A LOCAL ONE-ELECTRON OPERATOR FOR THE GENERALIZED-OVERLAP AMPLITUDES

摘要

An approach to the N-electron behavior is presented which emphasizes the dynamics of an individual electron. The generalized overlap amplitudes (GOAS), although formally defined by an integration over the coordinates of N - 1 electrons, are, instead, resolved as a column vector, eigenfunction to a local one-electron differential operator. These amplitudes have no restrictions of linear independence between them, but each satisfies the one-electron boundary conditions at the nuclei and at large distances. The one-electron (or charge) density is the sum of the squares of the elements of the column. The energy density, a constant times the one-electron density, maintains this one-to-one relationship throughout modifications in total number of electrons or external potential, although the constant of proportionality, the total energy of the system, may change in the process. Indistinguishability of electrons and antisymmetry is always observed by the dynamics of each electron. A numerical example, the ground state of helium, is presented. (C) 1995 John Wiley & Sons, Inc. [References: 38]