NONLINEAR WAVE-PACKET DYNAMICS FOR A GENERIC ONE-DIMENSIONAL TIME-INDEPENDENT SYSTEM AND ITS APPLICATION TO THE HYDROGEN-ATOM IN A WEAK MAGNETIC-FIELD

We study the time propagation of an initially localized wave packet fo r a generic one-dimensional time-independent system,using the ''nonlin ear wave-packet dynamics'' [S. Tomsovic and E. J. Heller, Phys. Rev. L ett. 67, 664 (1991)], a semiclassical approximation using a local line arization of the wave packet in the vicinity of classical reference tr ajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle var iables allows us to obtain a simple analytic expression for the autoco rrelation function, and to show that a universal behavior (quantum col lapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approac h is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show t hat the semiclassical expressions obtained by nonlinear wave-packet dy namics are extremely accurate.