Lie-algebraic interpretation of the maximal superintegrability and exact solvability of the Coulomb-Rosochatius potential in n dimensions

The potential group method is applied to the n-dimensional Coulomb-Rosochatius potential, whose bound states and scattering states are worked out in detail. As far as scattering is concerned, the S-matrix elements are computed by the method of intertwining operators and an integral representation is obtained for the scattering amplitude. It is shown that the maximal superintegrability of the system is due to the underlying potential group and that the 2n-1 constants of motion are related to Casimir operators of subgroups.