Time dependence in quantum mechanics
Institute for Advanced Study, Wallotstrasse 19,
14193 Berlin, Germany
Published online: 15 June 2000
It is shown that the time-dependent equations (Schrödinger 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.
PACS: 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell inequalities, Berry's phase) / 34.10.+x – General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) / 03.65.Sq – Semiclassical theories and applications
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000