On the physics of the $s{o}_q(4)$ hydrogen atom

In this work we investigate the $q$-deformation of the $so(4)$ dynamical symmetry of the hydrogen atom using the theory of the quantum group $s{u}_q(2)$. We derive the energy spectrum in a physically consistent manner and find a degeneracy breaking as well as a smaller Hilbert space. We point out that using the deformed Casimir as was done before leads to inconsistencies in the physical interpretation of the theory.