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Prog. Theor. Phys. Vol. 64 No. 1 (1980) pp. 18-27

[ Full Text PDF : FREE ACCESS (600K) ]

Rational Construction and Physical Signification of the Quantal Time Operator

Izuru Fujiwara

Department of Mathematical Sciences, University of Osaka Prefecture, Sakai 591

(Received February 29, 1980)

Abstract:

First a general expression for an eigenstate |t > of the time operator T defined by the commutation relation [ T, H ] = i \hbar is given in terms of the eigenvectors of the Hamiltonian H. Then the time operator itself is constructed as T = \intdt t | t ><t|. When a compound state corresponding to transitions is introduced, it leads directly to the time-energy uncertainty relationship formulated previously by the same author.


URL : http://ptp.ipap.jp/link?PTP/64/18/
DOI : 10.1143/PTP.64.18

[ Full Text PDF : FREE ACCESS (600K) ] Citation:

References:

  1. M. Razavy, Am. J. Phys. 35 (1967), 955; Nuovo Cim. B 63 (1969), 271; Can. J. Phys. 49 (1971), 3075.
    D. M. Rosenbaum, J. Math. Phys. 10 (1969), 1127[CrossRef].
    Other references being numerous in number are found in R. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40 (1968), 411[APS]; The Uncertainty Principle and Foundations of Quantum Mechanics, edited by W. C. Price and S. S. Chissick (John Wiley and Sons, 1977).
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  7. I. Fujiwara, Prog. Theor. Phys. 44 (1970), 1701[PTP]; ibid. 62 (1979), 1438[PTP].
  8. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University Press, 1958), p. 79.
  9. I. Fujiwara, K. Wakita and H. Yoro, Prog. Theor. Phys. 64 (1980), 363[PTP].
  10. G. R. Allcock, Ann. of Phys. 53 (1969), 235; ibid. 53 (1969), 286[CrossRef]; ibid. 53 (1969), 311[CrossRef].
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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 64 No. 2 (1980) pp. 363-379 :
    Explicit Construction of Time-Energy Uncertainty Relationship in Quantum Mechanics
    Izuru Fujiwara, Kazuki Wakita and Hisao Yoro
  2. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1525-1538 :
    On the Time Operator in Quantum Mechanics
    Tetsuo Gotō, Katsuhito Yamaguchi and Naoshi Sudō
  3. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 158-170 :
    Time Compound Nucleus for High Energy Nuclear Reactions
    Ko Izumo and Hitoshi Araseki

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