Distorted plane waves for the 3 body Schrödinger operator

Abstract

Distorted plane waves, incoming in the free region, are constructed for generalized 3 body Schrodinger operators on \( {\Bbb R}^N \) under the assumption that the 'two-body' potential functions are rapidly decreasing. The construction yields the form of the complete asymptotic expansion of the plane waves at infinity away from the collision planes, and gives an explicit construction and geometric characterization of the singularities of the free channel scattering matrix.