Foundations of Physics Letters

, Volume 2, Issue 2, pp 113–126

On the derivation of the Schrödinger equation from stochastic mechanics

  • Timothy C. Wallstrom


It is shown that the existing formulations of stochastic mechanics are not equivalent to the Schrödinger equation, as had previously been believed. It is argued that this is a reflection of fundamental inadequacies in the physical foundations of stochastic mechanics.

Key words

stochastic mechanics quantum mechanics Schrödinger equation Nelson hidden variables 


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  1. 1.
    Edward Nelson, “Derivation of the Schrödinger equation from Newtonian mechanics,”Phys. Rev. 150, 1079–1085 (1966).Google Scholar
  2. 2.
    Mark Davidson, “A generalization of the Fényes-Nelson stochastic model of quantum mechanics,”Lett. Math. Phys. 3, 271–277 (1979).Google Scholar
  3. 3.
    Kunio Yasue, “Stochastic calculus of variations,”J. Funct. Anal.,41, 327–340 (1981).Google Scholar
  4. 4.
    Francesco Guerra and Laura M. Morato, “Quantization of dynamical systems and stochastic control theory,”Phys. Rev. D 27, 1774–1786 (1983).Google Scholar
  5. 5.
    Laura M. Morato, “Path-wise stochastic calculus of variations with the classical action and quantum systems,”Phys. Rev. D 32, 1982–1987 (1985).Google Scholar
  6. 6.
    Rossana Marra, “Variational principles for conservative and dissipative diffusions,”Phys. Rev. D 36, 1724–1730 (1987).Google Scholar
  7. 7.
    John D. Lafferty, “The density manifold and configuration space quantization,”Trans. Am. Math. Soc. 633, 699–741 (1988).Google Scholar
  8. 8.
    Eric A. Carlen, “Conservative diffusions,”Commun. Math. Phys. 94, 293–315 (1984).Google Scholar
  9. 9.
    Imre Fényes, “Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik,”Z. Phys. 132, 81–106 (1952).Google Scholar
  10. 10.
    Edward Nelson,Dynamical Theories of Brownian Motion (Princeton University Press, Princeton, 1967).Google Scholar
  11. 11.
    Sergio Albeverrio and Raphael Høegh-Krohn, “A remark on the connection between stochastic mechanics and the heat equation,”J. Math. Phys. 15, 1745–1747 (1974).Google Scholar
  12. 12.
    Sheldon Goldstein, “Stochastic mechanics and quantum theory,”J. Stat. Phys. 47(5/6), 645–667 (1987); see especially the discussion of the Aharonov-Bohm effect, §10.1.Google Scholar
  13. 13.
    Edward Nelson, “Stochastic mechanics and random fields,” to appear.Google Scholar
  14. 14.
    Edward Nelson,Quantum Fluctuations (Princeton University Press, Princeton, NJ, 1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Timothy C. Wallstrom
    • 1
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.ArcadiaCalifornia

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