Improved Method for Quantum Mechanical Three-Body Problems. II. Repulsive Potentials

Abstract

We extend a method previously presented for the three-body problem with attractive interparticle potentials to the case of repulsive interparticle potentials, with periodic boundary conditions on each particle. As before, we decompose the wave function into three parts, and from the Schrödinger equation write equations for these parts. We observe that, in one-dimension and for δ-function potentials,these equations can be easily solved numerically, and we present these solutions for potential“strengths” ranging from zero to infinity. We then discuss a more general method for solving these equations, which method involves expansions in a certain set of two-body functions. This general method is not necessarily limited to either one dimension or δ-function potentials, but, as a check on it, we do apply it to that case and get good agreement with the previous numerical results. As a further exploration of the method, we apply it to square well potentials in one dimension. In an Appendix we discuss the set of two-body functions that we use.