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Approximate Eigenvalue and Eigenfunction Solutions for the Generalized Hulthén Potential with any Angular Momentum

An approximate solution of the Schrödinger equation for the generalized Hulthén potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov–Uvarov method is used in the computations. We have considered the time-independent Schrödinger equation with the associated form of Hulthén potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthén potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthén effective potential.

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References

  1. Hulthén L., Ark. Mat. Astron. Fys. 28 A (1942) 5; ibid., Ark. Mat. Astron. Fys. 29 B (1942) 1.

  2. Eckart C.,(1930). Phys. Rev 35: 1303

    Article  CAS  Google Scholar 

  3. Varshni Y.P., (1990). Phys. Rev A 41: 4682

    Article  CAS  Google Scholar 

  4. Lam C.S., Varshni Y.P., (1971). Phys. Rev. A 4: 1875

    Article  Google Scholar 

  5. Flügge S., (1974). Practical Quantum Mechanics. Springer-Verlag, Berlin

    Google Scholar 

  6. C.Lai S., Lim W.C., (1980). Phys. Lett. A 78: 335

    Article  Google Scholar 

  7. Dutt R., Mukherji U., (1982). Phys. Lett, A 90: 395

    Article  Google Scholar 

  8. Patil S.H., (1984). J. Phys. A 17: 575

    Article  CAS  Google Scholar 

  9. Popov V.S., Weiberg V.M., (1985). Phys. Lett. A 107: 371

    Article  Google Scholar 

  10. Roy B., Roychoudhury R., (1987). J. Phys. A 20: 3051

    Article  Google Scholar 

  11. Tang A.Z., Chan F.T., (1987). Phys. Rev. A 35: 911

    Article  Google Scholar 

  12. Lai C.H., (1987). J. Math. Phys 28: 1801

    Article  CAS  Google Scholar 

  13. Matthys P., De H., (1988). Phys. Rev. A 38: 1168

    Article  Google Scholar 

  14. Laha U., Bhattacharyya C., Roy K., Talukdar B., (1988). Phys. Rev. C 38: 558

    Article  CAS  Google Scholar 

  15. Talukdar B., Das U., Bhattacharyya C., Bera P.K., (1992). J. Phys. A 25: 4073

    Article  Google Scholar 

  16. Filho E.D., Ricotta R.M., (1995). Mod. Phys. Lett. A 10: 1613

    Article  Google Scholar 

  17. Cooper F., Khare A., Sukhatme U., (1995). Phys. Rep 251: 267

    Article  CAS  Google Scholar 

  18. Gönül B., Özer O., Cançelik Y., Koçak M., (2000). Phys. Lett. A 275: 238

    Article  Google Scholar 

  19. Nikiforov A.F., Uvarov V.B., (1988). Special Functions of Mathematical Physics. Birkhauser, Basel

    Google Scholar 

  20. Yeşiltaş Ö., Şimşek M., Sever R., Tezcan C., (2003). Physica Scripta 67: 472

    Article  Google Scholar 

  21. Berkdemir C., Berkdemir A., Sever R., Phys. Rev. C 72 (2005) 027001; Berkdemir A., Berkdemir C., R. Sever [arXiv:quant-ph/0410153].

  22. Berkdemir C., Han J., Chem. Phys. Lett. 409 (2005) 203; Berkdemir C., Berkdemir A., Han J., Chem. Phys. Letters 417 (2006) 326

  23. M. Aktaş and Sever R., J. Math. Chem. 37 (2005) 139; Faridfathi G., Sever R., Metin Aktaş, J. Math. Chem. 38 (2005) 533

  24. Greene R.L., Aldrich C., (1976). Phys. Rev. A 14: 2363

    Article  Google Scholar 

  25. Şimşek M., Eğrifes H., (2004). J. Phys. A. Math. Gen 37: 4379

    Article  Google Scholar 

  26. Gendenshtein L., (1983). JETP Lett 38: 356

    Google Scholar 

  27. Filho E.D., Ricotta R.M., (1995). Mod. Phys. Lett. A10: 1613

    Article  Google Scholar 

  28. Sezgo G., (1939). Orthogonal Polynomials. American Mathematical Society, New York

    Google Scholar 

  29. Ikhdair S.M., Sever R., To appear in Phys. Rev. C.

  30. Aktaş M., Sever R., (2004). J. Molec. Struc 710: 219

    Google Scholar 

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Correspondence to Sameer M. Ikhdair.

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Ikhdair, S.M., Sever, R. Approximate Eigenvalue and Eigenfunction Solutions for the Generalized Hulthén Potential with any Angular Momentum. J Math Chem 42, 461–471 (2007). https://doi.org/10.1007/s10910-006-9115-8

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  • DOI: https://doi.org/10.1007/s10910-006-9115-8

Keywords

  • energy eigenvalues and eigenfunctions
  • Hulthén potential
  • Nikiforov–Uvarov method

Pacs Number(s)

  • 03.65.-w;02.30.Gp
  • 03.65.Ge
  • 68.49.-h
  • 24.10.Ht
  • 03.65.Db
  • 12.39. Pn
  • 71.15.Dx
  • 02.30.Fn