Exact solution of a class of three-body scattering problems in one dimension

Abstract

We present an exact solution of the three-body scattering problem for a one-parameter family of one-dimensional potentials containing the Calogero and Wolfes potentials as special limiting cases. The result is an interesting nontrivial relationship between the final momenta p'_i and the initial momenta p_i of the three particles. We also discuss another one-parameter family of potentials for all of which p'_i = -p_i (i = 1,2,3).