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

Abstract

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 Hk, k = 1, 2, 3,…, on a plane. The elements of the dihedral group D2k are realized as operators on this plane and used to define some differential-difference operators Dr and Dφ. The latter serve to construct D2k-extended and invariant Hamiltonians [Formula: see text], from which the starting Hamiltonians Hk can be retrieved by projection in the D2k identity representation space.