Nonlinear wave-packet dynamics for a generic one-dimensional time-independent system and its application to the hydrogen atom in a weak magnetic field.

Abstract

We study the time propagation of an initially localized wave packet for a generic one-dimensional time-independent system, using the {open_quote}{open_quote}nonlinear wave-packet dynamics{close_quote}{close_quote} [S. Tomsovic and E. J. Heller, Phys. Rev. Lett. {bold 67}, 664 (1991)], a semiclassical approximation using a local linearization of the wave packet in the vicinity of classical reference trajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle variables allows us to obtain a simple analytic expression for the autocorrelation function, and to show that a universal behavior (quantum collapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approach is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show that the semiclassical expressions obtained by nonlinear wave-packet dynamics are extremely accurate. {copyright} {ital 1996 The American Physical Society.}