Uniform regularized semiclassical propagator for the x-2 potential.

Abstract

We apply recent methods for semiclassical time propagation involving non-Cartesian variables to the repulsive one-dimensional potential V(x)=${\mathit{x}}^{\mathrm{\ensuremath{-}}2}$,x\ensuremath{\ge}0. In order to properly treat non-Cartesian variables, a quantum regularization is first performed which leads to a Langer-type potential correction term in the Gutzwiller--Van Vleck propagator. A nonuniform semiclassical treatment of V(x)=${\mathit{x}}^{\mathrm{\ensuremath{-}}2}$ using this regularization improves earlier unregularized results, and a uniform regularized propagator is very nearly exact for all times. \textcopyright{} 1996 The American Physical Society.