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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Comment on derivation of the Schrödinger equation from Newtonian mechanics

Aloysius F. Kracklauer

Published Aug 15, 1974• 17 citations
Publisher

Abstract

Nelson's derivation of Schrödinger's equation with a stochastic argument is shown to be compatible with demonstrations that quantum probabilities evolve deterministically.Received 16 April 1973DOI:https://doi.org/10.1103/PhysRevD.10.1358©1974 American Physical Society

DOI
10.1103/physrevd.10.1358

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Nelson's derivation of Schrödinger's equation with a stochastic argument is shown to be compatible with demonstrations that quantum probabilities evolve deterministically.Received 16 April 1973DOI:https://doi.org/10.1103/PhysRevD.10.1358©1974 American Physical Society
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.