Skip to main content
SpringerLink
Log in

An alternative series solution to the isotropic quartic oscillator inN dimensions

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The series solution of theN-dimensional isotropic quartic oscillator weighted by an appropriate function which exhibits the correct asymptotic behavior of the wave function is presented. The numerical performance of the solution in Hill's determinant picture is excellent, and yields the energy spectrum of the system to any desired accuracy for the full range of the coupling constant. Furthermore, it converges to the well-known exact solution of the unperturbed harmonic oscillator wave function, when the anharmonic interaction vanishes.

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. S. Bell, R. Davidson and P.A. Warsop, J. Phys. B3 (1970) 113.

    Google Scholar 

  2. M.R.M. Witwit, J. Phys. A24 (1991) 4535.

    Google Scholar 

  3. E.R. Vrscay, Theor. Chim. Acta 73 (1988) 365.

    Google Scholar 

  4. M. Lakshmanan, P. Kaliappan, K. Larsson, F. Karlsson and P.O. Fröman, Phys. Rev. A49 (1994) 3296.

    Google Scholar 

  5. F.M. Fernandez and E.A. Castro, Phys. Rev. A24 (1981) 2883.

    Google Scholar 

  6. M. Seetharaman and S.S. Vasan, J. Math. Phys. 27 (1986) 1031.

    Google Scholar 

  7. H. Taşeli and A. Zafer, Int. J. Quant. Chem. 61 (1997) 759.

    Google Scholar 

  8. H. Taşeli and A. Zafer, Bessel basis with applications:N-dimensional isotropic polynomial oscillators, accepted for publication in Int. J. Quant. Chem.

  9. H. Taşeli, Int. J. Quant. Chem. 57 (1996) 63.

    Google Scholar 

  10. M. Abramowitz and I.A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1970) p. 781.

    Google Scholar 

  11. H. Taşeli and M. Demiralp, J. Phys. A21 (1988) 3903.

    Google Scholar 

  12. H.W. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling,Numerical Recipes (Cambridge University Press, Cambridge, 1986) p. 369.

    Google Scholar 

  13. A. Hautot, Phys. Rev. D33 (1986) 437.

    Google Scholar 

  14. E.T. Copson,Functions of a Complex Variable (Oxford University Press, Oxford, 1935) p. 269.

    Google Scholar 

  15. M. Znojil, J. Math. Phys. 33 (1992) 213.

    Google Scholar 

  16. F.M. Fernandez, Phys. Lett. A194 (1994) 343.

    Google Scholar 

  17. A.N. Drozdov, J. Phys. A28 (1995) 445.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    H. Taşeli

Authors
  1. H. Taşeli
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taşeli, H. An alternative series solution to the isotropic quartic oscillator inN dimensions. J Math Chem 20, 235–245 (1996). https://doi.org/10.1007/BF01165345

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01165345

Keywords

Search

Navigation