Quantum energy mapping — an interpretation based on classical orbits

Abstract

Nonintegrable space and time transformations in classical mechanics are extended to the quasi-classical regime by applying Ehrenfest's adiabatic hypothesis. The resulting mapping between quasi-classical orbits induces an approximative mapping between discrete energy spectra of different quantum systems which is correct up to the first order of Planck's constant. A further generalization of this quasi-classical energy mapping to the full quantum mechanical case is often possible by performing a successive renormalization of parameters. In this way we construct a mapping of classical orbits which constitutes the basis for the quantum energy mapping.