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

Abstract

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.

10 pages; major changes to section 3

References in corpus (3)

• Hydrogen atom on curved noncommutative space
• Laplace-Runge-Lenz vector in quantum mechanics in noncommutative space
• On the $\star$-product quantization and the Duflo map in three dimensions

Cited by in corpus (2)

• On the Hydrogen Atom in the Holographic Universe
• Computer Algebra in Physics: The hidden SO(4) symmetry of the hydrogen atom