Classical resonances and their quantum manifestations

Abstract

The quantum manifestations, in terms of resonant eigenstates, of a classical <i>m:n</i> resonance are discussed. Recent work demonstrated, numerically, that the slope of the classical resonance line as determined by the parameters of the spectroscopic Hamiltonian leads to progressions of quantum states along the resonance channel. The progressions comprise isomorphic states appearing with a specific periodicity. The periodicity is related to the slope of the classical resonance line as viewed in the corresponding discrete quantum number

space. In this paper we provide a proof for the observed periodicity. These progressions, independent of the dimensionality of the system, demonstrate a detailed classical-quantum correspondence for resonant systems.