On the Dynamics of Generalized Coherent States. I. Exact and Stable Evolution

The exact and stable evolutions of generalized coherent states (GCS) for quantum systems are considered by making use of the time-dependent integrals of motion method and of the Klauder approach to the relationship between quantum and classical mechanics. It is shown that one can construct for any quantum system overcomplete family of states (OFS), related to the unitary representations of the Lie group G by means of integral of motion generators, and the possibility of using this group as a dynamical symmetry group is pointed out. The relation of the OFS with quantum measurement theory is also established