Controlled quantum evolutions and transitions

We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or non stationary quantum states. In particular, we di scuss the stationary states of quantum systems with singular velocity field s. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions. Asa first signfic ant application we present a detailed treatment of the transition probabili ties and of the controlling time-dependent potentials associated to the tra nsitions between the stationary, the coherent, and the squeezed states of t he harmonic oscillator.