Whittaker–Hill Equation, Ince Polynomials, and Molecular Torsional Modes

摘要

We present an analysis of the Whittaker–Hill equation in view of its usefulness in quantum mechanics when periodic potentials are involved. The transformation due to Ince leads to polynomial solutions which have not attracted much attention so far in the applications.With respect to Mathieu equation, here we have an additional parameter, which permits to describe a variety of phenomena, including the treatment of the torsional motion of flexible molecules. Examples are discussed, with particular attention payed to the case of H2O2 and similar molecules.