Derivation of the Schrödinger equation IV: Stochastic and the Langevin Equations for Quantum Mechanics

Derivação da equação de Schrödinger IV: Estocástica e equações de Langevin para Mecânica Quântica

This is the fourth paper of a series devoted to mathematically derive the Schrödinger equation using stochastic constructs. We then show that Quantum Mechanics has a stochastic support by following two paths: we first present a stochastic derivation already known in the literature and show that it is equivalent to the characteristic function derivation, made by us in the first paper of this series. However, this approach does not furnish the true stochastic dynamics of the quantum mechanical system, but only an averaged one. We then present a new derivation of the Schrödinger equation based on Langevin equations that present all features of a true stochastic system. These two approaches then improve our understanding of Quantum Mechanics to encompass stochastic behavior.

Keywords:
Langevin equations; Schrödinger equation; Stochastic derivation; Teaching of Quantum Mechanics