Radial coherent states for the Coulomb problem

Abstract

Using the SO(2,1) radial (or spectrum-generating) subgroup of the SO(4,2) dynamical group of the Coulomb problem, we construct the associated coherent states that follow the classical radial motion. These wave packets evolve in a fictitious time variable proportional to the eccentric anomaly. The packets consist of a superposition of Coulomb Sturmian functions and do not disperse as they evolve although the width of the packets changes periodically.