  We perform a detailed analysis of the non stationary solutions of the
evolution (Fokker-Planck) equations associated to either stationary or non
stationary quantum states by the stochastic mechanics. For the excited
stationary states of quantum systems with singular velocity fields we
explicitely discuss the exact solutions for the HO case. Moreover the
possibility of modifying the original potentials in order to implement
arbitrary evolutions ruled by these equations is discussed with respect to both
possible models for quantum measurements and applications to the control of
particle beams in accelerators.
