Foundations of quantum mechanics: The Langevin equations for QM

Stochastic derivations of the Schrödinger equation are always developed on very general and abstract grounds. Thus, one is never enlightened which specific stochastic process corresponds to some particular quantum mechanical system, that is, given the physical system—expressed by the potential function, which fluctuation structure one should impose on a Langevin equation in order to arrive at results identical to those comming from the solutions of the Schrödinger equation. We show, from first principles, how to write the Langevin stochastic equations for any particular quantum system. We also show the relation between these Langevin equations and those proposed by Bohm in 1952. We present numerical simulations of the Langevin equations for some quantum mechanical problems and compare them with the usual analytic solutions to show the adequacy of our approach. The model also allows us to address important topics on the interpretation of quantum mechanics.

► It is shown that quantum phenomena can be modeled by Langevin equations. ► This generalizes Bohm’s approach, that is not a true fluctuation scheme. ► Simulations are done for some QM systems. Superpositions also modeled. ► Interpretation addressed using mathematical background. Waves/corpuscles. ► Positive definite phase-space distribution function is obtained.