Analytic WKB energy expressions for three-dimensional anharmonic oscillators
- 1 May 1982
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 15 (5), 1537-1547
- https://doi.org/10.1088/0305-4470/15/5/015
Abstract
A direct evaluation of the lowest-order WKB integral for three-dimensional quartic (V(r)=r4) and quartic anharmonic (V(r)=1/2 omega 2r2+ lambda r4) oscillators is carried out. The highly implicit relation for the energy defined by the WKB quantisation condition is expressed in terms of complete elliptic integrals. An approximate non-perturbative inversion of the implicit relation provides explicit analytic expressions for the energy which reproduce known energy values quite accurately. This study is believed to be the first to give explicit energy expressions via the WKB method for three-dimensional anharmonic oscillators.Keywords
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