A Remark on Continuum Eigenfunctions of N-Body Schrödinger Operators

Let H be a generalized N-body Schrödinger operator on IRⁿ. We study exponential decay properties of polynomially bounded solutions to Schrödinger's equation Hu = λu, where λ lies in the negative essential spectrum of H, using Agmon's method. Our results show that such solutions decay exponentially outside an infinite, closed subset of ⁿ depending on λ and so represent bound clusters of particles. These results partially characterize negative energy continuum eigenfunctions of H.