Skip to main content
SpringerLink
Log in

Accurate non-perturbative solution of eigenvalue problems with application to anharmonic oscillator

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

A method for eigenvalue problems is presented. As an example, we have obtained very accurate eigenvalues and eigenfunctions of the quartic anharmonic oscillator.

The method is non-perturbative and involves the use of an appropriately scaled set of basis functions for the determination of each eigenvalue. The claimed accuracy for all eigenvalues is 15 significant figures. The method does not deteriorate for higher eigenvalues.

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. HioeF.T. and MontrollE.W., J. Math. Phys. 16, 1945 (1975). This article contains the other important references.

    Google Scholar 

  2. See, e.g., WhittakerE.T. and WatsonG.N., Modern Analysis Cambridge University Press, Cambridge, 1927, Sec. 19.42.

    Google Scholar 

  3. KernerE.H., Phys. Rev. 83 17 (1951).

    Google Scholar 

  4. BiswasS., DattaK., SaxenaR., SrivastavaP., and VarmaV., J. Math. Phys. 14, 1190 (1973).

    Google Scholar 

  5. WilkinsonJ.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965, p. 461.

    Google Scholar 

  6. BazleyN. and FoxD., Phys. Rev. 124, 483 (1961).

    Google Scholar 

  7. ReidC.E., J. Mol. Spectrosc. 36, 183 (1970).

    Google Scholar 

Download references

Author information

Author notes

  1. K. Banerjee

    Present address: Dept. of Physics, Indian Institute of Technology, 208016, Kanpur, India

Authors and Affiliations

  1. International Centre for Theoretical Physics, Trieste, Italy

    K. Banerjee

Authors
  1. K. Banerjee
    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

Banerjee, K. Accurate non-perturbative solution of eigenvalue problems with application to anharmonic oscillator. Lett Math Phys 1, 323–327 (1976). https://doi.org/10.1007/BF00398488

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00398488

Keywords

Search

Navigation