Derivation of the Schrödinger Equation from Newtonian Mechanics

1966/10/28 by Edward Nelson · 33 citations
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Physics #Brownian motion #Diffusion process #Classical mechanics #Mathematical physics #Statistical mechanics #Wave function #Quantum mechanics

paper · doi:10.1103/physrev.150.1079

openalex publication_date 1966/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We examine the hypothesis that every particle of mass m is subject to a Brownian motion with diffusion coefficient \frac\ensuremathℏ2m and no friction. The influence of an external field is expressed by means of Newton's law F=ma, as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schr"odinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent.

Citations

• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• Statistical electrodynamics
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

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