10.3: Correlation - conditional probability

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Hartree-Fock theory does not properly describe correlation. In the Copenhagen Interpretation, the squared modulus of the wavefunction gives the probability of finding a particle in a given place. The many-body wave function gives the N-particle distribution function, i.e. \(|\Phi (r_1, ..., r_N )|^2\) is the probability density that particle 1 is at \({\bf r_1}, ...,\) and particle N is at \({\bf r_N}\).

But when trying to work out the interaction between electrons, what we want to know is the probability of finding an electron at \({\bf r}\), given the positions of all the other electrons \( {\bf \{r_i \}}\). This implies that the electron behaves quantum mechanically when we evaluate its wavefunction, but as a classical point particle when it contributes to the potential seen by the other electrons.