Numerical identification of regular and irregular spectra

Abstract

Polyatomic molecules are described by nonintegrable Hamiltonians. For such systems it has been predicted (Percival 1973) that there are two regions of the quantal spectrum with contrasting properties. Eigenvalues are obtained for the Henon-Heiles nonintegrable Hamiltonian (1964). Two regions of the quantal spectrum are found which behave differently under a slowly changing perturbation. This behaviour is required by Percival for the existence of regular and irregular spectra.