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Complete non-relativistic bound state solutions of the Tietz-Wei potential via the path integral approach

  • A. Khodja
  • A. Kadja
  • F. Benamira
  • L. GuechiEmail author
Regular Article

Abstract.

In this work, the bound state problem of some diatomic molecules in the Tietz-Wei potential with varying shapes is correctly solved by means of path integrals. Explicit path integration leads to the radial Green’s function in closed form for three different shapes of this potential. In each case, the energy equation and the wave functions are obtained from the poles of the radial Green’s function and their residues, respectively. Our results prove the importance of the optimization parameter ch in the study of this potential which has been completely ignored by the authors of the papers cited below. In the limit \( c_{h}\rightarrow 0\), the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.

References

  1. 1.
    T. Tietz, J. Chem. Phys. 38, 3036 (1963)ADSCrossRefGoogle Scholar
  2. 2.
    H. Wei, Phys. Rev. A 42, 2524 (1990)ADSCrossRefGoogle Scholar
  3. 3.
    G.A. Natanson, Phys. Rev. A 44, 3377 (1991)ADSCrossRefGoogle Scholar
  4. 4.
    J.A. Kunc, F.J. Gordillo-Vasquez, J. Phys. Chem. A 101, 1595 (1997)CrossRefGoogle Scholar
  5. 5.
    F.J. Gordillo-Vasquez, J.A. Kunc, J. Mol. Struct. (Theochem) 425, 263 (1998)CrossRefGoogle Scholar
  6. 6.
    M. Hamzavi, A.A. Rajabi, H. Hassanabadi, Mol. Phys. 110, 389 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    M. Hamzavi, A.A. Rajabi, K.E. Thylwe, Int. J. Quantum Chem. 112, 2701 (2012)CrossRefGoogle Scholar
  8. 8.
    C.L. Pekeris, Phys. Rev. 45, 98 (1934)ADSCrossRefGoogle Scholar
  9. 9.
    B.J. Falaye, K.J. Oyewumi, S.M. Ikhdair, M. Hamzavi, Phys. Scr. 89, 115204 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    D. Mikulski, M. Molski, J. Konarski, K. Eder, J. Math. Chem. 52, 162 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    B.J. Falaye, S.M. Ikhdair, M. Hamzavi, J. Math. Chem. 53, 1325 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    B.J. Falaye, S.M. Ikhdair, M. Hamzavi, J. Theor. Appl. Phys. 9, 151 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    H. Hassanabadi, B.H. Yazarloo, S. Zarrinkamar, M. Solaimani, Int. J. Quantum Chem. 112, 3706 (2012)CrossRefGoogle Scholar
  14. 14.
    A. Khodja, A. Kadja, F. Benamira, L. Guechi, Indian J. Phys. 91, 1561 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    D. Peak, A. Inomata, J. Math. Phys. 10, 1422 (1969)ADSCrossRefGoogle Scholar
  16. 16.
    A. Arai, J. Math. Anal. Appl. 158, 63 (1991)MathSciNetCrossRefGoogle Scholar
  17. 17.
    A. Arai, J. Phys. A 34, 4281 (2001)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    C.S. Jia, J.Y. Liu, P.Q. Wang, Phys. Lett. A 372, 4779 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976)ADSCrossRefGoogle Scholar
  20. 20.
    M.F. Manning, N. Rosen, Phys. Rev. 44, 953 (1933)Google Scholar
  21. 21.
    C. Grosche, J. Phys. A 38, 2947 (2005)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    A. Khodja, F. Benamira, L. Guechi, J. Math. Phys. 91, 1561 (2017)Google Scholar
  23. 23.
    C. Grosche, Phys. Rev. Lett. 71, 1 (1993)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    F. Benamira, L. Guechi, S. Mameri, M.A. Sadoun, J. Math. Phys. 48, 032102 (2007)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    F. Benamira, L. Guechi, S. Mameri, M.A. Sadoun, J. Math. Phys. 51, 032301 (2010)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    N. Rosen, P.M. Morse, Phys. Rev. 42, 210 (1932)ADSCrossRefGoogle Scholar
  27. 27.
    H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets, 5th ed. (World Scientific, Singapore, 2009)Google Scholar
  28. 28.
    P.M. Morse, Phys. Rev. 34, 57 (1929)ADSCrossRefGoogle Scholar
  29. 29.
    L.D. Landau, E.M. Lifchitz, Quantum Mechanics (Pergamon, Oxford, 1958)Google Scholar
  30. 30.
    S. Flügge, Practical Quantum Mechanics (Springer Verlag, Berlin, 1974)Google Scholar
  31. 31.
    A. Khodja, F. Benamira, L. Guechi, Int. J. Quantum Chem. 117, 5 (2017)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences ExactesUniversité des frères MentouriConstantineAlgeria

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