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HartreeFock exchange operator 
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#1
Sep1305, 08:31 PM

P: n/a

I'm trying to understand the HartreeFock mathematical formulation I understand the Coulomb operator, but I dont 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 any one explain me why this operator is like this. I understand that it is the interaction of the jth electron with the electrons' cloud but... how it come to be like that thanks in advance 


#2
Sep1305, 09:46 PM

P: 243

I don't know anything about that formulation, but this book on Google Print might help:
Google Print You can't see all the relevant information, but I think it might help you understand where the idea's headed. 


#3
Sep2605, 08:47 AM

P: 1,235

I guess the integral on the rhs is simply the matrix element <jKphi> of the electrostatic potential. Therefore Kphi> is indeed given by j><jKph> .



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