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Foundations of Physics

, Volume 10, Issue 1–2, pp 77–107 | Cite as

Physical foundations of quantum theory: Stochastic formulation and proposed experimental test

  • V. J. Lee
This Issue Is Dedicated To The Memory Of Wolfgang Yourgrau

Abstract

The time-dependent Schrödinger equation has been derived from three assumptions within the domain of classical and stochastic mechanics. The continuity equation isnot used in deriving the basic equations of the stochastic theory as in the literature. They are obtained by representing Newton's second law in a time-inversion consistent equation. Integrating the latter, we obtain the stochastic Hamilton-Jacobi equation. The Schrödinger equation is a result of a transformation of the Hamilton-Jacobi equation and linearization by assigning the arbitrary constant ħ=2mD. An experiment is proposed to determine ħ and to test a hypothesis of the theory directly. A mathematical apparatus is formulated from the Jacobian formalism to derive physical parameters from ψ(x, t) and to obtain operators for the boundary cases of the theory. The operator formalisms are compared by means of a well-known solution in the quantum theory.

Keywords

Physical Parameter Experimental Test Quantum Theory Continuity Equation Basic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    M. Jammer,The Philosophy of Quantum Mechanics (Wiley, New York, 1974), Preface and pp. 425–437, and references therein on early stochastic interpretation and later developments.Google Scholar
  2. 2.
    E. Schrödinger,Berliner Sitzungsberichte,1931, 144–153.Google Scholar
  3. 3.
    E. Nelson,Phys. Rev. 150 1079 (1966), and references therein.Google Scholar
  4. 4.
    L. de la Peña-Auerbach,Phys. Lett. 24 A, 603 (1967);27 A, 594 (1968).Google Scholar
  5. 5.
    L. de la Peña-Auerbach, E. Braun, and L. S. Garcia-Colin,J. Math. Phys. 9, 668 (1968).Google Scholar
  6. 6.
    L. de la Peña-Auerbach and L. S. Garcia-Colin,J. Math. Phys. 9, 916 (1968);9, 922 (1968);Rev. Mex. Fisica 16, 221 (1967);17, 327 (1968).Google Scholar
  7. 7.
    L. de la Peña-Auerbach,J. Math. Phys. 10, 1620 (1969); J. Ogunlana,J. Stat. Phys. 4, 217 (1972).Google Scholar
  8. 8.
    L. de la Peña-Auerbach and A. M. Cetto,Phys. Lett. 29 A, 562 (1969);Rev. Mex. Fisica 18, 253 (1969).Google Scholar
  9. 9.
    L. de la Peña-Auerbach,Rev. Mex. Fisica 19, 133 (1970);Phys. Lett. 31 A, 403 (1970).Google Scholar
  10. 10.
    L. de la Peña-Auerbach and A. M. Cetto,Phys. Rev. D 3, 795 (1971).Google Scholar
  11. 11.
    L. F. Favella,Ann. Inst. Henri Poincaré 7, 77 (1967).Google Scholar
  12. 12.
    Y. A. Rylov,Ann. Phys. 27, 1 (1971).Google Scholar
  13. 13.
    V. J. Lee,J. Stat. Phys. 8 (2), 189 (1973).Google Scholar
  14. 14.
    T. H. Boyer,Phys. Rev. D 11, 790 (1975), and references therein, esp. Refs. 2–7.Google Scholar
  15. 15.
    H. P. McKean, Jr.,Stochastic Integrals (Academic Press, New York, 1969), pp. 1, 32–35; also Ref. Ito (7) therein.Google Scholar
  16. 16.
    A. Dvoretzky, P. Erdos, and S. Kakutani, in 4th Berkeley Symp. Math.,Stat. Prob. 2, 103 (1961).Google Scholar
  17. 17.
    L. de la Peña-Auerbach and A. M. Cetto,Found. Phys. 5, 355 (1975).Google Scholar
  18. 18.
    A. F. Kracklauer,Phys. Rev. D 10, 1358 (1974).Google Scholar
  19. 19.
    S. Chandraskehar,Rev. Mod. Phys. 15, 191 (1943).Google Scholar
  20. 20.
    G. E. Uhlenbeck and L. S. Ornstein,Phys. Rev. 36, 823 (1930).Google Scholar
  21. 21.
    A. Einstein,Investigation on the Theory of Brownian Movement (Dover, New York, 1956).Google Scholar
  22. 22.
    M. C. Wang and G. E. Uhlenbeck,Rev. Mod. Phys. 323 (1945).Google Scholar
  23. 23.
    R. C. Buck,Advanced Calculus (McGraw-Hill, New York, 1956), pp. 180–186.Google Scholar
  24. 24.
    J. J. Sakurai,Invariance Principles and Elementary Particles (Princeton University Press, Princeton, N.J., 1964, pp. 79, 84–85.Google Scholar
  25. 25.
    D. ter Haar,Elements of Hamiltonian Mechanics (North-Holland, Amsterdam, 1964), p. 1.Google Scholar
  26. 26.
    E. P. Wigner,Proc. Am. Phil. Soc. 93, 521 (1949).Google Scholar
  27. 27.
    D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, N.J., 1961), pp. 268–271.Google Scholar
  28. 28.
    R. E. Collins,Found. Phys. 7, 475 (1977).Google Scholar
  29. 29.
    D. Bohm,Phys. Rev. 85, 166 (1952);85, 180 (1952); L. de Broglie,Compt. Rend. 183, 447 (1926).Google Scholar
  30. 30.
    E. Schrödinger,Collected Papers on Wave Mechanics (Blackie & Son, Toronto, 1928).Google Scholar
  31. 31.
    J. G. Gilson,Proc. Camb. Phil. Soc. 64, 1061 (1968), and references therein.Google Scholar
  32. 32.
    D. Kershaw,Phys. Rev. 136, 1850 (1964).Google Scholar
  33. 33.
    D. Bohm and J. P. Vigier,Phys. Rev. 96, 208 (1954).Google Scholar
  34. 34.
    E. P. Wigner,Group Theory and Its Applications to Quantum Mechanics of Atomic Spectra (Academic Press, New York, 1959), pp. 325–348.Google Scholar
  35. 35.
    D. Landau and E. M. Lifschitz,Quantum Mechanics (Pergamon Press, London, 1958); L. I. Schiff,Quantum Mechanics, 2nd ed. (McGraw-Hill, New York, 1955); J. L. Powell and B. Crasemann,Quantum Mechanics (Addison-Wesley, Reading, Mass., 1961); A. Messiah,Quantum Mechanics (North-Holland, Amsterdam, 1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • V. J. Lee
    • 1
  1. 1.Department of Chemical EngineeringUniversity of MissouriColumbia

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