Quantum Theory of ManyParticle Systems. II. Study of the Ordinary HartreeFock Approximation
Abstract
A system of N antisymmetric particles, moving under the influence of a fixed potential and their mutual manyparticle interactions, is investigated in the ordinary HartreeFock 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 ρ(x_{1}, x_{2}), which is identical with the firstorder density matrix. The HartreeFock equations are expressed in terms of this quantity. The HartreeFock equations are also solved by expanding the eigenfunctions in a given complete set, and applications to the MOLCAO theory of the electronic structure of molecules, and crystals are given. It is shown that, in this scheme, the entire physical situation depends on a charge and bondorder matrix R(νμ) with respect to the ordinary atomic spinorbitals involved. The HartreeFock equations for this matrix are investigated. Finally, the ionized and excited states are investigated, and it is shown that the HartreeFock scheme has a high degree of physical visuality also in case of manyparticle interactions. The excitation energy of the system is the difference (ω_{j}'ω_{i}) between two "spinorbital energies," being eigenvalues to the effective Hamiltonians associated with the two states under consideration.
 Publication:

Physical Review
 Pub Date:
 March 1955
 DOI:
 10.1103/PhysRev.97.1490
 Bibcode:
 1955PhRv...97.1490L