Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem

Bound and scattering states of a non-central extension of the three-dimensional Kepler-Coulomb Hamiltonian are worked out analytically within the framework of the potential groups of the problem, SO(7) for bound states and SO(6,1) for scattering states. In the latter case, the S matrix is calculated by the method of intertwining operators.