Time dependence in quantum mechanics

It is shown that the time-dependent equations (Schr?dinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically 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 mechanical perturbed stationary states to the impact parameter method in which the projectile ion beam is treated classically. Received 25 October 1999