Some remarks about electron-correlation

Abstract

A comparison is made between the theories of Wigner (1934), Wigner and Seitz (1934), and of Pines (1953, 1955). Bohm and Pines (1951, 1953), Pines and Bohm (1952), which both represent different approaches to an inclusion of correlation in the wave mechanical treatment of a free electron gas. Starting with a determinantal wave function for the electron gas, correlation is taken into account by means of a ‘modulating’ function by which the complete wave function must be multiplied. It can be shown that in both theories these modulating functions are nearly the same. A more detailed consideration of Wigner's treatment gives a ‘cut-off’ wavelength for the collective behaviour which is numerically nearly equal to the ‘out-off’ wavelength in the theory of Bohm and Pines.