Self-Interaction Corrections in a Nonrelativistic Stochastic Theory of Quantum Mechanics

L. DE LA Peña-Auerbach; Ana M. Cetto

doi:10.1103/PhysRevD.3.795

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Self-Interaction Corrections in a Nonrelativistic Stochastic Theory of Quantum Mechanics

L. DE LA Peña-Auerbach^*

Ana M. Cetto^†

Instituto de Física, Universidad Nacional de México, México, D. F.

Facultad de Ciencias, Universidad Nacional de México, México, D. F.

^*Technical consultant, Comisión Nacional de Energía Nuclear, México.
^†Fellow of the Ford Foundation, Facultad de Ciencias. Present address: Instituto de Física, Universidad Nacional de México, México, D. F.

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Phys. Rev. D 3, 795 – Published 15 February, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.795

Abstract

The radiation damping terms of classical electrodynamics are introduced into a set of stochastic equations of nonrelativistic quantum mechanics to study their effects on the energy levels of a stationary system to first order in perturbation theory. In the potential case there appear correction terms to Schrödinger's equation, one of which is calculated by solving a subsidiary equation. In particular, we obtain for the Lamb shift an expression of essentially stochastic origin, whose structure is in complete agreement with known results. According to this calculation, which has the advantage of being devoid of divergence problems, the non-relativistic spinless contribution to the Lamb shift of the $2 s$ level amounts of 60% of the total effect.

References (17)

D. Kershaw, Phys. Rev. 136, B1850 (1964)
E. Nelson, Phys. Rev. 150, B1079 (1966) E. Nelson, Dynamical Theories of Brownian Motion (Princeton U. P., Princeton, 1967)
E. Santos, Nuovo Cimento 59B, 65 (1969)
L. de la Peña-Auerbach, Phys. Letters 27A, 594 (1968) J. Math. Phys. 10, 1620 (1969)
L. de la Peña-Auerbach and A. M. Cetto, Rev. Mex. Fís. 18, 323 (1969)
R. Hakim, J. Math. Phys. 9, 1805 (1968)
L. de la Peña-Auerbach, Rev. Mex. Fís. 19, 133 (1970)
L. de la Peña-Auerbach, Phys. Letters 31A, 403 (1970) J. Math. Phys. 12, 453 (1971)
T. G. Dankel, Ph.D. thesis, Princeton, 1969 (unpublished)
L. Landau and E. Lifshitz, The Classical Theory of Fields (Addison-Wesley, Reading, Mass., 1951), Sec. 9-9
L. de la Peña-Auerbach and A. M. Cetto, Phys. Letters 29A, 562 (1969) Rev. Mex. Fís. 18, 253 (1969)
J. E. Krizan, Phys. Rev. 165, 1725 (1968)
L. de la Peña-Auerbach and R. M. Velasco, Rev. Mex. Fís. 18, 397 (1969) L. de la Peña-Auerbach, R. M. Velasco, and A. M. Cetto, 19, 193 (1970)
D. Ivanenko and A. Sokolov, Klassische Feldtheorie (Akademie-Verlag, Berlin, 1953)
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F. Röhrlich, Classical Charged Particles (Addison-Wesley, Reading, Mass., 1965), Chap. 6
T. A. Welton, Phys. Rev. 74, 1157 (1948)

[c1] D. Kershaw, Phys. Rev. 136, B1850 (1964)

[c2] E. Nelson, Phys. Rev. 150, B1079 (1966) E. Nelson, Dynamical Theories of Brownian Motion (Princeton U. P., Princeton, 1967)

[c3] E. Santos, Nuovo Cimento 59B, 65 (1969)

[c4] L. de la Peña-Auerbach, Phys. Letters 27A, 594 (1968) J. Math. Phys. 10, 1620 (1969)

[c5] L. de la Peña-Auerbach and A. M. Cetto, Rev. Mex. Fís. 18, 323 (1969)

[c6] R. Hakim, J. Math. Phys. 9, 1805 (1968)

[c7] L. de la Peña-Auerbach, Rev. Mex. Fís. 19, 133 (1970)

[c8] L. de la Peña-Auerbach, Phys. Letters 31A, 403 (1970) J. Math. Phys. 12, 453 (1971)

[c9] T. G. Dankel, Ph.D. thesis, Princeton, 1969 (unpublished)

[c10] L. Landau and E. Lifshitz, The Classical Theory of Fields (Addison-Wesley, Reading, Mass., 1951), Sec. 9-9

[c11] L. de la Peña-Auerbach and A. M. Cetto, Phys. Letters 29A, 562 (1969) Rev. Mex. Fís. 18, 253 (1969)

[c12] J. E. Krizan, Phys. Rev. 165, 1725 (1968)

[c13] L. de la Peña-Auerbach and R. M. Velasco, Rev. Mex. Fís. 18, 397 (1969) L. de la Peña-Auerbach, R. M. Velasco, and A. M. Cetto, 19, 193 (1970)

[c14] D. Ivanenko and A. Sokolov, Klassische Feldtheorie (Akademie-Verlag, Berlin, 1953)

[c15] H. A. Bethe and E. Salpeter, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1957), Vol. 34, Chap. 1

[c16] F. Röhrlich, Classical Charged Particles (Addison-Wesley, Reading, Mass., 1965), Chap. 6

[c17] T. A. Welton, Phys. Rev. 74, 1157 (1948)

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Self-Interaction Corrections in a Nonrelativistic Stochastic Theory of Quantum Mechanics

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