_a(q_1)\phi_b(q_2)-\phi_a(q_2)\phi_b(q_1) | \phi_a(q_1)\phi_b(q_2)-\phi_a(q_2)\phi_b(q_1) | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
=\frac{1}{2}\langle | =\frac{1}{2}\langle | ||
\phi_a(q_1)\phi_b(q_2) | \phi_a(q_1)\phi_b(q_2) | ||
行 33: | 行 35: | ||
\phi_a(q_1)\phi_b(q_2) | \phi_a(q_1)\phi_b(q_2) | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | |
+ | $$ | ||
-\frac{1}{2}\langle | -\frac{1}{2}\langle | ||
\phi_a(q_1)\phi_b(q_2) | \phi_a(q_1)\phi_b(q_2) | ||
行 40: | 行 43: | ||
\phi_a(q_2)\phi_b(q_1) | \phi_a(q_2)\phi_b(q_1) | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
-\frac{1}{2}\langle | -\frac{1}{2}\langle | ||
\phi_a(q_2)\phi_b(q_1) | \phi_a(q_2)\phi_b(q_1) | ||
行 47: | 行 50: | ||
\phi_a(q_1)\phi_b(q_2) | \phi_a(q_1)\phi_b(q_2) | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
+\frac{1}{2}\langle | +\frac{1}{2}\langle | ||
\phi_a(q_2)\phi_b(q_1) | \phi_a(q_2)\phi_b(q_1) | ||
行 54: | 行 57: | ||
\phi_a(q_2)\phi_b(q_1) | \phi_a(q_2)\phi_b(q_1) | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
=\frac{1}{2}\langle | =\frac{1}{2}\langle | ||
\phi_a(q)\phi_b(q' | \phi_a(q)\phi_b(q' | ||
行 62: | 行 65: | ||
\phi_a(q)\phi_b(q' | \phi_a(q)\phi_b(q' | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
-\frac{1}{2}\langle | -\frac{1}{2}\langle | ||
\phi_a(q)\phi_b(q' | \phi_a(q)\phi_b(q' | ||
行 69: | 行 72: | ||
\phi_a(q' | \phi_a(q' | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
-\frac{1}{2}\langle | -\frac{1}{2}\langle | ||
\phi_a(q)\phi_b(q' | \phi_a(q)\phi_b(q' | ||
行 76: | 行 79: | ||
\phi_a(q' | \phi_a(q' | ||
\rangle | \rangle | ||
- | </ | + | $$ |
- | < | + | $$ |
+\frac{1}{2}\langle | +\frac{1}{2}\langle | ||
\phi_a(q)\phi_b(q' | \phi_a(q)\phi_b(q' | ||
行 83: | 行 86: | ||
\phi_a(q)\phi_b(q' | \phi_a(q)\phi_b(q' | ||
\rangle | \rangle | ||
- | </ | + | $$ |
ab_initio/交換相関ポテンシャル.1597646488.txt.gz · 最終更新: 2022/08/23 13:34 (外部編集)