Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects

Per-Olov Löwdin

Phys. Rev. 97, 1509 – Published 15 March 1955

 

Abstract

In treating a system of $N$ antisymmetric particles, it is shown that, if the total Hamiltonian $H_{\mathrm{op}}$ is degenerate, the eigenstates of the operator used for classifying the corresponding degenerate states may be selected by means of a "projection operator" $O$. If the total wave function is approximated by such a projection of a single determinant, the description of the system may be reduced to the ordinary Hartree-Fock scheme treating this determinant, if the original Hamiltonian is replaced by a complete Hamiltonian ${\Omega }_{\mathrm{op}}=O^{†}{H}_{\mathrm{op}}O$ containing also many-particle interactions. This approach corresponds to a "fixed" configurational interaction, but the scheme has preserved the physical simplicity and visuality of the Hartree-Fock approximation. The idea of "doubly filled" orbitals is abandoned, and the orbitals associated with different spins will automatically try to arrange themselves in such a way that particles having antiparallel spins will tend to avoid each other due to their mutual repulsion.

• Received 8 July 1954

DOI:https://doi.org/10.1103/PhysRev.97.1509

©1955 American Physical Society

 

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