Discrete semiclassical methods in the theory of Rydberg atoms in external fields

The properties of the WKB method in the discrete representation are reviewed. The method provides the eigenvalues and the eigenvectors of the three-term recursion relations or, which is the same thing, the tridiagonal band matrices. Applications of the method to the splitting of the Rydberg atom lev...

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Bibliographic Details
Published in:Reviews of modern physics 1993-01, Vol.65 (1), p.115-161
Main Author: Braun, P. A.
Format: Article
Language:English
Subjects:
661100 > Classical & Quantum Mechanics-- (1992-)
ALKALI METALS
ATOMIC AND MOLECULAR PHYSICS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DOCUMENT TYPES
EIGENVALUES
ELEMENTS
ENERGY LEVELS
ENERGY SPECTRA
EXCITED STATES
HAMILTONIANS
HYDROGEN
MATHEMATICAL OPERATORS
METALS
NONMETALS
OSCILLATOR STRENGTHS
QUANTIZATION
QUANTUM OPERATORS
RECURSION RELATIONS
REVIEWS
RYDBERG STATES
SINGULARITY
SPECTRA 664100 > Theory of Electronic Structure of Atoms & Molecules-- (1992-)
VAN DER WAALS FORCES
WKB APPROXIMATION
ZEEMAN EFFECT
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Summary:The properties of the WKB method in the discrete representation are reviewed. The method provides the eigenvalues and the eigenvectors of the three-term recursion relations or, which is the same thing, the tridiagonal band matrices. Applications of the method to the splitting of the Rydberg atom levels in the external electric and magnetic fields are considered. Analytical treatment is given to the problem of the oscillator strength distribution in the quadratic Zeeman and the Stark-Zeeman spectra. In the case of the nonhydrogenic Rydberg atoms, the effect of the core on the pattern of the splitting is studied. Certain alternative applications of the discrete WKB method are considered in brief (the quasienergy spectra of nonlinear oscillators in resonant fields, rotational molecular spectra, calculation of infinite continued fractions).
ISSN:0034-6861
1539-0756
DOI:10.1103/RevModPhys.65.115