Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

doi:10.1088/0305-4470/37/45/012 We establish that by parametrizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite-dimensional representation spaces of a Lie algebra. We present explicitly the Gq2-case for which we construct the potentials by means of suitable gauge transformations. PACS numbers: 02.20.Sv, 03.65.−w 1