Symmetries of a quantized system moving on a pointed plane in a Coulomb potential

Quantization of systems that are localized on a pointed plane with a 1/r po tential is investigated. For this, the self-adjoint extensions of the Hamil tonian are classified, and quantization of classical constants of the motio n is considered. It is shown that only in special cases do their quantizati ons commute with the Hamiltonian. As a result, there arise degeneracies of the eigenspaces of the Hamiltonian.