Superintegrability of the Dunkl–Coulomb problem in three-dimensions

The superintegrability of the Dunkl–Coulomb model in three-dimensions is studied. The symmetry operators generalizing the Runge–Lenz vector operator are given. Together with the Dunkl angular momentum operators and reflection operators they generate the symmetry algebra of the Dunkl–Coulomb Hamiltonian which is a deformation of by reflections for bound states and is a deformation of by reflections for positive energy states. The spectrum of the Hamiltonian is derived algebraically using this symmetry algebra. The analog of the functional relation between the Coulomb Hamiltonian, Runge–Lenz operator and the angular momentum is given. (paper)