Skip to main content
SpringerLink
Log in

A perturbation approach to finite difference methods

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

Abstract

A perturbation theoretic approach to finite difference methods for the calculation of eigenvalues is shown to permit an increase in the accuracy of the calculations and also to make possible the calculation of expectation values along with the eigenvalues. An application of the virial theorem can then boost the order of accuracy of any given finite difference method. Integrated probabilities and point values of the normalized wavefunction can be found without any use of quadratures. Illustrative examples are given involving the Schrodinger equation for simple polynomial potentials.

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. Anastasi Z.A., Vlachos D.S., Simos T.E.: J. Math. Chem. 46, 621 (2009)

    Article  Google Scholar 

  2. Anastasi Z.A., Vlachos D.S., Simos T.E.: J. Math. Chem. 46, 652 (2009)

    Article  Google Scholar 

  3. Pathak R.K., Chandra A.K., Battacharyya K.: Phys. Rev. A 48, 4097 (1993)

    Article  CAS  Google Scholar 

  4. Chen R., Guo H.: Chem. Phys. Lett. 308, 123 (1999)

    Article  CAS  Google Scholar 

  5. Johnson B.R.: J. Chem. Phys. 67, 4086 (1977)

    Article  CAS  Google Scholar 

  6. Killingbeck J.P., Gordon N.A., Witwit M.R.M.: Phys. Lett. A 206, 279 (1995)

    Article  CAS  Google Scholar 

  7. Killingbeck J.P., Jolicard G.: Phys. Lett. A 228, 205 (1997)

    Article  CAS  Google Scholar 

  8. Lakhlifi A.: Eur. Phys. J. D 8, 211 (2000)

    Article  CAS  Google Scholar 

  9. Killingbeck J.: J. Phys. B At. Mol. Phys. 15, 829 (1982)

    Article  CAS  Google Scholar 

  10. Killingbeck J.: J. Phys. A Math. Gen. 20, 1411 (1987)

    Article  Google Scholar 

  11. Killingbeck J.: J. Phys. A Math. Gen. 21, 3399 (1988)

    Article  Google Scholar 

  12. Killingbeck J.P., Jolicard G.: J. Phys. A Math. Gen. 41, 125204 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Mathematics, University of Hull, Loten Building, Hull, HU6 7RX, UK

    J. P. Killingbeck

  2. Institut UTINAM (CNRS UMR 6213), 41 bis Avenue del’Observatoire, BP 1615, 25010, Besancon cedex, France

    J. P. Killingbeck & A. Lakhlifi

Authors
  1. J. P. Killingbeck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Lakhlifi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. P. Killingbeck.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Killingbeck, J.P., Lakhlifi, A. A perturbation approach to finite difference methods. J Math Chem 48, 1036–1043 (2010). https://doi.org/10.1007/s10910-010-9723-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-010-9723-1

Keywords

Search

Navigation