Skip to main content
SpringerLink
Log in

An improved approximation scheme for the centrifugal term and the Hulthén potential

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

We present a new approximation scheme for the centrifugal term to solve the Schrödinger equation with the Hulthén potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s -wave (l = 0analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. S.M. Ikhdair, R. Sever, J. Math. Chem. 42, 461 (2007).

    Google Scholar 

  3. B. Gönül, O. Özer, Y. Cançelik, M. Kocak, Phys. Lett. A 275, 238 (2000)

    Google Scholar 

  4. M. Aktaş, R. Sever, J. Mol. Struct. 710, 219 (2004).

    Google Scholar 

  5. O. Bayrak, G. Kocak, I. Boztosun, J. Phys. A: Math. Gen. 39, 11521 (2006).

    Google Scholar 

  6. S.M. Ikhdair, arXiv:0810.1590, to be published in Int. J. Mod. Phys. C 20, issue no. 1 (2009).

  7. C.-Y. Chen, F.-L. Lu, D.-S. Sun, Cent. Eur. J. Phys. 6, 884 (2008).

    Google Scholar 

  8. U. Myhrman, J. Phys. A: Math. Gen. 16, 263 (1983).

    Google Scholar 

  9. A. Bechlert, W. Bühring, J. Phys. B: At. Mol. Opt. Phys. 21, 817 (1988).

    Google Scholar 

  10. S.H. Dong, W.C. Qiang, G.H. Sun, V.B. Bezerra, J. Phys. A: Math. Theor. 40, 10535 (2007).

    Google Scholar 

  11. G.F. Wei, C.Y. Long, X.Y. Duan, S.H. Dong, Phys. Scr. 77, 035001 (2008).

    Google Scholar 

  12. C.Y. Chen, D.S. Sun, F.L. Lu, J. Phys. A: Math. Theor. 41, 035302 (2008).

    Google Scholar 

  13. L.H. Zhang, X.P. Li, C.S. Jia, Phys. Lett. A 372, 2201 (2008).

    Google Scholar 

  14. W.C. Qiang, S.H. Dong, Phys. Lett. A 368, 13 (2007).

    Google Scholar 

  15. G.F. Wei, C.Y. Long, S.H. Dong, Phys. Lett. A 372, 2592 (2008).

    Google Scholar 

  16. S.M. Ikhdair, R. Sever, Ann. Phys. (Berlin) 17, 897 (2008).

    Google Scholar 

  17. S.S. Dong, J. Garcia-Ravelo, S.H. Dong, Phys. Scr. 76, 393 (2007).

    Google Scholar 

  18. L. Hulthén, Ark. Mat. Astron. Fys. A 28, 5 (1942).

    Google Scholar 

  19. C.-S. Jia, X.-L. Zeng, L.-T. Sun, Phys. Lett. A 294, 185 (2002).

    Google Scholar 

  20. C.-S. Jia, Y. Li, Y. Sun, J.-Y. Liu, L.-T. Sun, Phys. Lett. A 311, 115 (2003).

    Google Scholar 

  21. S.M. Ikhdair, R. Sever, Int. J. Theor. Phys. 46, 1643 (2007).

    Google Scholar 

  22. S.M. Ikhdair, R. Sever, Ann. Phys. (Leipzig) 16, 218 (2007).

    Google Scholar 

  23. S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. E 17, 1107 (2008).

    Google Scholar 

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

    Google Scholar 

  25. C.S. Lam, Y.P. Varshni, Phys. Rev. A 4, 1874 (1971).

    Google Scholar 

  26. B. Durand, L. Durand, Phys. Rev. D 23, 1092 (1981).

    Google Scholar 

  27. R.L. Hall, Phys. Rev. A 32, 14 (1985).

    Google Scholar 

  28. R. Dutt, K. Chowdhury, Y.P. Varshni, J. Phys. A: Math. Gen. 18, 1379 (1985)

    Google Scholar 

  29. T. Tietz, J. Chem. Phys. 35, 1917 (1961)

  30. G. Malli, Chem. Phys. Lett. 26, 578 (1981).

    Google Scholar 

  31. J. Lindhard, P.G. Hansen, Phys. Rev. Lett. 57, 965 (1986).

    Google Scholar 

