Resonance overlapping in classical mechanics and avoided crossings in quantum mechanics

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Abstract
By implementing the algorithm of classical perturbation theory on the Schrödinger equation for a large class of periodically driven rotators, it is shown that the classical resonance overlapping criterion for the onset of chaotic motion implies the existence of avoided crossings among an arbitrarily large number of quantum quasienergy levels at the classical limit ħ small, nħ=A close to a classically resonant torus.