Theoretica chimica acta

, Volume 74, Issue 1, pp 39–54 | Cite as

Convergent perturbation studies in screened coulomb potential systems: a high precision numerical algorithm via Laguerre basis set

  • M. Demiralp
  • N. A. Baykara
  • H. Taşeli
Article

Abstract

In this work, a high precision algorithm is developed to determine the discrete spectrum of screened coulomb potential systems. The algorithm is mainly based upon the use of the perturbation of a hydrogen-like operator by a bounded operator. The Laguerre basis set expansion is employed in the procedure to obtain the operator inversion. Although a functional analytic analysis of errors and proof of convergence theorem are still lacking, it appears, numerically, that the method rapidly converges for bounded screened coulomb potential. Extremely accurate numerical results for the bound-state energies, in the case of Yukawa potential, are presented for illustrative purposes.

Key words

Screened coulomb potentials Perturbation theory Yukawa potential 

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References

  1. 1.
    Kato T (1966) Perturbation theory for linear operators, Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. 2.
    Reed M, Simon B (1978) Methods of modern mathematical physics, vol. 4. Academic Press, New York LondonGoogle Scholar
  3. 3.
    Chatelin F (1983) Spectral approximation of linear operators. Academic Press, New YorkGoogle Scholar
  4. 4.
    Kramer HP (1957) Pacific J Math 7:1405Google Scholar
  5. 5.
    Balslev E (1962) Math Scand 11:131Google Scholar
  6. 6.
    Yukawa M (1835) Proc Phys Soc Jpn 17:48Google Scholar
  7. 7.
    Foldy LL (1958) Phys Rev 111:1093Google Scholar
  8. 8.
    Rogers FJ, Graboske HC, Harwood DJ (1970) Phys Rev A1:1577Google Scholar
  9. 9.
    Pratt RH, Tsena HK (1972) Phys Rev A5:1063Google Scholar
  10. 10.
    Barut AO (1972) Dynamical groups and generalized symmetries in quantum theory. University of Canterbury Publications, Christchurch, New ZealandGoogle Scholar
  11. 11.
    Bednar M (1973) Ann Phys 75:305Google Scholar
  12. 12.
    Rotenberg M (1970) Adv Atom Mol Phys 6:233Google Scholar
  13. 13.
    Cizek J, Vrscay ER (1982) Int J Quantum Chem 21:27Google Scholar
  14. 14.
    Adams BG, Cizek J, Paldus J (1982) Int J Quantum Chem 21:153Google Scholar
  15. 15.
    Gazeau JP, Maquet A (1979) Phys Rev A20:727Google Scholar
  16. 16.
    McEnnan J, Kissel L, Pratt RH (1976) Phys Rev A13:532Google Scholar
  17. 17.
    Smith CR (1964) Phys Rev 134:A1235Google Scholar
  18. 18.
    Taseli H, Demiralp M (1987) Theor Chim Acta 71:315Google Scholar
  19. 19.
    Dold A, Eckmann B (eds) (1981) Lect Notes vol 888. Springer, Berlin Heidelberg New YorkGoogle Scholar
  20. 20.
    Dold A, Eckmann B (eds) (1984) Lect Notes Math vol 1071. Springer, Berlin Heidelberg New York TokyoGoogle Scholar
  21. 21.
    Baker GA (1965) Adv Theor Phys 1:1Google Scholar
  22. 22.
    Baker GA, Gammel JL (eds) (1970) The Padé approximant in theoretical physics. Academic Press, New York LondonGoogle Scholar
  23. 23.
    Baker GA (1975) Essentials of Padé approximants. Academic Press, New York LondonGoogle Scholar
  24. 24.
    Lai CS (1981) Phys Rev 23:455Google Scholar
  25. 25.
    Vrscay ER (1986) Phys Rev A33:1433Google Scholar
  26. 26.
    Friedman B (1966) Principles and techniques of applied mathematics. Wiley, New York London SydneyGoogle Scholar
  27. 27.
    Sneddon IN (1966) Special functions of mathematical physics and chemistry. Oliver and Boyd, EdinburghGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Demiralp
    • 1
  • N. A. Baykara
    • 1
  • H. Taşeli
    • 1
  1. 1.Research Institute for Basic Sciences, Applied Mathematics DepartmentTÜBİTAKGebze-KocaeliTurkey

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