Convergence of a Quantum Dynamic to a Classical Limit.

摘要

This article introduces, for the situation where the potential is time independent, a different diffusion with the probability measure associated to Schrodinger's equation. It is shown that, for the diffusion introduced here, the classical mechanics are recovered as the limit (in distribution) as H-0. Although this property is well established at a physical level, the arguments presented so far (eg Maslow's arguments, described in (2)) this is (to the knowledge of the authors) the first rigorous construction of a process with probability distributions associated to solutions of Schrodinger's equation which recovers the classical limit as h-0 and hence the first rigorous proof (in special situations) that classical dynamics is the h-0 limit of quantum dynamics. The diffusion process introduced in this article has thus already provided new information at a physical level.