NEW EXACTLY AND CONDITIONALLY EXACTLY SOLVABLE N-BODY PROBLEMS IN ONE-DIMENSION

We study a class of Calogero-Sutherland type one-dimensional N-body qu antum mechanical systems, with potentials given by [GRAPHICS] where U( root Sigma i<j(x(i)-x(j))(2)) of specific farm. It is shown that, only for a, few choices of U, the eigenvalue problems can be solved exactl y for arbitrary g'. The eigenspectra of these Hamiltonians, when g' no t equal 0, are nondegenerate and the scattering phase shifts are found to be energy-dependent. It is further pointed out that, tile eigenval ue problems are amenable to solution for wider choices of U, if g' is conveniently fixed. These conditionally exactly solvable problems also do not exhibit energy degeneracy and the scattering phase shifts can be computed only for a specific partial wave.