Time dependence in quantum mechanics

It is shown that the time-dependent equations (Schrodinger and Dirac) for a quantum system can be derived from the time-independent equation for the l arger object of the system interacting with its environment, in the limit t hat the dynamical variables of the environment can be treated semiclassical ly. The time which describes the quantum evolution is then provided paramet rically by the classical evolution of the environment variables. The method used is a generalization of that known for a long time in the field of ion -atom collisions, where it appears as a transition from the full quantum me chanical perturbed stationary states to the impact parameter method in whic h the projectile ion beam is treated classically.