Quantization of Non-Integrable Systems; the Hydrogen Atom in a Magnetic Field

  • Hiroshi Hasegawa
Part of the NATO ASI Series book series (NSSB, volume 144)


This article is to provide an account of the recent development in the subject of the spectrum of the hydrogen atom in a magnetic field from the correspondence viewpoint between classical and quantum mechanics. There exists a similar system which has achieved a considerable success; namely the anisotropic Kepler problem (AKP)1. In analogy with this, the present subject may be called the diamagnetic Kepler problem (DKP)2.


Riemann Surface Algebraic Curve Principal Quantum Number Maslov Index Semiclassical Quantization 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.C. Gutzwiller, the present workshop.Google Scholar
  2. 2.
    J.C. Gay, New Trends in Atomic Diamagnetism, D Reidel Publishing Company (1985) 631. See also J. de Phys. C2 suppl 11 (1982).Google Scholar
  3. 3.
    L.I. Schiff and H. Snyder, Phys. Rev. 55 (1939) 59.ADSMATHCrossRefGoogle Scholar
  4. 4a.
    H. Hasegawa in Physics of Solid in Intense Magnetic Fields ed by E.D.Google Scholar
  5. Heidemenakis (Plenum Press, 1969) Chap.10;Google Scholar
  6. 4b.
    H. Hasegawa J. Phys. Chem. Solid 21 (1961) 171.ADSCrossRefGoogle Scholar
  7. 5a.
    J. Avron, I. Herbst and B. Simon, Commn. Math. Phys. 79 (1981) 529;MathSciNetADSMATHCrossRefGoogle Scholar
  8. 5a.
    J. Avron, I. Herbst and B. Simon, **also Phys. Lett. 62A (1977) 214.ADSCrossRefGoogle Scholar
  9. 6a.
    M.L. Zimmerman, M.M. Kash and D. Kleppner, Phys. Rev. Lett. 45 (1980)Google Scholar
  10. 1092; also Phys.Google Scholar
  11. 6b.
    M.L. Zimmerman, M.M. Kash and D. Kleppner, **Rev. Lett. 40 (1978) 1083 andADSCrossRefGoogle Scholar
  12. 6c.
    M.L. Zimmerman, M.M. Kash and D. Kleppner, **45 (1980) 1780.Google Scholar
  13. 7a.
    E.A. Solovev, JETP 55 (1982) 45;Google Scholar
  14. 7b.
    E.A. Solovev, also JETP Lett. 34 (1981) 265.ADSGoogle Scholar
  15. 8.
    D.R. Herrick, Phys. Rev. A26 (1982) 323.MathSciNetADSGoogle Scholar
  16. 9.
    I.C. Percival, Adv. Chem. Phys. 36 (1977) 1.CrossRefGoogle Scholar
  17. 10.
    J.B. Keller, Ann. of Phys. 4 (1958) 180.ADSMATHCrossRefGoogle Scholar
  18. 11.
    D.W. Noid, M.L. Koszykowski and R.A. Marcus, Ann. Rev. Phys. Chem.(1981) 32;267.ADSCrossRefGoogle Scholar
  19. 12.
    J.B. Delos, S.K. Knudson and D.W. Noid, Phys. Rev. A28 (1983) 7.ADSGoogle Scholar
  20. 13.
    S. Adachi, Master Thesis, Kyoto University (1985) unpublished.Google Scholar
  21. 14.
    E. Kalnins, W. Miller and P. Winternitz, SIAM.J.Appl.Math.30 (1976) 630.MathSciNetMATHCrossRefGoogle Scholar
  22. 15.
    M. Lakshmanan and H. Hasegawa, J. Phys. A: Math. Gen. 17 (1984) L889.MathSciNetADSCrossRefGoogle Scholar
  23. 16.
    C.L. Siegel, Topics in complex function theory 1, Wiley-Interscience (1969).Google Scholar
  24. 17.
    M. Robnik, J. Phys. A: Math. Gen. 14 3195.Google Scholar
  25. 18a.
    H. Hasegawa, A. Harada and Y. Okazaki, J. Phys. A: Math. Gen. 17 (1984) L883;Google Scholar
  26. 18b.
    H. Hasegawa, A. Harada and Y. Okazaki, also J. Phys. A: Math. Gen. 16 (1983) L259.ADSCrossRefGoogle Scholar
  27. 19.
    Higher Transcendental Functions ed. by A. Erdelyi Vol II (1953) XIII.Google Scholar
  28. 20.
    H. Hasegawa, S. Adachi and A. Harada, J. Phys. A: M.Gen. 16 (1983) L503.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Hiroshi Hasegawa
    • 1
  1. 1.Department of PhysicsKyoto UniversityKyotoJapan

Personalised recommendations