Advertisement

Generalized Coherent States

  • T. S. Santhanam

Abstract

The coherent states of the harmonic oscillator and hence the radiation field (which is considered as an assembly of oscillators) can be defined in many different, but essentially equivalent ways.1

Keywords

Angular Momentum Coherent State Weyl Group Annihilation Operator Minimum Uncertainty 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A detailed discussion can be found in J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum optics 1968 ( New York: Benjamin).Google Scholar
  2. 2.
    E. Schrödinger, Naturwissenschaftern 14, 664 (1929). This has been discussed, for example, in L. I. Schiff, Quantum Mechanics (McGraw-Hill), N.Y., 1955), 2nd Ed. p. 67.Google Scholar
  3. 3.
    R. J. Glauber, Phys. Rev. 131, 2766 (1963).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    A. 0. Barut and L. Girardello, Commun. Math. Phys. 21, 41 (1971).MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    J. K. Sharma, C. L. Mehta and E. C. G. Sudarshan, J. Math. Phys. 19, 2089 (1978).ADSCrossRefGoogle Scholar
  7. 7.
    J. M. Radcliffe, J. Phys. A4, 313 (1971).MathSciNetADSGoogle Scholar
  8. 8.
    A. M. Perelemov, Commun. Math. Phys. 26, 222 (1972).ADSCrossRefGoogle Scholar
  9. 9.
    C. Aragone, E. Chalband and S. Salamo, J. Math. Phys. 17, 1963 (1976).ADSCrossRefGoogle Scholar
  10. C. Aragone et al., J. Phys. A7, L149 (1974).ADSGoogle Scholar
  11. 10.
    M. M. Nieto and L. M. Simmons, Phys. Rev. Lett. 41 207 (1978) Los Alamos preprints 78–2137.Google Scholar
  12. 11.
    T. S. Santhanam, Found. Phys. 7, 121 (1977), Phys. Lett. 56A, 345 (1976)MathSciNetADSCrossRefGoogle Scholar
  13. See also, J. M. Levy-Leblond, Rev. Mexi. Fis. 22, 15 (1973).Google Scholar
  14. 12.
    J. L. Martin, Proc. Roy. Soc. London. A251, 536 (1959).ADSMATHCrossRefGoogle Scholar
  15. 13.
    Y. Ohnuki and T. Kashiwa, Nagoya Univ. preprint 12–78.Google Scholar
  16. 14.
    J. Von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton, 1955 ).Google Scholar
  17. 15.
    V. Bargmann, P. Butera, L. Girardello and J. R. Klauder, Reports on Math. Phys. 2, 221 (1971).MathSciNetADSCrossRefGoogle Scholar
  18. 16.
    Hongoh, J. Math. Phys.18, 2081 (1977).MathSciNetADSMATHCrossRefGoogle Scholar
  19. 17.
    T. F. Jordan, N. Mukunda and S. V. Pepper, J. Math. Phys. 4, 1089 (1963).MathSciNetADSMATHCrossRefGoogle Scholar
  20. L. 0’ Raifeartaigh and C. Ryan, Proc. R. Irish, Acad. A62, 93 (1963).MATHGoogle Scholar
  21. 18.
    P. W. Atkins and J. C. Dobson, Proc. Roy. Soc. London A321, 321 (1971).MathSciNetADSCrossRefGoogle Scholar
  22. 19.
    F. Holstein and H. Primakoff, Phys. Rev., 58, 1048 (1940).ADSCrossRefGoogle Scholar
  23. 20.
    L. Kolodziejczyk and A. Ryter, J. Phys. A7, 213 (1974).ADSGoogle Scholar
  24. 21.
    A. M. Perelemov, Sov. Phys. Usp. 20(9), Sep 1977, Usp. Fiz. Nauk 123, 23 (1977).Google Scholar
  25. 22.
    F. T. Hioe, J. Math. Phys. 15, 11 74 (1974).Google Scholar
  26. 23.
    M. Hongoh, Rep. on Math. Phys. 13, 305 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
  27. 24.
    J. Bellissard and R. Holz, J. Math. Phys. 15, 1275 (1974).ADSCrossRefGoogle Scholar
  28. 25.
    J. Schwinger, Quantum Theory of Angular Momentum, Eds., L. C. Biedenharn and H. Van Dam (Academic Press, N.Y.) 1965 pp. 229–79.Google Scholar
  29. 26.
    T. S. Santhanam, Proc. International Conference on “Frontiers of Physics” held in Singapore, Singapore National Acad. of Sci. Eds. K. K. Phua et al., 1167–1196 (1978).Google Scholar
  30. 27.
    Y. Nambu, Phys. Rev. 7D, 2405 (1973).MathSciNetADSGoogle Scholar
  31. 28.
    S. Ruschin and Y. Ben-Aryeh, Phys. Lett. 58A, 207 (1976).MathSciNetCrossRefGoogle Scholar
  32. 29.
    H. Bacry, J. Math. Phys. 19, 1192 (1978) Phys. Rev. 18A, 617 (1978).Google Scholar
  33. 30.
    G. Vanden Berghe and H. De Meyer, J. Phys. A11, 1569 (1978).ADSGoogle Scholar
  34. 31.
    M. A. Rashid, J. Math. Phys. 19, 1391 and 1397 (1978).MathSciNetADSCrossRefGoogle Scholar
  35. 32.
    A detailed discussion of this appears in: P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 411 (1968).Google Scholar
  36. 33.
    K. Kraus, Z. Phys. 188, 374 (1965), 201, 134 (1967).MathSciNetGoogle Scholar
  37. 34.
    R. Jackiw, J. Math. Phys. 9 339 (1968).ADSMATHCrossRefGoogle Scholar
  38. 35.
    H. Bacry, A. Grassman, and J. Zak, Proc. 4th Int. Colloq. on Group Theoretical Methods in Physics. Nijmegen, 1975. Springer.Google Scholar
  39. 36.
    For generalizations to many unitary operators see A. Ramakrishnan, these proceedings.Google Scholar
  40. 37.
    T. S. Santhanam and A. R. Tekumalla, Found. Phys. 6, 583 (1976).ADSCrossRefGoogle Scholar
  41. T. S. Santhanam, in “Uncertainty Principle and Foundations of Quantum Mechanics” Eds. W. Price and S. S. Chissick, John Wiley, 1977. pp. 227–243.Google Scholar
  42. T. S. Santhanam, Nuovo. Cim. Lett. 20, 13 (1977).CrossRefGoogle Scholar
  43. T. S. Santhanam and K. B. Sinha, Aust. J. Phys. 31, 233 (1978).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • T. S. Santhanam
    • 1
    • 2
  1. 1.Department of Theoretical Physics Research School of Physical SciencesThe Australian National UniversityCanberraAustralia
  2. 2.The Institute of Mathematical SciencesMATSCIENCEMadrasIndia

Personalised recommendations