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The Analytical Transfer Matrix Method Combined with Supersymmetry: Coulomb Potential

  • Sun, Ho-Sung (Department of Chemistry, Sungkyunkwan University)
  • Published : 2007.03.20

Abstract

Combining the analytical transfer matrix method with supersymmetry algebra, a new quantization condition is suggested. To demonstrate the efficiency of the new quantization condition, the eigenenergies of the Coulomb potential are analytically derived. The scattering-led phase shifts are also determined and they are the same for all Coulomb potential states. It is found that the new quantization condition is mathematically simple and exact.

Keywords

References

  1. Ou, Y. C.; Cao, Z.; Shen, Q. J. Chem. Phys. 2004, 121, 8175 https://doi.org/10.1063/1.1799015
  2. Froman, N.; Froman, P. O. JWKB Approximation; North Holland: Amsterdam, 1965
  3. Friedrich, H.; Trost, J. Phys. Rep. 2004, 397, 359 https://doi.org/10.1016/j.physrep.2004.04.001
  4. Cao, Z.; Jiang, Y.; Shen, Q.; Dou, X.; Chen, Y. J. Opt. Soc. Am. A 1999, 16, 2209 https://doi.org/10.1364/JOSAA.16.002209
  5. Cao, Z.; Liu, Q.; Shen, Q.; Dou, X.; Chen, Y.; Ozaki, Y. Phys. Rev. A 2001, 63, 054103 https://doi.org/10.1103/PhysRevA.63.054103
  6. Ou, Y. C.; Cao, Z.; Shen, Q. Phys. Lett. A 2003, 318, 36 https://doi.org/10.1016/j.physleta.2003.09.026
  7. Zhou, F.; Cao, Z.; Shen, Q. Phys. Rev. A 2003, 67, 062112 https://doi.org/10.1103/PhysRevA.67.062112
  8. He, Y.; Cao, Z.; Shen, Q. Phys. Lett. A 2004, 326, 315 https://doi.org/10.1016/j.physleta.2004.04.051
  9. Sun, H. Phys. Lett. A 2005, 338, 309 https://doi.org/10.1016/j.physleta.2005.02.054
  10. Bijker, R.; Castanos, O.; Urrutia, L.; Fernandez, D.; Morales-Tecoti, H.; Villarreal, C. Supersymmetries in Physics and Its Applications (AIP Conf. Proc. Vol. 744); Springer-Verlag: New York, 2005
  11. Cooper, F.; Khare, A.; Sukhatme, U. P. Supersymmetry in Quantum Mechanics; World Scientific: Singapore, 2001
  12. Cooper, F.; Khare, A.; Sukhatme, U. P. Phys. Rep. 1995, 251, 267 https://doi.org/10.1016/0370-1573(94)00080-M
  13. Levine, I. N. Quantum Chemistry, 5th ed.; Prentice Hall: Upper Saddle River, New Jersey, 2000
  14. Chenaghlou, A.; Fakhri, H. Int. J. Quantum Chem. 2005, 101, 291 https://doi.org/10.1002/qua.20276
  15. Hruska, M.; Keung, W.-Y.; Sukhatme, U. Phys. Rev. A 1997, 55, 3345
  16. Sun, H. Bull. Korean Chem. Soc. 2006, 27, 515 https://doi.org/10.5012/bkcs.2006.27.4.515
  17. Kostelecký, V. A.; Nieto, M. M. Phys. Rev. Lett. 1984, 53, 2285 https://doi.org/10.1103/PhysRevLett.53.2285
  18. Gradshteyn, I. S.; Ryzhik, I. M. Tables of Integrals, Series, and Products; Academic Press: New York, 1965
  19. Sun, H. Bull. Korean Chem. Soc. 2005, 26, 1717 https://doi.org/10.5012/bkcs.2005.26.11.1717
  20. Sun, H. to be published
  21. Jia, C.-S.; Wang, J.-Y.; He, S.; Sun, L.-T. J. Phys. A: Math. Gen. 2000, 33, 5045
  22. Ivanov, I. A. J. Phys. A: Math. Gen. 1997, 30, 3977 https://doi.org/10.1088/0305-4470/30/11/024
  23. Haymaker, R. W.; Rau, A. R. P. Am. J. Phys. 1986, 54, 928 https://doi.org/10.1119/1.14794
  24. Lahiri, A.; Roy, P. K.; Bagchi, B. Int. J. Mod. Phys. 1990, 5, 1383 https://doi.org/10.1142/S0217751X90000647

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