Quantum time scales and the classical limit: Analytic results for some simple systems

We set up a semiclassical approximation which helps us clarify by means of several simple examples the rich variety of time scale in the quantum domain. The underlying structure of quantum and classical mechanics is so completly different that it is naive to expect to reach a classical regime by counting powers of the quantum scale h. We show although it is possible to define a time scale for nonclassical phenomena, but it is impossible to characterize quantum dynamics through a unique time scale, such as Ehrenfest's time. We use simple systems to critically discuss and illustrate these features of the quantum-classical limit.