Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock Approximation

Abstract

A system of $N$ antisymmetric particles, moving under the influence of a fixed potential and their mutual many-particle interactions, is investigated in the ordinary Hartree-Fock scheme, having the total wave function approximated by a single Slater determinant. It is shown that all the density matrices of various orders, the wave function, and the entire physical situation depends only on a fundamental invariant $\rho (x_1, x_2)$, which is identical with the first-order density matrix. The Hartree-Fock equations are expressed in terms of this quantity.