Use of Quantum Trajectories for Time-Dependent Problems

Abstract

Ehrenfest’s principle states the correspondence between a classical trajectory and the expectation values of the corresponding quantum operator. In most cases the equations of motion for the average values of momentum, position, etc. are not closed and, therefore, cannot be solved without further assumptions. It is then useful to rewrite the Schrodinger equation as a time-dependent eigenvalue equation. In the following we shall outlines (1) how to solve the eigenvalue problem within variational perturbation theory, (2) how to calculate quantum trajectories, and (3) how to determine transition probabilities from trajectories. The method presented here will be illustrated by two examples from scattering theory.