High-Order Perturbation Theory and its Application to Atoms in Strong Fields

  • Harris J. Silverstone
Part of the NATO ASI Series book series (NSSB, volume 212)

Abstract

Schrödinger invented quantum mechanical perturbation theory in the third1 of his four seminal papers of 1926 to explain the LoSurdo2-Stark3 effect—hydrogen in an external electric field. Following an idea of Lord Rayleigh for treating vibrations, Schrödinger’s expectation was that a few terms in the power series expansion in the external field strength would be sufficient to match the experimental results. Higher-order terms could be obtained recursively from lower-order terms. This initial application of Rayleigh-Schrödinger perturbation theory (RSPT) was so straightforward and successful that it served as a paradigm for what has become a standard tool applied to countless problems in quantum physics.

Keywords

Ionization Rate Perturbation Series Anharmonic Oscillator Zeeman Effect Stokes Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Schrödinger, Ann. Physik 80:437 (1926).CrossRefMATHGoogle Scholar
  2. 2.
    A. LoSurdo, Atti della Reale Accademia dei Lincei 22:664 (1913).Google Scholar
  3. 3.
    J. Stark, Berliner Berichte 1913:932 (1913).Google Scholar
  4. 4.
    S. Graffi and V. Grecchi, Commun. Math. Phys. 62:83 (1978).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    H. J. Silverstone, Phys. Rev. A 18:1853 (1978).ADSCrossRefGoogle Scholar
  6. 6.
    T. Yamabe, A. Tachibana, and H. J. Silverstone, Phys. Rev. A 16:877 (1977).ADSCrossRefGoogle Scholar
  7. 7.
    H. J. Silverstone, E. Harrell, and C. Grot, Phys. Rev. A 24:1925 (1981).ADSCrossRefGoogle Scholar
  8. 8.
    W. P. Reinhardt, Int. J. Quantum Chem. 21:133 (1982).CrossRefGoogle Scholar
  9. 9.
    V. Franceschini, V. Grecchi, and H. J. Silverstone, Phys. Rev. A 32:1338 (1985).ADSCrossRefGoogle Scholar
  10. 10.
    C. Bender and T. T. Wu, Phys. Rev. Lett. 21:406 (1968).ADSCrossRefGoogle Scholar
  11. 11.
    R. J. Damburg and R. Propin, J. Phys. B 1:681 (1968).ADSCrossRefGoogle Scholar
  12. 12.
    J. Cizek, R. J. Damburg, S. Graffi, V. Grecchi, E. M. Harrell II, J. G. Harris, S. Nakai, J. Paldus, R. Kh. Propin, and H. J. Silverstone, Phys. Rev. A 33:12 (1986).MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    B. G. Adams, J. E. Avron, J. Čížek, P. Otto, J. Paldus, R. K. Moats, and H. J. Silverstone, Phys. Rev. A 21:1914 (1980).ADSCrossRefGoogle Scholar
  14. 14.
    H. J. Silverstone and R. K. Moats, Phys. Rev. A 23:1645 (1981).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    W. Voigt, Ann. Physik 4:197 (1901).ADSCrossRefMATHGoogle Scholar
  16. 16.
    J. Stark, Nature 92:401 (1913).ADSCrossRefGoogle Scholar
  17. 17.
    M. Jammer, The conceptual development of quantum mechanics (McGraw-Hill, New York, 1966), p. 107.Google Scholar
  18. 18.
    Nuovo Cimento 8:CXI-CXIII (1914).Google Scholar
  19. 19.
    R. Brunetti, l’Atomo e le sue radiazioni (Nicola Zanichelli, Bologna, 1932).Google Scholar
  20. 20.
    I. W. Herbst and B. Simon, Phys. Rev. Lett. 41:67 (1978).MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    L. Benassi, V. Grecchi, E. Harrell, and B. Simon, Phys. Rev. Lett. 42:704 and 1430(E) (1979).ADSCrossRefGoogle Scholar
  22. 22.
    H. J. Silverstone, B. G. Adams, J. Cizek, and P. Otto., Phys. Rev. Lett. 43:1498 (1979).ADSCrossRefGoogle Scholar
  23. 23.
    J. R. Oppenheimer, Phys. Rev. 31:66 (1928).ADSCrossRefMATHGoogle Scholar
  24. 24.
    I. Herbst, Commun. Math. Phys. 64:279 (1979).MathSciNetADSCrossRefMATHGoogle Scholar
  25. 25.
    L. Benassi and V. Grecchi, J. Phys. B 13:911 (1980).ADSCrossRefGoogle Scholar
  26. 26.
    R. J. Damburg, R. Kh. Propin, S. Graffi, V. Grecchi, E. M. Harrell II, J. Cizek, J. Paldus, and H. J. Silverstone, Phys. Rev. Lett. 52:1112 (1984).ADSCrossRefGoogle Scholar
  27. 27.
    S. Graffi, V. Grecchi, E. Harrell, and H. J. Silverstone, Ann. Phys. (N.Y.) 165:441 (1985).MathSciNetADSCrossRefMATHGoogle Scholar
  28. 28.
    J. D. Morgan and B. Simon, Int. J. Quantum Chem. 17:1143 (1980).CrossRefGoogle Scholar
  29. 29.
    H. J. Silverstone, S. Nakai, and J. G. Harris, Phys. Rev. A 32:1341 (1985).ADSCrossRefGoogle Scholar
  30. 30.
    M. Gailitis and H. J. Silverstone, Theor. Chim. Acta 73:105 (1988).CrossRefGoogle Scholar
  31. 31.
    H. J. Silverstone, Phys. Rev. Lett. 55: 2523 (1985).MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    H. J. Silverstone, Int. J. Quantum Chem. 29:261 (1986).CrossRefGoogle Scholar
  33. 33.
    H. J. Silverstone and R. K. Moats, Phys. Rev. A 23:1645 (1981).MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    G. Alvarez, S. Graffi, and H. J. Silverstone, Phys. Rev. A 38:1687 (1988).ADSCrossRefGoogle Scholar
  35. 35.
    S. Graffi and T. Paul, Comm. Math. Phys. 108:25 (1987).MathSciNetADSCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Harris J. Silverstone
    • 1
  1. 1.Department of ChemistryThe Johns Hopkins UniversityBaltimoreUSA

Personalised recommendations