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Cited by 1,725Quantum Mechanics and ApplicationsStatistical Mechanics and EntropyNoncommutative and Quantum Gravity Theories

Derivation of the Schrödinger Equation from Newtonian Mechanics

Nelson, Edward·1966·Physical Review
DOI 10.1103/physrev.150.1079
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Abstract

We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external field is expressed by means of Newton's law $\mathbf{F}=m\mathbf{a}$, 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.

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Crossref · 10.1103/physrev.150.1079

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16 of 16 references verified0 citation errors · 0 not checkable

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Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Nelson's stochastic mechanics describes particle motion in accord with a stochastic differential equation.

    “Another example is Nelson's stochastic mechanics that describes particle motion in accord with a stochastic differential equation.”

    From Governing Without A Fundamental Direction of Time: Minimal Primitivism about Laws of Nature (2022) · cites this paper as Nelson (1966)

  • All arguments and results of the paper can be transferred to stochastic mechanics without significant modification.

    “In view of the similarity between Bohmian mechanics and stochastic mechanics [44,45,46], for which similarity see [35,28], all of our arguments and results can be transferred to stochastic mechanics without significant modification.”

    From Quantum equilibrium and the origin of absolute uncertainty (1992) · cites this paper as [44]

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Related

Authors
Nelson, E.
Affiliations
Princeton University (US)
Corresponding author
Nelson, Edward
Venue
Physical Review
Publisher
American Physical Society (APS)
Published
1966-10-28
Volume
150
Issue
4
Pages
1079-1085
ISSN
0031-899X (ISSN-L)
DOI
10.1103/physrev.150.1079
OpenAlex
W2223094112
Cited by
1,725
References
17
Citations by year
2026: 53 · 2025: 54 · 2024: 61 · 2023: 53 · 2022: 38 · 2021: 65 · 2020: 56 · 2019: 71 · 2018: 50 · 2017: 40 · 2016: 50 · 2015: 37 · 2014: 44 · 2013: 45 · 2012: 59
FWCI
3.87
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical Review (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
Keywords
Schrödinger equation derivation, Brownian motion, diffusion coefficient, classical mechanics, Ornstein-Uhlenbeck process, classical trajectories, wave function interpretation, quantum measurement, classical limit of quantum mechanics

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