Skip to main content
SpringerLink
Log in

Polynomial Solution of Non-Central Potentials

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

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.

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. Kibler, M., Negadi, T.: Int. J. Quantum Chem. 26, 405 (1984)

    Article  Google Scholar 

  2. Sökmen, İ.: Phys. Lett. A 118, 249 (1986)

    Article  Google Scholar 

  3. Kibler, M., Winternitz, P.: J. Phys. A 20, 4097 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  4. Lutsenko, L.V., et al.: Teor. Mat. Fiz. 83, 419 (1990)

    Google Scholar 

  5. Hartmann, H., et al.: Theor. Chim. Acta 24, 201 (1972)

    Article  Google Scholar 

  6. Hartmann, H., Schuch, D.: Int. J. Quantum Chem. 18, 125 (1980)

    Article  Google Scholar 

  7. Carpido-Bernido, M.V., Bernido, C.C.: Phys. Lett. A 134, 315 (1989)

    Article  Google Scholar 

  8. Carpido-Bernido, M.V.: J. Phys. A 24, 3013 (1991)

    Article  ADS  Google Scholar 

  9. Gal’bert, O.F., Granovskii, Y.L., Zhedabov, A.S.: Phys. Lett. A 153, 177 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  10. Quesne, C.: J. Phys. A 21, 3093 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  11. Kibler, M., Negadi, T.: Phys. Lett. A 124, 42 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  12. Guha, A., Mukherjee, S.: J. Math. Phys. 28, 840 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  13. Draganescu, G.E., Campiogotto, C., Kibler, M.: Phys. Lett. A 170, 339 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  14. Kibler, M., Campiogotto, C.: Phys. Lett. A 181, 1 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  15. Villalba, V.M.: Phys. Lett. A 193, 218 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Aharonov, Y., Bohm, D.: Phys. Rev. 115, 485 (1959)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. Dirac, P.A.M.: Proc. Roy. Soc. Lond. Ser. A 133, 60 (1931)

    Article  MATH  ADS  Google Scholar 

  18. Mandal, B.P.: Int. J. Mod. Phys. A 15, 1225 (2000)

    MATH  ADS  MathSciNet  Google Scholar 

  19. Gönül, B., Zorba, İ., Phys. Lett. A 269, 83 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  21. Eğrifes, H., Demirhan, D., Büyükkiliç, F.: Phys. Scr. 59, 90 (1999)

    Article  ADS  Google Scholar 

  22. Eğrifes, H., Demirhan, D., Büyükkiliç, F.: Phys. Scr. 60, 195 (1999)

    Article  ADS  Google Scholar 

  23. Eğrifes, H., Demirhan, D., Büyükkiliç, F.: Theor. Chim. Acta 98, 192 (1997)

    Google Scholar 

  24. Yeşiltaş, Ö., Şimşek, M., Sever, R., Tezcan, C.: Phys. Scr. 67, 472 (2003)

    Article  ADS  Google Scholar 

  25. Znojil, M.: Phys. Lett. A 264, 108 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Aktaş, M., Sever, R.: Mod. Phys. Lett. A 19, 2871 (2004)

    Article  ADS  Google Scholar 

  27. Ikhdair, S.M., Sever, R.: arXiv:quant-ph/0507272, Int. J. Theor. Phys., to appear, doi: 10.1007/s10773.006.9317-7

  28. Ikhdair, S.M., Sever, R.: arXiv:quant-ph/0508009, J. Math. Chem., to appear, doi: 10.1007/s10910.006.9115-8

  29. Eğrifes, H., Sever, R.: Phys. Lett. A 344, 117 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  30. Yasuk, F., Durmuş, A., Boztosun, I.: J. Math. Phys. 47, 082302 (2006)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Ikhdair, S.M., Sever, R.: arXiv:quant-ph/0605045, Int. J. Mod. Phys. E, accepted

  33. Ikhdair, S.M., Sever, R.: Ann. Phys. (Leipzig) 16(4), 218 (2007), arXiv:quant-ph/0610183

    MATH  MathSciNet  Google Scholar 

  34. Berkdemir, C., Berkdemir, A., Sever, R.: Phys. Rev. C 72, 027001 (2005)

    Article  ADS  Google Scholar 

  35. Berkdemir, C., Berkdemir, A., Sever, R.: J. Phys. A: Math. Gen. 39, 13455 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. Berkdemir, C., Berkdemir, A., Sever, R.: Nucl. Phys. A 779, 32 (2005)

    Google Scholar 

  37. Makarov, A.A., et al.: Nuovo Cimento A 52, 1061 (1967)

    Google Scholar 

  38. Liboff, R.L.: Introductory Quantum Mechanics. Addison–Wesley, San Fransisco (2003)

    Google Scholar 

  39. Chetouani, L., Guechi, L., Hammann, T.F.: J. Math. Phys. 33, 3410 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. Kibler, M., Campiogotto, C.: Int. J. Quantum Chem. 4, 209 (1993)

    Article  Google Scholar 

  41. Gerry, C.C.: Phys. Lett. A 118, 445 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  42. Hoang, L.V., et al.: J. Phys. A 25, 6461 (1992)

    Article  MATH  ADS  Google Scholar 

  43. Ikhdair, S.M., Sever, R., J. Mol. Struct.: THEOCHEM 806, 155 (2007); 809, 173 (2007), arXiv:quant-ph/0611183

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Near East University, Nicosia, North Cyprus, Mersin 10, Turkey

    Sameer M. Ikhdair

  2. Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

    Ramazan Sever

Authors
  1. Sameer M. Ikhdair
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramazan Sever
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sameer M. Ikhdair.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ikhdair, S.M., Sever, R. Polynomial Solution of Non-Central Potentials. Int J Theor Phys 46, 2384–2395 (2007). https://doi.org/10.1007/s10773-007-9356-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-007-9356-8

Keywords

Search

Navigation