HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 9 (1953) > Number 3
| Next Article >

Prog. Theor. Phys. Vol. 9 No. 3 (1953) pp. 187-222

[ Full Text PDF (2933K) ]  [ Buy This Article ]

Remarks on the Formulation of Quantum Mechanics with Classical Pictures and on Relations between Linear Scalar Fields and Hydrodynamical Fields

Takehiko Takabayasi

Physical Institute, Nagoya University

(Received December 15, 1952)

Abstract:

The formulation of quantum mechanics in terms of the picture of trajectory ensemble or of the hydrodynamical picture, developed in a previous article, is further supplemented for some points. Individual trajectories for some typical non-stationary state are explicitly obtained, illustrating that they generally show complicated fluctuations due to the action of quantum potential. Next, emphasis is placed on the fact that the Schrödinger field admits a mechanical model. Also the Klein-Gordon field is represented with a quasi-irrotational flow under some additional scalar field. This representation of Klein-Gordon field suggests its possible generalization to include the vortical motion. Such treatments of interacting Klein-Gordon and electromagnetic fields involve the formalism of Dirac's recent classical electrodynamics as a limiting case. Some remarks are given on this Dirac's theory. Finally, the picture of trajectory ensemble is generalized so as to represent wave equations with sources. In an appendix criticism is given on the attempt to interpret quantum mechanics in terms of Markoff process.


URL : http://ptp.ipap.jp/link?PTP/9/187/
DOI : 10.1143/PTP.9.187

[ Full Text PDF (2933K) ]  [ Buy This Article ]  Citation:

References:

  1. L. de Broglie, Introduction a l'étude de la Mécanique ondulatoire (Hermann, Paris, 1930).
  2. D. Bohm, Phys. Rev. 84 (1952), 166[APS]; ibid. 84 (1952), 180[APS].
  3. T. Takabayasi, Prog. Theor. Phys. 8 (1952), 143[IPAP].
  4. I. Fényes, Z. Phys. 132 (1952), 81.
  5. P. A. M. Dirac, Proc. Roy. Soc. A 209 (1951), 291.
  6. O. Halpern, Phys. Rev. 87 (1952), 389[APS].
  7. a) For this also see, D. Bohm, Phys. Rev. 87 (1952), 389[APS].
    b) See e.g., H. A. Lorentz, The Theory of Electrons (1916), p. 213.
  8. P. A. M. Dirac, Proc. R. Soc. A 212 (1952), 330.
  9. Such a connection between Klein-Gordon field and Dirac's new theory was already pointed out by
    E. Schrödinger, Nature 169 (1952), 538.
  10. R. P. Feynman, Phys. Rev. 76 (1949), 749[APS].
  11. R. Furth, Z. Phys. 81 (1933), 143.
  12. S. Chandrasekhar, Rev. Mod. Phys. 15 (1943), 1[APS].
    J. G. Kirkwood, J. Chem. Phys. 14 (1956), 180[AIP Scitation].
  13. See, e.g.; E. Schrödinger, Ann. de. Phys. 82 (1927), 265.
    W. Pauli, Die allgemeine Prinzipien der Wellenmechanik (1933) A Ziff. 4.
    S. Tomonaga, Quantum Mechanics (I), §40 (In Japanese).
  14. H. Bateman, Partial Differential Equations of Mathematical Physics (1932), 164.
    H. Itô, Busseiron Kenkyu 37 (1951), 63 (in Japanese).
  15. F. London, Rev. Mod. Phys. 17 (1945), 310[APS].
  16. Cf. W. Pauli, Relativitätstheorie (1932), Ziff. 45.
  17. S. Sakata and O. Hara, Prog. Theor. Phys. 2 (1947), 30[IPAP].
    O. Hara, Prog. Theor. Phys. 3 (1948), 188[IPAP].
  18. A. Pais, Verh. Kon. Ac. Amsterdam, vol. 19 (1947).
  19. E. C. G. Stueckelberg, Helv. Phys. Acta 14 (1941), 51.
  20. J. A. Wheeler and R. P. Feynman, Rev. Mod. Phys. 17 (1945), 157[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 9 No. 6 (1953) pp. 681-683 :
    On the Separability of Dirac Equation
    Takehiko Takabayasi
  2. Progress of Theoretical Physics Vol. 10 No. 1 (1953) pp. 121-122 :
    Equivalence between the Formulation of Quantum Mechanics in terms of Quantum Potential and the One in terms of Markoff-like Process
    Takehiko Takabayasi
  3. Progress of Theoretical Physics Vol. 11 No. 4 (1954) pp. 341-373 :
    The Formulation of Quantum Mechanics in terms of Ensemble in Phase Space
    Takehiko Takabayasi
  4. Progress of Theoretical Physics Vol. 12 No. 6 (1954) pp. 810-812 :
    On the Hydrodynamical Representation of Non-Relativistic Spinor Equation
    Takehiko Takabayasi
  5. Progress of Theoretical Physics Vol. 13 No. 2 (1955) pp. 222-224 :
    Relativistic Hydrodynamics Equivalent to the Dirac Equation
    Takehiko Takabayasi
  6. Progress of Theoretical Physics Vol. 14 No. 4 (1955) pp. 283-302 :
    The Vector Representation of Spinning Particle in the Quantum Theory, I
    Takehiko Takabayasi
  7. Progress of Theoretical Physics Vol. 15 No. 6 (1956) pp. 588-590 :
    On the Hydrodynamical Description of the Behaviours of Elementary Particles
    Minoru Hamaguchi
  8. Progress of Theoretical Physics Vol. 34 No. 3 (1965) pp. 473-497 :
    Proposal for the Quantum Mechanical Orbit Equation
    Yoshio Nishiyama
  9. Progress of Theoretical Physics Vol. 43 No. 4 (1970) pp. 861-869 :
    Formulation of the Uncertainty Principle According to the Hydrodynamic Model of Quantum Mechanics
    H. E. Wilhelm
  10. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 313-328 :
    Hamiltonian Dynamics and the Schrödinger Equation
    L. Bess
  11. Progress of Theoretical Physics Vol. 53 No. 6 (1975) pp. 1831-1833 :
    Electromagnetic Interaction in the Schrödinger Equation Model
    L. Bess
  12. Progress of Theoretical Physics Vol. 69 No. 5 (1983) pp. 1323-1344 :
    Hydrodynamical Formalism of Quantum Mechanics and Aharonov-Bohm Effect
    Takehiko Takabayasi
  13. Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 1-17 :
    Vortex, Spin and Triad for Quantum Mechanics of Spinning Particle.I
    Takehiko Takabayasi

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2010 All rights reserved.