The Dunkl–Coulomb system in three-dimensions is introduced. The energy spectrum and the wave functions of the system are solved by means of spectrum generating algebra techniques based on the Lie algebra. An explicit h-spherical harmonics basis is given in terms of Jacobi polynomials.
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.
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