ENERGY-DEPENDENT BOUNDARY-CONDITIONS AND THE FEW-BODY SCATTERING PROBLEM

An exactly solvable problem with energy dependent interaction is inves tigated in the present paper. The selfadjoint model operator describes the scattering problem for three one-dimensional particles. It is sho wn that this problem is equivalent to the diffraction problem in the s ector with energy dependent boundary conditions. The problem is solved with the help of the Sommerfeld-Maluzhinetz representation, which tra nsforms the partial differential equation for the eigenfunctions to a functional equation on the integral densities. The solution of the fun ctional equation can be constructed explicitly in the case of identica l particles. The three-body scattering matrix describing rearrangement and excitation processes is represented in terms of analytic function s.