Soviet Physics Journal

, Volume 21, Issue 6, pp 741–746 | Cite as

The Hermitian phase operator and the Heisenberg commutation relations

  • E. V. Damaskinskii
  • V. S. Yarunin
Article
Received:
  • 43 Downloads

Abstract

A family of unitarily equivalent self-adjoint operators φ is constructed which satisfy the commutation relation [φ, N]=i, on a dense domain in the space of states; here N is the operator of the number of particles for the harmonic oscillator.

Keywords

Harmonic Oscillator Commutation Relation Phase Operator Dense Domain Heisenberg Commutation 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, Mass. (1959).Google Scholar
  2. 2.
    P. A. M. Dirac, Proc. R. Soc. (London),A114, 243 (1927).Google Scholar
  3. 3.
    N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hubert Space, Ungar.Google Scholar
  4. 4.
    V. A. Fock, Works on Quantum Field Theory [Russian translation], Leningrad State Univ. (1957).Google Scholar
  5. 5.
    A. S. Davydov, Quantum Mechanics, Pergamon (1965).Google Scholar
  6. 6.
    A. I. Baz', Ya. B. Zel'dovich, and A. M. Perelomov, Scattering Reactions and Decay in Nonrelativistic Quantum Mechanics [in Russian] (1971).Google Scholar
  7. 7.
    P. Carruthers and M. Nieto, in: Coherent States in Quantum Mechanics [Russian translation], No. 1, NFF, Mir (1972).Google Scholar
  8. 8.
    J. C. Garrison and J. Wong., J. Math. Phys.,11, 2243 (1970).Google Scholar
  9. 9.
    V. S. Popov and V. S. Yarunin, Vestn. Leningr. Gos. Univ., No. 22, 7–12 (1973).Google Scholar
  10. 10.
    F. Rocco and M. Sirugue, Commun. Math. Phys.,34, 111 (1973).Google Scholar
  11. 11.
    G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, WileyInterscience, New York (1972).Google Scholar
  12. 12.
    P. R. Halmos, Hubert Space Problem Book, Springer-Verlag (1974).Google Scholar
  13. 13.
    R. Cooke, Infinite Matrices and Sequence Spaces, Macmillan, London (1950).Google Scholar
  14. 14.
    J. Klauder and E. Sudarshan, Fundamentals of Quantum Optics, Benjamin, New York (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • E. V. Damaskinskii
    • 1
  • V. S. Yarunin
    • 1
  1. 1.Leningrad Institute for Aviation EngineeringUSSR

Personalised recommendations