Schrodinger's equation derived from the collision-less Boltzmann's equation

A classical particle's probability density in phase space is completely determined by its initial values over phase space and by Boltzmann's collision-less equation. If Schrodinger's equation can be shown to be consistent with Boltzmann's classical collision-less equation then quantum mechanics is understood as no more than the application of special initial conditions in classical mechanics. We show that this is the case for the free particle, i.e. when V(x) = 0.