The European Physical Journal A

, Volume 39, Issue 3, pp 307–314 | Cite as

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

  • S. M. Ikhdair
Regular Article - Theoretical Physics

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.

PACS

03.65.Ge Solutions of wave equations: bound states 12.39.Jh Nonrelativistic quark model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976).Google Scholar
  2. 2.
    S.M. Ikhdair, R. Sever, J. Math. Chem. 42, 461 (2007).Google Scholar
  3. 3.
    B. Gönül, O. Özer, Y. Cançelik, M. Kocak, Phys. Lett. A 275, 238 (2000)Google Scholar
  4. 4.
    M. Aktaş, R. Sever, J. Mol. Struct. 710, 219 (2004).Google Scholar
  5. 5.
    O. Bayrak, G. Kocak, I. Boztosun, J. Phys. A: Math. Gen. 39, 11521 (2006).Google Scholar
  6. 6.
    S.M. Ikhdair, arXiv:0810.1590, to be published in Int. J. Mod. Phys. C 20, issue no. 1 (2009).Google Scholar
  7. 7.
    C.-Y. Chen, F.-L. Lu, D.-S. Sun, Cent. Eur. J. Phys. 6, 884 (2008).Google Scholar
  8. 8.
    U. Myhrman, J. Phys. A: Math. Gen. 16, 263 (1983).Google Scholar
  9. 9.
    A. Bechlert, W. Bühring, J. Phys. B: At. Mol. Opt. Phys. 21, 817 (1988).Google Scholar
  10. 10.
    S.H. Dong, W.C. Qiang, G.H. Sun, V.B. Bezerra, J. Phys. A: Math. Theor. 40, 10535 (2007).Google Scholar
  11. 11.
    G.F. Wei, C.Y. Long, X.Y. Duan, S.H. Dong, Phys. Scr. 77, 035001 (2008).Google Scholar
  12. 12.
    C.Y. Chen, D.S. Sun, F.L. Lu, J. Phys. A: Math. Theor. 41, 035302 (2008).Google Scholar
  13. 13.
    L.H. Zhang, X.P. Li, C.S. Jia, Phys. Lett. A 372, 2201 (2008).Google Scholar
  14. 14.
    W.C. Qiang, S.H. Dong, Phys. Lett. A 368, 13 (2007).Google Scholar
  15. 15.
    G.F. Wei, C.Y. Long, S.H. Dong, Phys. Lett. A 372, 2592 (2008).Google Scholar
  16. 16.
    S.M. Ikhdair, R. Sever, Ann. Phys. (Berlin) 17, 897 (2008).Google Scholar
  17. 17.
    S.S. Dong, J. Garcia-Ravelo, S.H. Dong, Phys. Scr. 76, 393 (2007).Google Scholar
  18. 18.
    L. Hulthén, Ark. Mat. Astron. Fys. A 28, 5 (1942).Google Scholar
  19. 19.
    C.-S. Jia, X.-L. Zeng, L.-T. Sun, Phys. Lett. A 294, 185 (2002).Google Scholar
  20. 20.
    C.-S. Jia, Y. Li, Y. Sun, J.-Y. Liu, L.-T. Sun, Phys. Lett. A 311, 115 (2003).Google Scholar
  21. 21.
    S.M. Ikhdair, R. Sever, Int. J. Theor. Phys. 46, 1643 (2007).Google Scholar
  22. 22.
    S.M. Ikhdair, R. Sever, Ann. Phys. (Leipzig) 16, 218 (2007).Google Scholar
  23. 23.
    S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. E 17, 1107 (2008).Google Scholar
  24. 24.
    M. Şimşek, H. Eğrifes, J. Phys. A: Math. Gen. 37, 4379 (2004).Google Scholar
  25. 25.
    C.S. Lam, Y.P. Varshni, Phys. Rev. A 4, 1874 (1971).Google Scholar
  26. 26.
    B. Durand, L. Durand, Phys. Rev. D 23, 1092 (1981).Google Scholar
  27. 27.
    R.L. Hall, Phys. Rev. A 32, 14 (1985).Google Scholar
  28. 28.
    R. Dutt, K. Chowdhury, Y.P. Varshni, J. Phys. A: Math. Gen. 18, 1379 (1985)Google Scholar
  29. 29.
    T. Tietz, J. Chem. Phys. 35, 1917 (1961)Google Scholar
  30. 30.
    G. Malli, Chem. Phys. Lett. 26, 578 (1981).Google Scholar
  31. 31.
