International Journal of Theoretical Physics

, Volume 39, Issue 4, pp 1119–1128 | Cite as

Exact Solutions of the Two-Dimensional Schrödinger Equation with Certain Central Potentials

  • Shi-Hai Dong
Article

Abstract

By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrödinger equation in two dimension is obtained with the potentials V(r) =ar2 + br4 + cr6,V(r) = ar + br2 + cr−1,and V(r) = ar2 + br−2+ cr−4 + dr−6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.

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REFERENCES

  1. 1.
    A. Share and S. N. Behra, Pramana J. Phys. 14 (1980).Google Scholar
  2. 2.
    D. Amin, Phys. Today 35, 35(1982); Phys. Rev. Lett. 36, 323 (1976).Google Scholar
  3. 3.
    S. Coleman, Aspects of Symmetry, (Cambridge University Press, Cambridge, 1988), p. 234.Google Scholar
  4. 4.
    H. Hashimoto, Int. J. Electron. 46, 125 (1979); Opt. Commun. 32, 383 (1980).Google Scholar
  5. 5.
    C. E. Reid, J. Mol. Spectrosc. 36, 183 (1970).Google Scholar
  6. 6.
    R. S. Kaushal, Ann. Phys. (N.Y.) 206, 90 (1991).Google Scholar
  7. 7.
    R. S. Kaushal and D. Parashar, Phys. Lett. A 170, 335 (1992).Google Scholar
  8. 8.
    R. S. Kaushal, Phys. Lett. A 142, 57 (1989).Google Scholar
  9. 9.
    S. K. Bose and N. Varma, Phys. Lett. A 147, 85 (1990).Google Scholar
  10. 10.
    S. K. Bose, Nuovo Cimento B 109, 1217 (1994).Google Scholar
  11. 11.
    A. Voros, J. Phys. A 32, 5993 (1999).Google Scholar
  12. 12.
    Y. P. Varshni, Phys. Lett. A 183, 9 (1993).Google Scholar
  13. 13.
    S. Özcelik and M. Simsek, Phys. Lett. A 152, 145 (1991).Google Scholar
  14. 14.
    M. Simsek and S. Özcelik, Phys. Lett. A 186, 35 (1994).Google Scholar
  15. 15.
    M. Simsek, Phys. Lett. A 259, 215 (1999).Google Scholar
  16. 16.
    Shi-Hai Dong and Zhong-Qi Ma, J. Phys. A 31, 9855 (1998).Google Scholar
  17. 17.
    Shi-Hai Dong, Zhong-Qi Ma, and G. Esposito, Found. Phys. Lett. 12, 465 (1999).Google Scholar
  18. 18.
    M. Znojil, J. Math. Phys. 30, 23 (1989).Google Scholar
  19. 19.
    M. Znojil, J. Math. Phys. 31, 108 (1990).Google Scholar
  20. 20.
    M. Znojil, J. Phys. A 15, 2111 (1982).Google Scholar
  21. 21.
    V. de Alfaro and T. Regge, Potential Scattering (North-Holland, Amsterdam, 1965).Google Scholar
  22. 22.
    S. Fubini and R. Stroffolini, Nuovo Cimento 37, 1812 (1965).Google Scholar
  23. 23.
    F. Calogero, Variable Phase Approach to Potential Scattering (Academic, Press, New York, 1967).Google Scholar
  24. 24.
    R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1967).Google Scholar
  25. 25.
    W. M. Frank, D. J. Land, and R. M. Spector, Rev. Mod. Phys. 43, 36 (1971).Google Scholar
  26. 26.
    R. Stroffolini, Nuovo Cimento A 2, 793 (1991).Google Scholar
  27. 27.
    G. Esposito, J. Phys. A 31, 9493 (1998).Google Scholar
  28. 28.
    G. Esposito, Found. Phys. Lett. 11, 535 (1998).Google Scholar
  29. 29.
    A. O. Barut, J. Math. Phys. 21, 568 (1980).Google Scholar
  30. 30.
    B. H. Bransden and C. J. Joachain, Physics of Atoms and Molecules (Longman, London, 1983).Google Scholar
  31. 31.
    G. C. Maitland, M. M. Higby, E. B. Smith, and V. A. Wakoham, Intermolecular Forces (Oxford University Press, Oxford, 1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Shi-Hai Dong
    • 1
    • 2
  1. 1.Physical and Theoretical Chemistry LaboratoryUniversity of OxfordOxfordU.K.
  2. 2.Department of Physics, Cardwell HallKansas State UniversityManhattan

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