General Character of Quantum Regular Motion and Quantum-Classical Correspondence

In order to have a complete description of the spatio-temporal evolution of a quantum state,the initial state should be properly specified as the coherent state corresponding to a definite dynamical symmetry.Then we have qualitatively different situations where the initial coherent state evolves under the action of a system having or not having the same dynamical symmetry.In the former case,we have regular motion with the general character which tends to that of the corresponding classical case in the limit n→0.While in the latter case,we may have energy regions of global stochasticity with characters closely related to the initial dynamical symmetry strongly violated.