Skip to main content
SpringerLink
Log in

A Laplace transform approach to find the exact solution of the \(N\)-dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators

  • Original Paper
  • Published:

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The second order \(N\)-dimensional Schrödinger equation with Mie-type potentials is reduced to a first order differential equation by using the Laplace transformation. Exact bound state solutions are obtained using convolution theorem. The Ladder operators are also constructed for the Mie-type potentials in \(N\)-dimensions. Lie algebra associated with these operators are studied and it is found that they satisfy the commutation relations for the SU(1,1) group.

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. H. Hassanabadi, S. Zarrinkamar, A.A. Rajabi, Commun. Theor. Phys. 55, 541 (2011)

    Article  Google Scholar 

  2. D. Agboola, Chin. Phys. Lett. 27, 040301 (2010)

    Article  Google Scholar 

  3. S.H. Dong, G.H. Sun, Phys. Lett. A. 314, 261 (2003)

    Article  CAS  Google Scholar 

  4. S.H. Dong, Phys. Scr. 65, 289 (2002)

    Article  CAS  Google Scholar 

  5. S.M. Ikhdair, R. Server, Int. J. Mod. Phys. C 18, 1571 (2007)

    Article  CAS  Google Scholar 

  6. D. Agboola, Phys. Scr. 80, 065304 (2009)

    Article  Google Scholar 

  7. L.Y. Wang, X.Y. Gu, Z.Q. Ma, S.H. Dong, Found. Phys. Lett. 15, 569 (2002)

    Article  Google Scholar 

  8. D. Agboola, Phys. Scr. 81, 067001 (2010)

    Article  Google Scholar 

  9. K.J. Oyewumi, F.O. Akinpelu, A.D. Agboola, Int. J. Theor. Phys. 47, 1039 (2008)

    Article  Google Scholar 

  10. G.R. Khan, Eur. Phys. J. D 53, 123 (2009)

    Article  CAS  Google Scholar 

  11. H. Hassanabadi, M. Hamzavi, S. Zarrinkamar, A.A. Rajabi, Int. J. Phy. Science 6(3), 583 (2011)

    Google Scholar 

  12. R. Kumar, F. Chand, Phys. Scr. 85, 055008 (2012)

    Article  Google Scholar 

  13. R. Kumar, F. Chand, Commun. Theor. Phys. 59, 528 (2013)

    Article  CAS  Google Scholar 

  14. D. Agboola, ACTA PHYSICA POLONIOCA A 120, 371 (2011)

    CAS  Google Scholar 

  15. S.M. Ikhdair, R. Server, Int. J. Mod. Phys. C 19, 1425 (2008)

    Article  CAS  Google Scholar 

  16. S. Erkoc, R. Sever, Phys. Rev. D 33, 588 (1986)

    Article  CAS  Google Scholar 

  17. S. Ikhdair, R. Server, Int. J. Mod. Phys. C 19, 221 (2008)

    Article  Google Scholar 

  18. E. Schrödinger, Ann. Physik. 79, 361 (1926)

    Article  Google Scholar 

  19. M.J. Englefield, J. Math. Anal. Appl. 48, 270 (1974)

    Article  Google Scholar 

  20. A. Arda, R. Sever, J. Math. Chem. 50, 971 (2012)

    Article  CAS  Google Scholar 

  21. A.S. de Castro, Rev. Bras. Ens. Fis. 34, 4301 (2012)

    Google Scholar 

  22. A. Arda, R. Sever, Commun. Theor. Phys. 58, 27 (2012)

    Article  Google Scholar 

  23. D.R.M. Pimentel, A.S. de Castro, Eur. J. Phys. 34, 199 (2013)

    Article  Google Scholar 

  24. G. Chen, Chin. Phys. 14, 1075 (2005)

    Article  Google Scholar 

  25. R.A. Swainson, G.W.F. Drake, J. Phys. A: Math. Gen. 24, 79 (1991)

    Article  CAS  Google Scholar 

  26. S. Erkoc, R. Sever, Phys. Rev. D 30, 2117 (1984)

    Article  Google Scholar 

  27. S. Ikhdair, R. Server, Cent. Eur. J. Phys. 6, 697 (2008)

    Article  Google Scholar 

  28. A. Chatterjee, Phys. Rep. 186, 249 (1990)

    Article  CAS  Google Scholar 

  29. N. Shimakura, Partial Differential Operator of Elliptic Type (American Math-Society, Providence, 1992)

    Google Scholar 

  30. G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, 5th edn. (Academic Press, New York, 2001)

    Google Scholar 

  31. J.L. Schiff, The Laplace Transform: Theory and Applications (Springer, New York, 1999)

    Book  Google Scholar 

  32. I.S. Gradshteyn, I.M. Ryzhik, Table of integrals, Series, and Products, 7th edn. (Academic Press, New York, 2007)

    Google Scholar 

  33. H. Casimir, Proc.R. Acad. 34, 844 (1931)

    Google Scholar 

  34. F.M. Fernandez, J. Phys. A: Math. Gen. 37, 6173 (2004)

    Article  Google Scholar 

  35. T. Barakat, Phys. Lett. A. 344, 411 (2005)

    Article  CAS  Google Scholar 

  36. T. Barakat, J. Phys. A: Math. Gen. 36, 823 (2006)

Download references

Acknowledgments

The author is grateful to the kind referee for his/her invaluable suggestions which have improved the present paper. He also wishes to dedicate this paper to his Father Late N. G. Das.

Author information

Authors and Affiliations

  1. Kodalia Prasanna Banga High School (H.S), South 24 Parganas, 700146, India

    Tapas Das

Authors
  1. Tapas Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tapas Das.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, T. A Laplace transform approach to find the exact solution of the \(N\)-dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators. J Math Chem 53, 618–628 (2015). https://doi.org/10.1007/s10910-014-0444-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-014-0444-8

Keywords

Search

Navigation