Time Operators, Partial Stationarity, and the Energy-Time Uncertainty Relation

Joseph H. Eberly; L. P. S. Singh

doi:10.1103/PhysRevD.7.359

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Time Operators, Partial Stationarity, and the Energy-Time Uncertainty Relation

Joseph H. Eberly^*

L. P. S. Singh

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305 and Department of Physics, Stanford University, Stanford, California 94305

Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627

^*Permanent address: Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627.

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Phys. Rev. D 7, 359 – Published 15 January, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.359

Abstract

The reciprocal time operator which is suggested by the notion of partial stationarity is shown to permit an unambiguous and nonsingular statement of the energy-time uncertainty relation.

References (10)

Y. Aharonov and D. Bohm, Phys. Rev. 122, 1649 (1961) V. A. Fock, Zh. Eksp. Teor. Fiz. 42, 1135 (1962) [Sov. Phys. JETP 15, 784 (1962)] Y. Aharonov and D. Bohm, Phys. Rev. 134, B1417 (1964)
P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 411 (1968)
L. Mandelstam and I. Tamm, J. Phys. U.S.S.R. 9, 249 (1945) A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), pp. 319-320
F. T. Smith, Phys. Rev. 118, 349 (1960)
B. A. Lippmann, Phys. Rev. 151, 1023 (1966)
Omitted endnote
Y. Kano, Ann. Phys. (N.Y.) 30, 127 (1964)
J. H. Eberly and A. Kujawski, Phys. Letters 24A, 426 (1967) D. Dialetis and C. L. Mehta, Nuovo Cimento 56B, 89 (1968)
D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, N. J., 1951), pp. 227-228
V. F. Weisskopf and E. Wigner, Z. Physik 63, 54 (1930) G. Källén, Encyclopedia of Physics, edited by S. Flügge (Springer, Berlin, 1958), Vol. V J. R. Ackerhalt, J. H. Eberly, and P. L. Knight, in Proceedings of the Third Rochester Conference on Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, to be published)

[c1] Y. Aharonov and D. Bohm, Phys. Rev. 122, 1649 (1961) V. A. Fock, Zh. Eksp. Teor. Fiz. 42, 1135 (1962) [Sov. Phys. JETP 15, 784 (1962)] Y. Aharonov and D. Bohm, Phys. Rev. 134, B1417 (1964)

[c2] P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 411 (1968)

[c3] L. Mandelstam and I. Tamm, J. Phys. U.S.S.R. 9, 249 (1945) A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), pp. 319-320

[c4] F. T. Smith, Phys. Rev. 118, 349 (1960)

[c5] B. A. Lippmann, Phys. Rev. 151, 1023 (1966)

[c6] Omitted endnote

[c7] Y. Kano, Ann. Phys. (N.Y.) 30, 127 (1964)

[c8] J. H. Eberly and A. Kujawski, Phys. Letters 24A, 426 (1967) D. Dialetis and C. L. Mehta, Nuovo Cimento 56B, 89 (1968)

[c9] D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, N. J., 1951), pp. 227-228

[c10] V. F. Weisskopf and E. Wigner, Z. Physik 63, 54 (1930) G. Källén, Encyclopedia of Physics, edited by S. Flügge (Springer, Berlin, 1958), Vol. V J. R. Ackerhalt, J. H. Eberly, and P. L. Knight, in Proceedings of the Third Rochester Conference on Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, to be published)

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Time Operators, Partial Stationarity, and the Energy-Time Uncertainty Relation

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