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| documentation:standard_operators:coulomb_repulsion [2017/02/27 13:30] – Maurits W. Haverkort | documentation:standard_operators:coulomb_repulsion [2017/02/27 13:38] – Maurits W. Haverkort | ||
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| - | Note that in the general case you need to sum over all possible permutations of $n_1l_1$, $n_2l_2$, $n_3l_3$ and $n_4l_4$. Permuting $n_1l_1$ with $n_2l_2$ and at the same time $n_3l_3$ with $n_4l_4$ will not change the value and if $n_1l_1$ is different from $n_2l_2$ and $n_3l_3$ is different from $n_4l_4$ one can add a factor of two. If one of them is the same a permutation will not lead to a new configuration and the factor of two disappears. If you just sum over all possible $n_il_i$ combinations things go right automatically. | + | Note that in the general case you need to sum over all possible permutations of $n_1l_1$, $n_2l_2$, $n_3l_3$ and $n_4l_4$. Permuting $n_1l_1$ with $n_2l_2$ and at the same time $n_3l_3$ with $n_4l_4$ will not change the value and form of the operator. If $n_1l_1$ is different from $n_2l_2$ and $n_3l_3$ is different from $n_4l_4$ one can add a factor of two in front of the operator and only add one of the permutations. If one of the $n_1l_1$ |
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