Accuracy of the Semi--Classical Approximation: the Pullen Edmonds Hamiltonian

Details Accuracy of the Semi--Classical Approximation: the Pullen Edmonds Hamiltonian Accuracy of the Semi--Classical Approximation: the Pullen Edmonds Hamiltonian

1994-09-28

arxiv.org/abs/hep-th/9409173v1

NuovoCim.B109:1147-1154,1994

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 5 figures (available upon request to the authors), LaTex, DFPD/93/TH/47, to be published in Nuovo Cimento B

Scientific paper

10.1007/BF02726678

A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the resonant harmonic oscillator. A perturbative interpretation is obtained of the recently observed phenomenon of the accuracy decrease on the approximation of individual energy levels at the increase of the principal quantum number. Moreover, the accuracy provided by the semiclassical approximation formula is on the average the same as that provided by quantum perturbation theory.

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