EXCHANGE OPERATOR FORMALISM FOR AN INFINITE FAMILY OF SOLVABLE AND INTEGRABLE QUANTUM SYSTEMS ON A PLANE

The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians H(k), k=1,2,3,..., on a plane. The elements of the dihedral group D(2k) are realized as operators on this plane and used to define some differential-difference operators D(r) and D(phi). The latter serve to construct D(2k)-extended and invariant Hamiltonians H(k), from which the starting Hamiltonians H(k) can be retrieved by projection in the D(2k) identity representation space.