Scattering states in conformally invariant quantum mechanics

We present a general algebraic analysis of scattering in conformally invariant quantum mechanical systems. The dynamical group is the most elementary non-Abelian noncompact Lie group, SU(1, 1). The Hamiltonians we investigate Contain the noncompact generators of SU(1, 1) and hence possess a purely continuous spectrum. We diagonalize these generators showing that their generalized eigenvectors (the scattering states) have an elegant representation in terms of SU(1, 1) coherent states. We revisit the well-known examples of the nonrelativistic point particle in an inverse square potential and the Aharonov-Bohm system. We discuss the connection of our algebraic approach with previous studies.