Separable N-particle hookean models

Abstract

A model of N particles, where interactions between disjoint pairs are described by two-particle potentials which depend only on the distance between the particles and the remaining interaction are harmonic is considered. If the coupling constants in the quadratic form describing the harmonic part of the interaction potential fulfill certain separability conditions then the model is separable. Several systems known in the literature as the Hookean two-electron atom (harmonium) and the Hookean hydrogen molecules, appear to be special cases of this model. Some properties of this model are discussed in detail. © 2010 IOP Publishing Ltd.