- #1
cire
I'm trying to understand the Hartree-Fock mathematical formulation I understand the Coulomb operator, but I don't understand the exchange operator:
[tex]
\hat{K_{j}}[\Psi](\textbf{x})=\Phi_{j}(\textbf{x})\int
d\textbf{x}'\frac{\Phi_{j}^{*}(\textbf{x}')\Psi(\textbf{x}')}{|\textbf{r}-\textbf{r}'|}[/tex]
Can anyone explain me why this operator is like this. I understand that it is the interaction of the j-th electron with the electrons' cloud but... how it come to be like that
thanks in advance
[tex]
\hat{K_{j}}[\Psi](\textbf{x})=\Phi_{j}(\textbf{x})\int
d\textbf{x}'\frac{\Phi_{j}^{*}(\textbf{x}')\Psi(\textbf{x}')}{|\textbf{r}-\textbf{r}'|}[/tex]
Can anyone explain me why this operator is like this. I understand that it is the interaction of the j-th electron with the electrons' cloud but... how it come to be like that
thanks in advance