Large-order perturbation theory of the Zeeman effect in hydrogen from a four-dimensional anisotropic anharmonic oscillator

Journal Article · Fri Jun 01 04:00:00 EDT 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.41.6071· OSTI ID:7058949

Janke, W ^[1]

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1. Institut fuer Theorie der Elementarteilchen, Freie Universitaet Berlin, Arnimallee 14, D-1000 Berlin 33 (Federal Republic of Germany)

The Zeeman Hamiltonian for (spinless) hydrogen in a constant magnetic field is shown to be equivalent to a four-dimensional anisotropic anharmonic oscillator. Using this relation, Rayleigh-Schroedinger perturbation series expansions of both systems can be related to each other and analyzed in a unified way. Special emphasis is laid upon analytical estimates of their behavior in large orders of perturbation theory. Employing the path-integral approach, a new large-order formula is derived for the expansion of the ground-state energy of the oscillator system. With use of known Bender-Wu formulas for isotropic anharmonic oscillators, the major part of this calculation becomes straightforward. Combined with the new equivalence, this calculation represents the simplest path-integral derivation of large-order formulas for the Zeeman system.

• OSTI ID: 7058949
• Journal Information: Physical Review, A (General Physics); (USA), Journal Name: Physical Review, A (General Physics); (USA) Vol. 41:11; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ANHARMONIC OSCILLATORS
ATOMS
ELECTRONIC EQUIPMENT
ELEMENTS
EQUIPMENT
HAMILTONIANS
HYDROGEN
MATHEMATICAL OPERATORS
NONMETALS
OSCILLATORS
PERTURBATION THEORY
QUANTUM OPERATORS
RAYLEIGH-SCHROEDINGER FORMULA
SERIES EXPANSION
SIMULATION
ZEEMAN EFFECT