Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom

Abstract

We explore the classical limit of the hydrogen atom by constructing a minimum-uncertainty wave packet that travels along a Kepler orbit. The dynamics of the wave packet display both classical and quantum-mechanical properties. Over a limited period of time, during which the dynamics of the wave packet may be considered linear, the motion of the wave packet can be described by classical equations of motion. After this time, the quantum dynamics, whose most prominent features are decays and revivals of the wave packet, becomes dominant. We discuss decays and revivals of the wave packet in detail.