On the Dynamics of Generalized Coherent States. II. Classical Equations of Motions

Abstract

Using the Klauder approach the stable evolution of generalized coherent states (GCS) for some groups (SU(2), SU(1,1) and SU(N)) is considered and it is shown that one and the same classical solution z(t) can correctly characterize the quantum evolution of many different (in general nonequivalent) systems. As examples some concrete systems are treated in greater detail: it is obtained that the nonstationary systems of the singular oscillator, of the particle motion in a magnetic field, and of the oscillator with friction all have stable SU(1,1) GCS whose quantum evolution is determined by one and the same classical function z(t). The physical properties of the constructed SU(1,1) GCS are discussed and it is shown particularly that in the case of discrete series D_k^+ they are those states for which the quantum mean values coincide with the statistical ones for an oscillator in a thermostat.