HAMILTON-JACOBI DYNAMICS FOR THE SOLUTION OF TIME-DEPENDENT QUANTUM PROBLEMS .1. FORMALISM AND WAVE-PACKET PROPAGATION IN ONE-DIMENSION


YURTSEVER E., BRICKMANN J.

BERICHTE DER BUNSEN-GESELLSCHAFT-PHYSICAL CHEMISTRY CHEMICAL PHYSICS, vol.98, no.4, pp.554-559, 1994 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 98 Issue: 4
  • Publication Date: 1994
  • Doi Number: 10.1002/bbpc.19940980404
  • Title of Journal : BERICHTE DER BUNSEN-GESELLSCHAFT-PHYSICAL CHEMISTRY CHEMICAL PHYSICS
  • Page Numbers: pp.554-559

Abstract

Two methods for the numerical integration of the time-dependent Schrodinger equation with given initial conditions (initial wave packet) are presented. The first method (method A) is based on the Schrodinger representation of the quantum-dynamical system while the second one (method B) is based upon the intermediate representation. In both cases the quantum dynamical equation is transformed into a system of Hamilton-Jacobi type equations of motion as occurring in multi particle classical dynamics, i.e. standard molecular dynamics techniques can be applied for the integration. The dynamics of a minimum uncertainty Gaussian wave packet in a strongly anharmonic oscillator is taken as an example.