Motion of wave packets in regular and chaotic systems

Abstract

The quantum energy spectrum of a system which is classically integrable consists of families of nearly equidistant levels. There is no such regularity for a classically chaotic system. As a consequence, a small wave packet, initially centered in a regular region of phase space, will slowly disperse while following the (almost) periodic classical trajectory. A wave packet placed in a chaotic region will disperse much more rapidly. These predictions are illustrated by calculating the evolution of two wave packets with the same mean energy in the Hénon–Heiles model.