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International Journal of Theoretical Physics

, Volume 46, Issue 8, pp 2119–2137 | Cite as

Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials

  • Ming-Guang Hu
  • Jing-Ling Chen
Article

Abstract

In this paper, we establish the underlying quantum dynamical algebra SU(1,1) for some one-dimensional exactly solvable potentials by using the shift operators method. The connection between SU(1,1) algebra and the radial Hamiltionian problems is also discussed.

Keywords

quantum dynamical algebra exactly solvable potentials 

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References

  1. Blockley, C. A., and Stedman, G. E. (1985). European Journal of Physics 6, 218.CrossRefADSGoogle Scholar
  2. Celeghini, E., Magnolley, P., Tarlini, M., and Vitiello, G. (1985). Physics Letters B 162, 133.CrossRefADSMathSciNetGoogle Scholar
  3. Chen, J. L., Liu, Y., and Ge, M. L. (1998). Journal of Physics A 31, 6473.MATHCrossRefMathSciNetGoogle Scholar
  4. Chen, J. L., Zhang, H. B., Wang, X. H., Jing, H., and Zhao, X. G. (2000). International Journal of Theoretical Physics 39, 2043–2050.MATHCrossRefMathSciNetGoogle Scholar
  5. Cooper, F., Ginocchio, J. N., and Wipf, A. (1988). Physics Letters A 129, 145 (1988).CrossRefADSMathSciNetGoogle Scholar
  6. Crawford, M. G. A., and Vrsay, E. R. (1998). Physical Review A 57, 106.CrossRefADSGoogle Scholar
  7. Díaz, J. I., Negro, J., Nieto, L. M., and Rosas-Ortiz, O. (1999). Journal of Physics A 32, 8447.MATHCrossRefGoogle Scholar
  8. Dabrowska, J., Khare, A., and Sukhatme, U. (1988). Journal of Physics A 21, L195.CrossRefADSMathSciNetGoogle Scholar
  9. De Lange, O. L., and Raab, R. E. (1991). Operator Methods in Quantum Mechanics, Clarendon Press, Oxford.Google Scholar
  10. Delbecq, C., and Quesne, C. (1993). Journal of Physics A 26, L127.MATHCrossRefADSMathSciNetGoogle Scholar
  11. Dutt, R., Khare, A., and Sukhatme, U. (1986). Physics Letters B 181, 295.CrossRefADSGoogle Scholar
  12. Dutt, R., Khare, A., and Varshni, Y. P. (1995). Journal of Physics A 28, L107.MATHCrossRefADSMathSciNetGoogle Scholar
  13. Flügge, S. (1974). Practical Quantum Mechanics, Springer Verlag, Berlin, Heidelberg, New York.Google Scholar
  14. Fukui, T., and Aizawa, N. (1993). Physics Letters A 180, 308.CrossRefADSMathSciNetGoogle Scholar
  15. Ge, M.-L., Kwek, L. C., Liu, Y., Oh, C. H., and Wang, X. B. (2000). Physical Review A 62, 052110.CrossRefADSGoogle Scholar
  16. Gendenstein, I. (1983). JETP Letters 38, 356.ADSGoogle Scholar
  17. Grosche, C. (1989). Journal of Physics A 22, 5073.MATHCrossRefMathSciNetGoogle Scholar
  18. Haymaker, R. W., and Rau, A. R. P. (1986). American Journal of Physics 54, 928.CrossRefADSGoogle Scholar
  19. Hoppe, J. (1992). Lectures on Integrable Systems, Springer Verlag, Berlin.MATHGoogle Scholar
  20. Infeld, L., and Hull, T. E. (1951). Reviews of Modern Physics 23, 21.MATHCrossRefADSMathSciNetGoogle Scholar
  21. Kamran, N., and Olver, P. J. (1990). Journal of Mathematical Analysis and Applications 145, 342.MATHCrossRefMathSciNetGoogle Scholar
  22. Khare, A., and Sukhatme, U. (1988). Journal of Physics A 21, L501.CrossRefADSMathSciNetGoogle Scholar
  23. Mielnik, B. (1984). Journal of Mathematical Physics 25, 3387.MATHCrossRefADSMathSciNetGoogle Scholar
  24. Morse, P. M. (1929). Physical Review 34, 57.CrossRefADSGoogle Scholar
  25. Natanzon, G. A. (1979). Teoreticheskaya i Matematicheskaya Fizika 38, 146.MATHMathSciNetGoogle Scholar
  26. Newmarch, J. D., and Golding, R. M. (1978). American Journal of Physics 46, 658.CrossRefADSGoogle Scholar
  27. Pöschl, G., and Teller, E. (1933). Zeitschrift für Physik 83, 143.MATHCrossRefADSGoogle Scholar
  28. Quesne, C. (1999). Journal of Physics A 32, 6705.MATHCrossRefMathSciNetGoogle Scholar
  29. Rosen, N., and Morse, P. M. (1932). Physical Review 42, 210.MATHCrossRefADSGoogle Scholar
  30. Roychoudhury, R., Roy, P., Znojil, M., and Lévai, G. (2001). Journal of Mathematical Physics 42, 1996.MATHCrossRefADSMathSciNetGoogle Scholar
  31. Spiridonov, V. (1992). Physical Review Letters 69, 398.MATHCrossRefADSMathSciNetGoogle Scholar
  32. Stahlhofen, A. (1989). Journal of Physics A 22, 1053.CrossRefMathSciNetGoogle Scholar
  33. Stahlhofen, A., and Bleuler, K. (1989). Nuovo Cimento B 104, 447.ADSMathSciNetGoogle Scholar
  34. Sukumar, C. V. (1980). Journal of Physics A 19, 2297.CrossRefMathSciNetGoogle Scholar
  35. Wehrhahn, R. F. (1992). Journal of Mathematical Physics 33, 174.CrossRefADSMathSciNetGoogle Scholar
  36. Znojil, M., Lévai, G., Roy, P., and Roychoudhury, R. (2001). Physics Letters B 290, 249.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Theoretical Physics DivisionChern Institute of Mathematics, Nankai UniversityTianjinP. R. China

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