Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone (Q2467709)

In this interesting paper, the authors consider the physics of a particle confined to a cone surface with definite angle and bound to its tip by certain potentials. It is showsn that the bound orbits are close, as well as the existence of accidental degeneracies are pointed out. It is further proved that the representations of the accidental \(\mathfrak{su}(2)\)-symmetry are larger than the representations of degenerate states. This systems presents interesting and puzzling features, such as the behavior of degenerate states with respect to the Casimir spin. Possible systems where simmilar accidental degeneracies could be observed are commented.