Skip to main content
SpringerLink
Log in

The Scaled Hermite–Weber Basis Still Highly Competitive

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

Abstract

The effectiveness of the usual harmonic oscillator basis is demonstrated on a wide class of Schrödinger Hamiltonians with various spectral properties. More specifically, it is shown numerically that an appropriately scaled Hermite–Weber basis yields extremely accurate results not only for the energy eigenvalues which differ slighly from the harmonic oscillator levels, but also for the states which reflect a purely anharmonic character.

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. C.M. Bender and T.T. Wu, Phys. Rev. 184 (1969) 1231.

    Google Scholar 

  2. P.K. Patnaik, Phys. Rev. D 33 (1986) 3145.

    Google Scholar 

  3. M. Znojil, Phys. Rev. A 35 (1987) 2448.

    PubMed  Google Scholar 

  4. G.S. Tschumper and M.R. Hoffmann, J. Math. Chem. 31 (2002) 105.

    Google Scholar 

  5. C.E. Reid, J. Mol. Spectr. 36 (1970) 183.

    Google Scholar 

  6. I.N. Sneddon, Special Functions of Mathematical Physics and Chemistry (Oliver and Boyd, Edinburgh, 1966).

    Google Scholar 

  7. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980).

    Google Scholar 

  8. R.L. Somorjai and D.F. Hornig, J. Chem. Phys. 36 (1962) 1980.

    Google Scholar 

  9. M. Znojil, J. Math. Phys. 35 (1992) 213.

    Google Scholar 

  10. C.G. Diaz, F.M. Fernandez and E.A. Castro, J. Phys. A 21 (1988) L11.

    Google Scholar 

  11. H. Taşeli, Int. J. Quantum Chem. 60 (1996) 641.

    Google Scholar 

  12. P.M. Morse, Phys. Rev. 34 (1929) 57.

    Google Scholar 

  13. H. Taşeli, J. Comput. Appl. Math. 115 (2000) 535.

    Google Scholar 

  14. H. Taşeli, J. Phys. A 31 (1998) 779.

    Google Scholar 

  15. E. Gildener and A. Patrascioui, Phys. Rev. D 16 (1977) 423.

    Google Scholar 

  16. K. Banerjee and S.P. Bhatnagar, Phys. Rev. D 18 (1978) 4767.

    Google Scholar 

  17. C.S. Hsue and J.L. Chern, Phys. Rev. D 29 (1984) 643.

    Google Scholar 

  18. J. Killingbeck, J. Phys. A 20 (1987) 601.

    Google Scholar 

  19. N. Bessis, G. Bessis and B. Joulakian, J. Phys. A 15 (1982) 3679.

    Google Scholar 

  20. C.S. Lai, J. Phys. A 16 (1983) L181.

    Google Scholar 

  21. M. Cohen, J. Phys. A 17 (1984) L101.

    Google Scholar 

  22. K. Banerjee, S.P. Bhatnagar, V. Choudhry and S.S. Kanwal, Proc. Roy. Soc. London Ser. A 360 (1978) 575.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    H. Taşeli & M. Bahar Erseçen

Authors
  1. H. Taşeli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Bahar Erseçen
    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., Erseçen, M.B. The Scaled Hermite–Weber Basis Still Highly Competitive. Journal of Mathematical Chemistry 34, 177–187 (2003). https://doi.org/10.1023/B:JOMC.0000004067.16089.02

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOMC.0000004067.16089.02

Search

Navigation