SU(1, 1) solution for the Dunkl-Coulomb problem in two dimensions and its coherent states

We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the SU(1,1) symmetry. We introduce two different realizations of the su(1,1) Lie algebra and use the theory of irreducible representations to obtain the energy spectrum and eigenfunctions. For the first algebra realization, we apply the Schrödinger factorization to the radial part of the Dunkl-Coulomb problem to construct the algebra generators. In the second realization, we introduce three operators, one of them proportional to the Hamiltonian of the radial Schrödinger equation. Finally, we use the SU(1,1) Sturmian basis to construct the radial coherent states in a closed form.