EXPLICIT SOLUTION OF THE QUANTUM THREE-BODY CALOGERO-SUTHERLAND MODEL
The class of quantum integrable systems associated with root systems was introduced by Olshanetsky and Perelomov as a generalization of the Calogero - Sutherland systems. It was recently shown by one of the authors that for such systems with a potential , the series in the product of two wavefunctions is the -deformation of the Clebsch - Gordan series. This yields recursion relations for the wavefunctions of those systems and, related to them, for generalized zonal spherical functions on symmetric spaces. In this letter this approach is used to compute the explicit expressions for the three-body Calogero - Sutherland wavefunctions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation (-deformation) introduced by Macdonald.