The generator coordinate method, path integrals, and quantized time-dependent mean field motion

Abstract

The two parameter generator coordinate (GCM) method is used to derive the equation of motion for time-dependent mean fields associated to large amplitude vibrations. To achieve this a semclassical assumption and the gaussian overlap approximation is introduced into the GCM before the variational principle is applied. The result consists in time-dependent Hartree-Fock equations with periodic boundary conditions and a semiclassical quantization rule to select those TDHF orbits which correspond to the stationary states. The prescription turns out to be identical to the one obtained recently by path integral techniques and gauge invariant quantization.