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American Journal of Physics

How Good is the Hartree-Fock Approximation

M. Moshińsky

Published Jan 1, 1968• 134 citations
Publisher

Abstract

The problem of two particles in a common harmonic oscillator potential interacting through harmonic oscillator forces is discussed from the standpoint of the Hartree-Fock approximation and compared with the exact solution.
DOI
10.1119/1.1974410

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The exactly soluble model, originally considered by Moshinsky, consisting of two spin-1/2 particles interacting through harmonic-oscillator forces and moving in a common harmonic-oscillator potential is extended to include the effects of an external electric field. We solve for the energy exactly, exactly in the Hartree–Fock approximation, and also compare to the results of Hartree–Fock perturbation theory. We find that the Hartree–Fock method yields the same result for the electric polarizability as the exact solution even though the field-independent part of the energy is not the same. However, when second-order Hartree–Fock perturbation theory is employed, the results for the polarizability can be substantially in error. Similar results obtain for the calculation of the matrix element for optical absorption in the dipole approximation.
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