Cellular dynamics: A new semiclassical approach to timehyphen;dependent quantum mechanics

摘要

A new semiclassical approach that constructs the full semiclassical Greenrsquo;s function propagation of any initial wave function directly from an ensemble of real trajectories, without root searching, is presented. Each trajectory controls a cell of initial conditions in phase space, but the cell area is not constrained by Planckrsquo;s constant. The method is shown to be accurate for rather long times in anharmonic oscillators, indicating the semiclassical timehyphen;dependent Greenrsquo;s function is clearly worthy of more study. The evolution of wave functions in anharmonic potentials is examined and a spectrum from the semiclassical correlation function is calculated, comparing with exact fast Fourier transform results.