Bulletin of the Korean Chemical Society

Korean Chemical Society (대한화학회)
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Phase Shifts of Bound State Waves Scattered at Classical Turning Points: Morse Potential

  • Sun, Ho-Sung (Department of Chemistry and School of Molecular Science (BK21), Sungkyunkwan University)
  • Published : 2005.11.20
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Abstract

The analytical transfer matrix method suggests a new quantization condition for calculating bound state eigenenergies exactly. In the quantization condition, the phase shifts of bound state wave functions scattered at classical turning points are explicitly introduced. We calculate the phase shifts of eigenfunctions of the Morse potential with various boundary conditions in order to understand the physical meaning of phase shifts. The Morse potential is known to adequately describe the interaction energy between two atoms and, therefore, it is frequently used to determine the vibrational energy levels of diatomic molecules. The variation of Morse potential eigenenergies influenced upon by changing boundary conditions is also investigated.

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References

  1. Morse, P. M. Phys. Rev. 1929, 34, 57 https://doi.org/10.1103/PhysRev.34.57
  2. Herzberg, G. Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules; Van Nostrand Reinhold: New York, 1950
  3. Dong, S.; Lemus, R.; Frank, A. Int. J. Quantum Chem. 2002, 86, 433 https://doi.org/10.1002/qua.10038
  4. Molnar, B.; Foldi, P.; Benedict, M. G.; Bartha, F. Europhys. Lett. 2003, 61, 445 https://doi.org/10.1209/epl/i2003-00328-9
  5. Cho, S.; Sun, H. Chem. Phys. Lett. 2003, 377, 406 https://doi.org/10.1016/S0009-2614(03)01204-1
  6. Cho, S.; Sun, H. Bull. Korean Chem. Soc. 2004, 25, 1397 https://doi.org/10.1007/s11814-008-0229-5
  7. Cho, S.; Sun, H. Chem. Phys. 2004, 304, 281 https://doi.org/10.1016/j.chemphys.2004.07.016
  8. Morse, P. M.; Feshbach, H. Methods of Theoretical Physics; McGraw-Hill: New York, 1953; Vol. II
  9. Zhou, F.; Cao, Z.; Shen, Q. Phys. Rev. A 2003, 67, 062112 https://doi.org/10.1103/PhysRevA.67.062112
  10. Ou, Y. C.; Cao, Z.; Shen, Q. J. Chem. Phys. 2004, 121, 8175 https://doi.org/10.1063/1.1799015
  11. Ou, Y. C.; Cao, Z.; Shen, Q. Phys. Lett. A 2003, 318, 36 https://doi.org/10.1016/j.physleta.2003.09.026
  12. He, Y.; Cao, Z.; Shen, Q. Phys. Lett. A 2004, 326, 315 https://doi.org/10.1016/j.physleta.2004.04.051
  13. Froman, N.; Froman, P. O. JWKB Approximation; North Holland: Amsterdam, 1965
  14. Friedrich, H.; Trost, J. Phys. Rep. 2004, 397, 359 https://doi.org/10.1016/j.physrep.2004.04.001
  15. Hruska, M.; Keung, W.-Y.; Sukhatme, U. Phys. Rev. A 1997, 55, 3345 https://doi.org/10.1103/PhysRevA.55.3345
  16. 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
  17. Jia, C.-S.; Wang, J.-Y.; He, S.; Sun, L.-T. J. Phys. A: Math. Gen.2000, 33, 5045
  18. Ivanov, I. A. J. Phys. A: Math. Gen. 1997, 30, 3977 https://doi.org/10.1088/0305-4470/30/11/024
  19. Friedrich, H.; Trost, J. Phys. Rev. Lett. 1996, 26, 4869
  20. Friedrich, H.; Trost, J. Phys. Rev. A 1996, 54, 1136 https://doi.org/10.1103/PhysRevA.54.1136
  21. Comet, A.; Bandurak, A.; Campbell, D. K. Phys. Lett. B 1985, 150, 159 https://doi.org/10.1016/0370-2693(85)90160-1
  22. Khare, A. Phys. Lett. B 1985, 161, 131 https://doi.org/10.1016/0370-2693(85)90623-9
  23. Ter Harr, D. Phys. Rev. 1946, 70, 222 https://doi.org/10.1103/PhysRev.70.222
  24. Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979
  25. Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions; Wiley: New York, 1972
  26. Morse, P. M.; Fisk, J. B.; Schiff, L. I. Phys. Rev. 1936, 50, 748 https://doi.org/10.1103/PhysRev.50.748
  27. Sun, H. Phys. Lett. A 2005, 338, 309 https://doi.org/10.1016/j.physleta.2005.02.054
  28. Cooper, F.; Khare, A.; Sukhatme, U. P. Phys. Rep. 1995, 251, 267 https://doi.org/10.1016/0370-1573(94)00080-M
  29. Cooper, F.; Khare, A.; Sukhatme, U. P. Supersymmetry in Quantum Mechanics; World Scientific: Singapore, 2001
  30. Guerin, H. Chem. Phys. Lett. 1996, 262, 759 https://doi.org/10.1016/S0009-2614(96)01142-6

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