Skip to main content
SpringerLink
Log in

The exact bound-state ansaetze as zero-order approximations in perturbation theory I. The formalism and padé oscillators

  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

A new perturbative prescription is proposed. It differs from the textbook Rayleigh-Schroedinger (RS) theory by the assumption of the user's incomplete knowledge of the unperturbed spectra. We only need a single eigenvalue and eigenstate ofH 0. In our quasi-RS (QRS) formulas, this eigenstate keeps its “unperturbed” RS interpretation, while the role of the (non-available) RS unperturbed spectrum is taken over by certain auxiliary matrix continued fractions. These quantities represent a weaker though entirely sufficient “compressed” information aboutH 0 and, after a suitable partitioning, enable one to combine the usual (i.e., sufficiently simple, here: harmonic-oscillator) working basis ¦n> with a very broad (here: arbitrary Padé-anharmonic) class of the zero-order HamiltoniansH 0.

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. Singh V., Biswas S. N., Datta K.: Phys. Rev. D18 (1978) 1901.

    Google Scholar 

  2. Flessas G. P.: Phys. Lett. A72 (1979) 289; A83 (1981) 121.

    Google Scholar 

  3. Flessas G. P., Das K. P.: Phys. Lett. A78 (1980) 19.

    Google Scholar 

  4. Magyari E.: Phys. Lett. A81 (1981) 116.

    Google Scholar 

  5. Znojil M.: J. Phys. A, Math. Gen.16 (1983) 279.

    Google Scholar 

  6. Morozov A. J., Perelomov A. M., Rosly A. A., Shifman M. A., Turbiner A. V.: Int. J. Mod. Phys. A5 (1990) 803.

    Google Scholar 

  7. Ushveridze A. G.: Lebedev Physics Institute Reports 1988, to appear in Soviet Physics (Allerton Press).

  8. Chaudhuri R. N.: Phys. Rev. D26 (1985) 3750.

    Google Scholar 

  9. Turbiner A. V.: Commun. Math. Phys.118 (1988) 467.

    Google Scholar 

  10. Shifman M. A.: New findings in quantum mechanics, CERN-TH.5265/88 (preprint); Int. J. Mod. Phys. A4 (1989) 2897.

    Google Scholar 

  11. Waken H.:in Laser Theory, Encyclopedia of Physics XXV/2. Van Nostrand, Princeton, 1970.

    Google Scholar 

  12. Mitra A. K.: J. Math. Phys.19 (1978) 2081.

    Google Scholar 

  13. Itzykson C., Zuber J. B.: Quantum Field Theory. McGraw-Hill, New York, 1982.

    Google Scholar 

  14. Kumar K.: Perturbation Theory and the Nuclear Many-Body Problem. North Holland, Amsterdam, 1962.

    Google Scholar 

  15. Znojil M.: J. Math. Phys.29 (1989) 2611; Czech. J. Phys. B, to appear.

    Google Scholar 

  16. Shiff L. I.: Quantum Mechanics. McGraw-Hill, New York, 1968.

    Google Scholar 

  17. Wilkinson J. H.: The Algebraic Eigenvalue Problem, Clarendon, Oxford, 1965.

    Google Scholar 

  18. Znojil M.: Czech. J. Phys. B37 (1987) 1072.

    Google Scholar 

  19. Whitehead R. R., Watt A., Flessas G. P., Nagarajan M. A.: J. Phys. A, Math. Gen.15 (1982) 1217.

    Google Scholar 

  20. Znojil M.: Czech. J. Phys. (to be published).

  21. Bender C. M. et al.: Phys. Rev. B37 (1988) 1472.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Nuclear Physics, Czechosl. Acad. Sci., 250 68, Řež near Prague, Czechoslovakia

    M. Znojil

Authors
  1. M. Znojil
    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

Znojil, M. The exact bound-state ansaetze as zero-order approximations in perturbation theory I. The formalism and padé oscillators. Czech J Phys 41, 397–408 (1991). https://doi.org/10.1007/BF01597944

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01597944

Keywords

Search

Navigation