    J. Lindhard, P.G. Hansen, Phys. Rev. Lett. 57, 965 (1986).Google Scholar
  32. 32.
    I.S. Bitensky, V.K. Ferleger, I.A. Wojciechowski, Nucl. Instrum. Methods B 125, 201 (1997).Google Scholar
  33. 33.
    C.-S. Jia, J.Y. Wang, S. He, L.-T.Sun, J. Phys. A: Math. Gen. 33, 6993 (2000).Google Scholar
  34. 34.
    P. Pyykko, J. Jokisaari, Chem. Phys. 10, 293 (1975).Google Scholar
  35. 35.
    J.A. Olson, D.A. Micha, J. Chem. Phys. 68, 4352 (1978).Google Scholar
  36. 36.
    S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1974).Google Scholar
  37. 37.
    Y.P. Varshni, Phys. Rev. A 41, 4682 (1990).Google Scholar
  38. 38.
    M.A. Nunez, Phys. Rev. A 47, 3620 (1993).Google Scholar
  39. 39.
    S.H. Patil, J. Phys. A: Math. Gen. 34, 3153 (2001).Google Scholar
  40. 40.
    P. Matthys, H.D. Meyer, Phys. Rev. A 38, 1168 (1988).Google Scholar
  41. 41.
    A.Z. Tang, F.T. Chan, Phys. Rev. A 35, 911 (1987)Google Scholar
  42. 42.
    S. Haouat, L. Chetouani, Phys. Scr. 77, 025005 (2008).Google Scholar
  43. 43.
    C.-S. Jia, J.-Y. Liu, P.-Q. Wang, Phys. Lett. 372, 4779 (2008).Google Scholar
  44. 44.
    A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhauser, Bassel, 1988).Google Scholar
  45. 45.
    S.M. Ikhdair, R. Sever, Z. Phys. C 56, 155 (1992)Google Scholar
  46. 46.
    S.M. Ikhdair, Chin. J. Phys. 46, 291 (2008)Google Scholar
  47. 47.
    G.T. Einevoll, P.C. Hemmer, J. Thomson, Phys. Rev. B 42, 3485 (1990).Google Scholar
  48. 48.
    F. Dominguez-Adame, Phys. Lett. A 136, 175 (1989).Google Scholar
  49. 49.
    L. Chetouani, L. Guechi, A. Lecheheb, T.F. Hammann, A. Messouber, Physics A 234, 529 (1996).Google Scholar
  50. 50.
    B. Talukdar, A. Yunus, M.R. Amin, Phys. Lett. A 141, 326 (1989).Google Scholar
  51. 51.
    H. Eğrifes, R. Sever, Int. J. Theor. Phys. 46, 935 (2007).Google Scholar
  52. 52.
    G. Chen, Z.D. Chen, Z.M. Lou, Phys. Lett. A 331, 374 (2004).Google Scholar
  53. 53.
    X.-C. Zhang, Q.-W. Liu, C.-S. Jia, L.-Z. Wang, Phys. Lett. A 340, 59 (2005).Google Scholar
  54. 54.
    E.D Filho, R.M. Ricotta, Mod. Phys. Lett. A 10, 1613 (1995).Google Scholar
  55. 55.
    V.B. Mandelzweig, Ann. Phys. (N.Y.) 321, 2810 (2006).Google Scholar
  56. 56.
    I.S. Gradshteyn, I.M Ryzhik, Tables of Integrals, Series, and Products, 5th edition (Academic, New York, 1994).Google Scholar
  57. 57.
    G. Sezgo, Orthogonal Polynomials (American Mathematical Society, New York, 1939).Google Scholar
  58. 58.
    W. Magnus, F. Oberhettinger, R.P. Soni, Formulas and Theorems for the Special Function of Mathematical Physics, 3rd edition (Berlin, Springer, 1966).Google Scholar
  59. 59.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964)Google Scholar
  60. 60.
    S.M. Ikhdair, R. Sever, arXiv:0809.2485, submitted to Ann. Phys. (Berlin) (2008).Google Scholar
  61. 61.
    S.M. Ikhdair, R. Sever, arXiv:0807.2085, submitted to Int. J. Mod. Phys. B (2008)Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • S. M. Ikhdair
    • 1
  1. 1.Department of PhysicsNear East UniversityNicosiaTurkey

Personalised recommendations