Algebraic Approach to the Scattering Matrix

A purely algebraic procedure is presented for calculating recursion relations for $S$ matrices belonging to problems associated with the group SU(1,1). The procedure involves supplementing a recently introduced group-theoretic approach to scattering by an algebraic framework that characterizes asymptotic behavior. Our formulation makes use of the Euclidean group, which contains the symmetry transformations for a free particle. The Coulomb and Pöschl-Teller potentials are discussed to illustrate our methods.