Classical and Quantum Description of Rydberg Atom

  • Vladimir S. Lebedev
  • Israel L. Beigman
Part of the Springer Series on Atoms+Plasmas book series (SSAOPP, volume 22)

Abstract

This Chapter is devoted to an isolated highly excited atom which is not affected by any external interactions or fields. We start with a purely classical consideration of highly excited electron motion, and then give a review of various methods for describing the Rydberg atom wave functions in the coordinate and momentum representations. In addition to quantum expressions, we describe the semiclassical methods including the standard JWKB approximation for the radial and angular wave functions as well as the action variables approach. Special attention is paid to the derivation of explicit expressions for the Coulomb Green’s function, the density matrix, classical and quantum distribution functions of the Rydberg electron momentum and coordinate. The methods presented in this chapter are widely used in modern theory of Rydberg states. They will be the basis for the majority of the problems considered in this book.

Keywords

Manifold cosB 

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Reference List

  1. [2.1]
    L.D. Landau, E.M. Lifshitz: Mechanics (Pergamon, Oxford 1969)Google Scholar
  2. [2.2]
    L.D. Landau, E.M. Lifshitz: Quantum Mechanics (Pergamon, Oxford 1977)Google Scholar
  3. [2.3]
    H.A. Bethe, E.E. Salpeter: Quantum Mechanics of One- and Two- Electron atoms (Springer-Verlag, New York 1957)MATHGoogle Scholar
  4. [2.4a]
    H. Bateman, A. Erdelyi: Higher Transcendental Functions (McGraw-Hill, New York, Toronto, London 1953);Google Scholar
  5. [2.4b]
    I.S. Gradshteyn, I.W. Ryzhik: Tables of Integrals, Series and Products (Academic, New York 1965);Google Scholar
  6. [2.4c]
    M. Abramovitz, I.A. Stegun: Handbook of Mathematical Functions (Dover, New York 1965)Google Scholar
  7. [2.5]
    E. de Prunele: J. Phys. B13, 3921(1980)ADSGoogle Scholar
  8. [2.6]
    A.B. Migdal: Qualitative Methods in Quantum Theory (Nauka, Moscow 1975)Google Scholar
  9. [2.7]
    R.M. More, K.H. Warren: Ann. Phys. 207, 282(1991)ADSCrossRefGoogle Scholar
  10. [2.8]
    D.A. Varshalovich, A.N. Moskalev, V.K. Khersonsky: Quantum Theory of the Angular Momentum (World Scientific, Singapore 1988)Google Scholar
  11. [2.9]
    D.R. Bates, A. Damgaard: Philos. Trans. R. Soc. 242, 101(1949)ADSMATHCrossRefGoogle Scholar
  12. [2.10]
    M. Matsuzawa: J. Phys. B8, 2114(1975), corrigendum 9, 2559(1976)ADSGoogle Scholar
  13. [2.11]
    S.W. Qian, X.Y. Huang: Phys. Lett. A115, 319(1986)MathSciNetADSGoogle Scholar
  14. [2.12A]
    L. Hostler: J. Math. Phys. 5, 591(1964);MathSciNetADSCrossRefGoogle Scholar
  15. [2.12]
    L. Hostler, R. Pratt: Phys.Rev. 10, 469(1963)MathSciNetADSMATHGoogle Scholar
  16. [2.13]
    V. Fock: Zeitschr. f. Phys. 98, 145(1935)ADSMATHCrossRefGoogle Scholar
  17. [2.14]
    E.P. Wigner: Phys. Rev. 40, 749(1932)ADSMATHCrossRefGoogle Scholar
  18. [2.15]
    M.V. Berry: Phil. Trans. Roy. Soc. 287, 237 (1977)ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Vladimir S. Lebedev
    • 1
  • Israel L. Beigman
    • 1
  1. 1.Optical Division, P. N. Lebedev Physical Inst.Russian Academy of SciencesMoscowRussia

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