Advertisement

Journal of Mathematical Chemistry

, Volume 48, Issue 4, pp 876–882 | Cite as

Exact solutions of a new Coulomb ring-shaped potential

  • Min-Cang Zhang
  • Bo An
  • Huang-Fu Guo-Qing
Original Paper

Abstract

A new Coulomb ring-shaped potential is proposed, which results from adding a potential proportional to(cos θ/r 2 sin2 θ)to a Coulomb potential. The Schrödinger equation with this new model potential is separated into angular and radial components. The exactly wavefunctions and the spectrum equation for bound state are presented by the standard approach.

Keywords

Noncentral potential Coulomb ring-shaped potential Schrödinger equation Bound state 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Makarov A.A., Smorodinsky J.A., Valiev K.h., Winternitz P.: Nuovo Cimento A 52, 1061 (1967)CrossRefGoogle Scholar
  2. 2.
    Kibler M., Mardoyan L.G., Pogosyan G.S.: Int. J. Quant. Chem. 52, 1301 (1994)CrossRefGoogle Scholar
  3. 3.
    Kibler M., Lamot G.H., Winternitz P.: Int. J. Quant. Chem. 43, 625 (1992)CrossRefGoogle Scholar
  4. 4.
    Quesne C.: J. Phys. A: Math. Gen. 21, 3093 (1988)CrossRefGoogle Scholar
  5. 5.
    Dutt R., Gangopadhyaya A., Sukhatme U.: Am. J. Phys. 65, 400 (1997)CrossRefGoogle Scholar
  6. 6.
    Khare A., Bhaduri R.K.: Am. J. Phys. 62, 1008 (1994)CrossRefGoogle Scholar
  7. 7.
    Dong S.H., Chen C.Y., Lozada-Cassou M.: Int. J. Quant. Chem. 105, 453 (2005)CrossRefGoogle Scholar
  8. 8.
    Kerimov G.A.: J. Phys. A: Math. Gen. 40, 7297 (2007)CrossRefGoogle Scholar
  9. 9.
    Berkdemir C.: J. Math. Chem. 46, 139 (2009)CrossRefGoogle Scholar
  10. 10.
    Hartmann H.: Theor. Chim. Acta 24, 201 (1972)CrossRefGoogle Scholar
  11. 11.
    Hartmann H., Schuck R.: J. Radtke, Theor. Chim. Acta 46, 1 (1976)CrossRefGoogle Scholar
  12. 12.
    Hartmann H., Schuch D.: Int. J. Quant. Chem. 18, 125 (1980)CrossRefGoogle Scholar
  13. 13.
    Kibler M., Negadi T.: Int. J. Quant. Them. 26, 405 (1984)CrossRefGoogle Scholar
  14. 14.
    Kibler M., Negadi T.: Theor. Chim. Acta 66, 31 (1984)CrossRefGoogle Scholar
  15. 15.
    Blado G.G.: Int. J. Quant. Chem. 58, 431 (1996)CrossRefGoogle Scholar
  16. 16.
    Blado G.G.: Theor. Chim. Acta 94, 53 (1996)Google Scholar
  17. 17.
    Chen C.Y.: Phys. Lett. A 339, 283 (2005)CrossRefGoogle Scholar
  18. 18.
    Aktas M., Sever R.: J. Math. Chem. 37, 139 (2005)CrossRefGoogle Scholar
  19. 19.
    Chen C.Y., Lu F.L., Sun D.S.: Phys. Lett. A 329, 420 (2004)CrossRefGoogle Scholar
  20. 20.
    Kibler M., Winternitz P.: J. Phys. A: Math. Gen. 20, 4097 (1992)CrossRefGoogle Scholar
  21. 21.
    Granovskii Y.I., Zhedanov A.S., Lutzenko I.M.: J. Phys. A: Math. Gen. 24, 3887 (1991)CrossRefGoogle Scholar
  22. 22.
    Zhedanov A.S.: J. Phys. A: Math. Gen. 26, 4633 (1993)CrossRefGoogle Scholar
  23. 23.
    Sökmen I.: Phys. Lett. A 115, 249 (1986)CrossRefGoogle Scholar
  24. 24.
    Mandal B.P.: Int. J. Mod. Phys. A 15, 1225 (2000)Google Scholar
  25. 25.
    Schulze-Halberg A., Zamora-Gallardo E., Pena J.J.: Int. J. Quant. Chem. 109, 1464 (2009)CrossRefGoogle Scholar
  26. 26.
    Zhang M.C.: Acta. Phys. Sin. 58, 712 (2009)Google Scholar
  27. 27.
    Zhang M.C.: Cent. Eur. J. Phys. 7, 768 (2009)CrossRefGoogle Scholar
  28. 28.
    Flügge S.: Practical Quantum Mechanics. Springer, Berlin (1971)Google Scholar
  29. 29.
    Wang Z.X., Guo D.R.: Special Functions. Word Scientific, Singapore (1989)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.College of Physics and Information TechnologyShaanxi Normal UniversityXi’anPeople’s Republic of China
  2. 2.Department of Physics and Electronic EngineeringWeinan Teachers UniversityWeinanPeople’s Republic of China

Personalised recommendations