International Journal of Theoretical Physics

, Volume 46, Issue 10, pp 2384–2395 | Cite as

Polynomial Solution of Non-Central Potentials

Article

Abstract

We show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov–Bohm potentials as special cases. The results are in exact agreement with other methods.

Keywords

Schrödinger equation Energy eigenvalues and eigenfunctions Non-central potentials Nikiforov and Uvarov method 

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References

  1. 1.
    Kibler, M., Negadi, T.: Int. J. Quantum Chem. 26, 405 (1984) CrossRefGoogle Scholar
  2. 2.
    Sökmen, İ.: Phys. Lett. A 118, 249 (1986) CrossRefGoogle Scholar
  3. 3.
    Kibler, M., Winternitz, P.: J. Phys. A 20, 4097 (1987) CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Lutsenko, L.V., et al.: Teor. Mat. Fiz. 83, 419 (1990) Google Scholar
  5. 5.
    Hartmann, H., et al.: Theor. Chim. Acta 24, 201 (1972) CrossRefGoogle Scholar
  6. 6.
    Hartmann, H., Schuch, D.: Int. J. Quantum Chem. 18, 125 (1980) CrossRefGoogle Scholar
  7. 7.
    Carpido-Bernido, M.V., Bernido, C.C.: Phys. Lett. A 134, 315 (1989) CrossRefGoogle Scholar
  8. 8.
    Carpido-Bernido, M.V.: J. Phys. A 24, 3013 (1991) CrossRefADSGoogle Scholar
  9. 9.
    Gal’bert, O.F., Granovskii, Y.L., Zhedabov, A.S.: Phys. Lett. A 153, 177 (1991) CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Quesne, C.: J. Phys. A 21, 3093 (1988) CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Kibler, M., Negadi, T.: Phys. Lett. A 124, 42 (1987) CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Guha, A., Mukherjee, S.: J. Math. Phys. 28, 840 (1989) CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Draganescu, G.E., Campiogotto, C., Kibler, M.: Phys. Lett. A 170, 339 (1992) CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Kibler, M., Campiogotto, C.: Phys. Lett. A 181, 1 (1993) CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Villalba, V.M.: Phys. Lett. A 193, 218 (1994) MATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Aharonov, Y., Bohm, D.: Phys. Rev. 115, 485 (1959) MATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Dirac, P.A.M.: Proc. Roy. Soc. Lond. Ser. A 133, 60 (1931) MATHCrossRefADSGoogle Scholar
  18. 18.
    Mandal, B.P.: Int. J. Mod. Phys. A 15, 1225 (2000) MATHADSMathSciNetGoogle Scholar
  19. 19.
    Gönül, B., Zorba, İ., Phys. Lett. A 269, 83 (2000) MATHCrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Nikiforov, A.F., Uvarov, V.B.: Special Functions of Mathematical Physics. Birkhauser, Basel (1988) MATHGoogle Scholar
  21. 21.
    Eğrifes, H., Demirhan, D., Büyükkiliç, F.: Phys. Scr. 59, 90 (1999) CrossRefADSGoogle Scholar
  22. 22.
    Eğrifes, H., Demirhan, D., Büyükkiliç, F.: Phys. Scr. 60, 195 (1999) CrossRefADSGoogle Scholar
  23. 23.
    Eğrifes, H., Demirhan, D., Büyükkiliç, F.: Theor. Chim. Acta 98, 192 (1997) Google Scholar
  24. 24.
    Yeşiltaş, Ö., Şimşek, M., Sever, R., Tezcan, C.: Phys. Scr. 67, 472 (2003) CrossRefADSGoogle Scholar
  25. 25.
    Znojil, M.: Phys. Lett. A 264, 108 (1999) MATHCrossRefADSMathSciNetGoogle Scholar
  26. 26.
    Aktaş, M., Sever, R.: Mod. Phys. Lett. A 19, 2871 (2004) CrossRefADSGoogle Scholar
  27. 27.
    Ikhdair, S.M., Sever, R.: arXiv:quant-ph/0507272, Int. J. Theor. Phys., to appear, doi:  10.1007/s10773.006.9317-7
  28. 28.
    Ikhdair, S.M., Sever, R.: arXiv:quant-ph/0508009, J. Math. Chem., to appear, doi:  10.1007/s10910.006.9115-8
  29. 29.
    Eğrifes, H., Sever, R.: Phys. Lett. A 344, 117 (2005) CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    Yasuk, F., Durmuş, A., Boztosun, I.: J. Math. Phys. 47, 082302 (2006) CrossRefMathSciNetGoogle Scholar
  31. 31.
    Şimşek, M., Eğrifes, H.: J. Phys. A: Math. Gen. 37, 4379 (2004) CrossRefADSGoogle Scholar
  32. 32.
    Ikhdair, S.M., Sever, R.: arXiv:quant-ph/0605045, Int. J. Mod. Phys. E, accepted Google Scholar
  33. 33.
    Ikhdair, S.M., Sever, R.: Ann. Phys. (Leipzig) 16(4), 218 (2007), arXiv:quant-ph/0610183 MATHMathSciNetGoogle Scholar
  34. 34.
    Berkdemir, C., Berkdemir, A., Sever, R.: Phys. Rev. C 72, 027001 (2005) CrossRefADSGoogle Scholar
  35. 35.
    Berkdemir, C., Berkdemir, A., Sever, R.: J. Phys. A: Math. Gen. 39, 13455 (2006) MATHCrossRefADSMathSciNetGoogle Scholar
  36. 36.
    Berkdemir, C., Berkdemir, A., Sever, R.: Nucl. Phys. A 779, 32 (2005) Google Scholar
  37. 37.
    Makarov, A.A., et al.: Nuovo Cimento A 52, 1061 (1967) Google Scholar
  38. 38.
    Liboff, R.L.: Introductory Quantum Mechanics. Addison–Wesley, San Fransisco (2003) Google Scholar
  39. 39.
    Chetouani, L., Guechi, L., Hammann, T.F.: J. Math. Phys. 33, 3410 (1992) MATHCrossRefADSMathSciNetGoogle Scholar
  40. 40.
    Kibler, M., Campiogotto, C.: Int. J. Quantum Chem. 4, 209 (1993) CrossRefGoogle Scholar
  41. 41.
    Gerry, C.C.: Phys. Lett. A 118, 445 (1986) CrossRefADSMathSciNetGoogle Scholar
  42. 42.
    Hoang, L.V., et al.: J. Phys. A 25, 6461 (1992) MATHCrossRefADSGoogle Scholar
  43. 43.
    Ikhdair, S.M., Sever, R., J. Mol. Struct.: THEOCHEM 806, 155 (2007); 809, 173 (2007), arXiv:quant-ph/0611183 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsNear East UniversityNicosiaTurkey
  2. 2.Department of PhysicsMiddle East Technical UniversityAnkaraTurkey

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