Generalized coherent states and classical limits in quantum mechanics

Abstract

Coherent states in the harmonic oscillator have long been thought of as a bridge from quantum mechanics to classical mechanics. Many of their important properties (most notably those involving time evolution) are only valid in the harmonic oscillator and are at best approximations elsewhere. This thesis is an investigation into several means of generalizing coherent states for other systems and examines the resultant states for some systems. One system of interest is the harmonic oscillator with centripetal barrier for which coherent states of several disparate definitions coincide. Also studied is this spherical rotator, a system which is particularly amenable to defining annihilation operator coherent states. A third system under investigation is the hydrogen atom. This system serves as an arena for the development of an extension to a generalization due to Klauder [J. Phys. A. 29(12):L293-L298. 1996]. Klauder's construction is only applicable to systems without energy degeneracies and must be extended for application where degeneracies are present. The author provides a means for this extension and applies the complete construction to the hydrogen atom problem. As a demonstration of how this construction may be adapted, the author constructs Rydberg wave packets which are initially localized and exhibit full and fractional revivals in the long time evolution.