Semiclassical mechanics of the quadratic Zeeman effect

Journal Article · Sun Mar 01 04:00:00 EST 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.3093· OSTI ID:7234505

Krantzman, K D; Milligan, J A ^[1]; Farrelly, D ^[2]

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1. Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024-1569 (United States)
2. Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300 (United States)

A comprehensive approach to semiclassical quantization of the quadratic Zeeman effect in the hydrogen atom (QZE) is presented which utilizes the connection between the Kepler system and the four-dimensional harmonic oscillator. Past attempts to quantize the QZE have encountered problems associated with singularities arising because of a classical separatrix. Here, a uniform semiclassical quantization scheme that passes smoothly through the separatrix is developed using classical perturbation theory. This method accounts for the topologically distinct kinds of dynamics that arise in the QZE, and provides good estimates of tunneling splittings. Extension to the quantization of arbitrarily-high-order classical perturbation expansions is straightforward.

• OSTI ID: 7234505
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 45:5; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

664200* -- Spectra of Atoms & Molecules & their Interactions with Photons-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
ELEMENTS
HYDROGEN
MAGNETIC FIELDS
NONMETALS
QUANTIZATION
SEMICLASSICAL APPROXIMATION
SYMMETRY BREAKING
ZEEMAN EFFECT