  32. I.S. Bitensky, V.K. Ferleger, I.A. Wojciechowski, Nucl. Instrum. Methods B 125, 201 (1997).

    Google Scholar 

  33. C.-S. Jia, J.Y. Wang, S. He, L.-T.Sun, J. Phys. A: Math. Gen. 33, 6993 (2000).

    Google Scholar 

  34. P. Pyykko, J. Jokisaari, Chem. Phys. 10, 293 (1975).

    Google Scholar 

  35. J.A. Olson, D.A. Micha, J. Chem. Phys. 68, 4352 (1978).

    Google Scholar 

  36. S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1974).

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

    Google Scholar 

  38. M.A. Nunez, Phys. Rev. A 47, 3620 (1993).

    Google Scholar 

  39. S.H. Patil, J. Phys. A: Math. Gen. 34, 3153 (2001).

    Google Scholar 

  40. P. Matthys, H.D. Meyer, Phys. Rev. A 38, 1168 (1988).

    Google Scholar 

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

    Google Scholar 

  42. S. Haouat, L. Chetouani, Phys. Scr. 77, 025005 (2008).

    Google Scholar 

  43. C.-S. Jia, J.-Y. Liu, P.-Q. Wang, Phys. Lett. 372, 4779 (2008).

    Google Scholar 

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

  45. S.M. Ikhdair, R. Sever, Z. Phys. C 56, 155 (1992)

    Google Scholar 

  46. S.M. Ikhdair, Chin. J. Phys. 46, 291 (2008)

    Google Scholar 

  47. G.T. Einevoll, P.C. Hemmer, J. Thomson, Phys. Rev. B 42, 3485 (1990).

    Google Scholar 

  48. F. Dominguez-Adame, Phys. Lett. A 136, 175 (1989).

    Google Scholar 

  49. L. Chetouani, L. Guechi, A. Lecheheb, T.F. Hammann, A. Messouber, Physics A 234, 529 (1996).

    Google Scholar 

  50. B. Talukdar, A. Yunus, M.R. Amin, Phys. Lett. A 141, 326 (1989).

    Google Scholar 

  51. H. Eğrifes, R. Sever, Int. J. Theor. Phys. 46, 935 (2007).

    Google Scholar 

  52. G. Chen, Z.D. Chen, Z.M. Lou, Phys. Lett. A 331, 374 (2004).

    Google Scholar 

  53. X.-C. Zhang, Q.-W. Liu, C.-S. Jia, L.-Z. Wang, Phys. Lett. A 340, 59 (2005).

    Google Scholar 

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

    Google Scholar 

  55. V.B. Mandelzweig, Ann. Phys. (N.Y.) 321, 2810 (2006).

    Google Scholar 

  56. I.S. Gradshteyn, I.M Ryzhik, Tables of Integrals, Series, and Products, 5th edition (Academic, New York, 1994).

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

  58. W. Magnus, F. Oberhettinger, R.P. Soni, Formulas and Theorems for the Special Function of Mathematical Physics, 3rd edition (Berlin, Springer, 1966).

  59. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964)

  60. S.M. Ikhdair, R. Sever, arXiv:0809.2485, submitted to Ann. Phys. (Berlin) (2008).

  61. S.M. Ikhdair, R. Sever, arXiv:0807.2085, submitted to Int. J. Mod. Phys. B (2008)

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Near East University, Nicosia, North Cyprus, Turkey

    S. M. Ikhdair

Authors
  1. S. M. Ikhdair
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

B. Ananthanarayan

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ikhdair, S.M. An improved approximation scheme for the centrifugal term and the Hulthén potential. Eur. Phys. J. A 39, 307–314 (2009). https://doi.org/10.1140/epja/i2008-10715-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epja/i2008-10715-2

PACS

Search

Navigation