Stochastic model of quantum mechanics

Quantum mechanics is formulated in terms of ordinary probability theory. For this, the wave function is associated with a function that has the meaning of a probability density and describes the dynamics of a Markov random process in a complex phase space. All quantum-mechanical expectation values can be obtained from this “genuine” probability density without recourse to the concept of a probability amplitude. Stochastic ordinary differential equations that describe the evolution of the probability density in terms of random trajectories are obtained. The semiclassical case and the case of a quadratic potential are analyzed separately.