Explicit solution of the quantum three-body Calogero-Sutherland model

摘要

Quantum integrable systems generalizing Calogero-Sutherland systems wereintroduced by Olshanetsky and Perelomov (1977). Recently, it was proved thatfor systems with trigonometric potential, the series in the product of two wavefunctions is a deformation of the Clebsch-Gordan series. This yields recursionrelations for the wave functions of those systems. In this note, this approachis used to compute the explicit expressions for the three-bodyCalogero-Sutherland wave functions, which are the Jack polynomials. Weconjecture that similar results are also valid for the more generaltwo-parameters deformation introduced by Macdonald.