Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.C. Gutzwiller, the present workshop.
J.C. Gay, New Trends in Atomic Diamagnetism, D Reidel Publishing Company (1985) 631. See also J. de Phys. C2 suppl 11 (1982).
L.I. Schiff and H. Snyder, Phys. Rev. 55 (1939) 59.
H. Hasegawa in Physics of Solid in Intense Magnetic Fields ed by E.D.
Heidemenakis (Plenum Press, 1969) Chap.10;
H. Hasegawa J. Phys. Chem. Solid 21 (1961) 171.
J. Avron, I. Herbst and B. Simon, Commn. Math. Phys. 79 (1981) 529;
J. Avron, I. Herbst and B. Simon, **also Phys. Lett. 62A (1977) 214.
M.L. Zimmerman, M.M. Kash and D. Kleppner, Phys. Rev. Lett. 45 (1980)
1092; also Phys.
M.L. Zimmerman, M.M. Kash and D. Kleppner, **Rev. Lett. 40 (1978) 1083 and
M.L. Zimmerman, M.M. Kash and D. Kleppner, **45 (1980) 1780.
E.A. Solovev, JETP 55 (1982) 45;
E.A. Solovev, also JETP Lett. 34 (1981) 265.
D.R. Herrick, Phys. Rev. A26 (1982) 323.
I.C. Percival, Adv. Chem. Phys. 36 (1977) 1.
J.B. Keller, Ann. of Phys. 4 (1958) 180.
D.W. Noid, M.L. Koszykowski and R.A. Marcus, Ann. Rev. Phys. Chem.(1981) 32;267.
J.B. Delos, S.K. Knudson and D.W. Noid, Phys. Rev. A28 (1983) 7.
S. Adachi, Master Thesis, Kyoto University (1985) unpublished.
E. Kalnins, W. Miller and P. Winternitz, SIAM.J.Appl.Math.30 (1976) 630.
M. Lakshmanan and H. Hasegawa, J. Phys. A: Math. Gen. 17 (1984) L889.
C.L. Siegel, Topics in complex function theory 1, Wiley-Interscience (1969).
M. Robnik, J. Phys. A: Math. Gen. 14 3195.
H. Hasegawa, A. Harada and Y. Okazaki, J. Phys. A: Math. Gen. 17 (1984) L883;
H. Hasegawa, A. Harada and Y. Okazaki, also J. Phys. A: Math. Gen. 16 (1983) L259.
Higher Transcendental Functions ed. by A. Erdelyi Vol II (1953) XIII.
H. Hasegawa, S. Adachi and A. Harada, J. Phys. A: M.Gen. 16 (1983) L503.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Plenum Press, New York
About this chapter
Cite this chapter
Hasegawa, H. (1986). Quantization of Non-Integrable Systems; the Hydrogen Atom in a Magnetic Field. In: Gorini, V., Frigerio, A. (eds) Fundamental Aspects of Quantum Theory. NATO ASI Series, vol 144. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5221-1_21
Download citation
DOI: https://doi.org/10.1007/978-1-4684-5221-1_21
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-5223-5
Online ISBN: 978-1-4684-5221-1
eBook Packages: Springer Book Archive