ACCURACY OF THE SEMICLASSICAL APPROXIMATION - THE PULLEN-EDMONDS HAMILTONIAN

A test on the numerical accuracy of the semi-classical 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 semi-classical approximation formula is on average the same as that provided by quantum perturbation theory.