CLASSICAL AND QUANTUM PERTURBATION-THEORY FOR 2 NONRESONANT OSCILLATORS WITH QUARTIC INTERACTION

We study the classical and quantum perturbation theory for two non-res onant oscillators coupled by a nonlinear quartic interaction. In parti cular, we analyze the question of quantum corrections to the torus qua ntization of the classical perturbation theory (semiclassical mechanic s). We obtain up to the second order of perturbation theory an explici t analytical formula for the quantum energy levels, which is the semic lassical one plus quantum corrections. We compare the 'exact' quantum levels obtained numerically to the semiclassical levels studying also the effects of quantum corrections.