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The Classical Limit of the Quantum Kepler Problem
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México D.F., México
Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Básicas, Cunduacán, México
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México D.F., México;Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México D.F., México
Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Básicas, Cunduacán, México
- 1 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México D.F., México
- 2 Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Básicas, Cunduacán, México
- 3 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México D.F., México;Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México D.F., México
- 4 Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Básicas, Cunduacán, México
Journal of Modern Physics·Volume 04 (2013)·Pages 818–822·Published 13 June 2013·DOI10.4236/jmp.2013.46112
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Abstract
The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck ’s limit and Bohr ’s correspon dence principle. We discuss the confinement effect in macroscopic systems.
KeywordsKepler ProblemClassical Limits
- A. J. Makowski, European Journal of Physics, Vol. 27, 2006, pp. 1133-1139. doi:10.1088/0143-0807/27/5/012
- L. E. Ballentine, “Quantum Mechanics: A Modern Development,” World Scientific, New York, 1998.
- L. E. Ballentine, Y. M. Yang and J. P. Zibin, Physical Review A, Vol. 50, 1994, pp. 2854-2859. doi:10.1103/PhysRevA.50.2854
- M. Berry, Physica Scripta, Vol. 40, 1989, pp. 335-336. doi:10.1088/0031-8949/40/3/013
- L. S. Brown, American Journal of Physics, Vol. 40, 1972, pp. 371-376. doi:10.1119/1.1986554
- L. S. Brown, American Journal of Physics, Vol. 41, 1973, pp. 525-530. doi:10.1119/1.1987282
- D. Bhaumik, B. Dutta-Roy and G. Ghosh, Journal of Physics A: Mathematical and General, Vol. 19, 1986, pp. 1355-1364. doi:10.1088/0305-4470/19/8/017
- S. Nandi and C. S. Shastry, Journal of Physics A: Mathematical and General, Vol. 22, 1989, pp. 1005-1016. doi:10.1088/0305-4470/22/8/016
- G. Yoder, American Journal of Physics, Vol. 74, 2006, p. 404. doi:10.1119/1.2173280
- R. W. Robinett, American Journal of Physics, Vol. 63, 1995, pp. 823-832. doi:10.1119/1.17807
- E. G. P. Rowe, European Journal of Physics, Vol. 8, 1987, pp. 81-87. doi:10.1088/0143-0807/8/2/002
- A. R. Edmonds, “Angular Momentum in Quantum Mechanics,” Princeton University Press, Princeton, 1974.
- J. Bernal, A. Martn-Ruiz and J. Garca-Melgarejo, Journal of Modern Physics, Vol. 4, 2013, pp. 108-112. doi:10.4236/jmp.2013.41017
- H. Goldstein, C. P. Poole and J. P. Safko, “Classical Mechanics,” Addison-Wesley, San Francisco, 2002.
- R. Liboff, “Introductory Quantum Mechanics,” 4th Edition, Addison-Wesley, Boston, 2002.
- H. M. Srivastava, H. A. Mavromatis and R. S. Alassar, Applied Mathematics Letters, Vol. 16, 2003, pp. 1131-1136. doi:10.1016/S0893-9659(03)90106-6
- A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, “Integrals and Series, Vol. 3: More Special Functions,” Gordon and Breach Science Publishers, New York, 1989.
- L. J. Slater, “Generalized Hypergeometric Functions,” Cambridge University Press, Cambridge, 2008.
- M. Abramowitz and I. Stegun, “Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables,” Dover Publications, New York, 1965.