The role of the zero-point fluctuations in the classical stochastic Schrodinger-like equation

We study the statistical evolution of a charged particle moving in phase sp ace under the action of the vacuum fluctuations of the zero-point electroma gnetic field. Our starting point is the Liouville equation, from which we d erive a classical stochastic Schrodinger-like equation for the probability amplitude in configuration space. It should be stressed that we are not der iving the Schrodinger wave equation. An equation formally identical to the Schrodinger equation used in quantum mechanics is obtained as a particular case of the classical stochastic Schrodinger-like equation. An inconsistenc y appearing in the standard Schrodinger equation, when we take into account the vacuum electromagnetic fluctuations and the radiation reaction, is cle arly identified by means of two examples using different sources of electro magnetic noise. The classical stochastic Schrodinger-like equation, however , is consistently interpreted within the realm of stochastic electrodynamic s.