Quantum mechanical states as attractors for Nelson processes

In this paper we reconsider in the light of the Nelson stochastic mechanics the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probabil ity densities always relax in time toward the quantum mechanical density j j derived from the Schr odinger equation The analysis of a few general propositions and of some physical examples show that the choice of the L metrics and of the Nelson stochastic ux are correct for a particular class of quantum states but can not be adopted in general This indicates that the question if the quantum mechanical densities attract other solution of the classical Fokker Planck equations associated to the Schr odinger equation is physically meaningful even if a classical probabilistic model good for every quantum state is still not available A few suggestion in this direction are nally discussed