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10.3: Correlation - conditional probability

Last updated

Sep 28, 2020
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- 10.2: Self-consistent fields
- 10.4: Lattice methods - Variational method by computer

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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.

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