  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.
