Analytic Coherent States for Generalized Potentials

  • Michael Martin Nieto
  • L. M. SimmonsJr.


This is work(1,2) which I (MMN) and Mike Simmons have been doing at Los Alamos.† It’s hopefully going to be short, sweet, and to the point. I have divided the talk into sections. In Section 2 I’m going to review in some detail the properties of the coherent states for the harmonic oscillator. Then (in Section 3) I’m going to describe what I will call the “classical motion generalization.” By that I mean I will define “coherent states” not only for the simple harmonic oscillator but for particles in different potentials. These coherent states should follow the classical motion of a particle in such a classical potential. Finally, to show that our proposed generalization is indeed a good one, I am going to present in Section 4 a specific example which we have analytically beaten to death, and then close with a discussion.


Harmonic Oscillator Coherent State Classical Motion Associate Legendre Function Simple Harmonic Oscillator 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and Notes

  1. 1.
    M. M. Nieto and L. M. Simmons, Jr., Phys. Rev. Lett. 41, 207 (1978).ADSCrossRefGoogle Scholar
  2. 2.
    M. M. Nieto and L. M. Simmons, Jr., Phys. Rev. A 19, 438 (1979).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    A. O. Barut and L. Girardello, Commun. Math. Phys. 21, 41 (1971).MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    M. Perelomov, Commun. Math. Phys. 26, 222 (1972)MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. M. Perelomov, Usp. Fiz. Nauk 123, 23 (1977)CrossRefGoogle Scholar
  6. M. Perelomov, [English translation in Soy. Phys. Usp. 20, 703 (1977)].ADSCrossRefGoogle Scholar
  7. 5.
    E. Schrödinger, Naturwissenschaften 14, 664 (1926).ADSzbMATHCrossRefGoogle Scholar
  8. 6.
    J. Mostowski, Lett. Math. Phys. 2, 1 (1977).MathSciNetADSCrossRefGoogle Scholar
  9. 7.
    N. Rosen and P. M. Morse, Phys. Rev. 42, 210 (1932).ADSCrossRefGoogle Scholar
  10. 8.
    M. M. Nieto, Phys. Rev. A 17, 1273 (1978).ADSCrossRefGoogle Scholar
  11. 9.
    L. Infeld and T. E. Hull, Rev. Mod. Phys. 23, 21 (1951).MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. 10.
    R. B. Walker and R. K. Preston, J. Chem. Phys. 67, 2017 (1977).MathSciNetADSCrossRefGoogle Scholar
  13. 11.
    V. P. Gutschick, M. M. Nieto, and F. Baker, Time evolution of coherent states for general potentials, movie (13 min., 16 mm, color, sound) available for $130 from Cinesound Co., 915 N. Highland Ave., Hollywood, California 90038. A review of this film is given in C. A. Nelson, Am. J. Phys. 47, 755 (1979).ADSCrossRefGoogle Scholar
  14. 12.
    A detailed series of articles on the work started in References 1 and 2 is in progress. See M. M. Nieto and L. M. Simmons, Jr., Phys. Rev. D 20, 1321, 1332, 1342 (1979)Google Scholar
  15. M. M. Nieto, Los Alamos preprint LA-UR-79–2101Google Scholar
  16. V. P. Gutschick and M. M. Nieto, Los Mamas preprint LA-UR-79–2925Google Scholar
  17. M. M. Nieto, L. M. Simmons, Jr., and V. P. Gutschick, Los Alamos preprint (in preparation).Google Scholar
  18. 13.
    C. Aragone, G. Guerri, S. Salamô, and J. L. Tani, J. Phys. A 7, L149 (1974)ADSCrossRefGoogle Scholar
  19. H. Bacry, Phys. Rev. A 18, 617 (1978).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Michael Martin Nieto
    • 1
  • L. M. SimmonsJr.
    • 1
  1. 1.Theoretical Division, Los Alamos Scientific LaboratoryUniversity of CaliforniaLos AlamosUSA

Personalised recommendations