Analytic Coherent States for Generalized Potentials
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.
KeywordsHarmonic Oscillator Coherent State Classical Motion Associate Legendre Function Simple Harmonic Oscillator
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References and Notes
- 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
- 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
- M. M. Nieto, Los Alamos preprint LA-UR-79–2101Google Scholar
- V. P. Gutschick and M. M. Nieto, Los Mamas preprint LA-UR-79–2925Google Scholar
- M. M. Nieto, L. M. Simmons, Jr., and V. P. Gutschick, Los Alamos preprint (in preparation).Google Scholar