## Runge-Lenz Vector, Accidental SU(2) Symmetry, and Unusual Multiplets for Motion on a Cone

##### Authors
Al-Hashimi, M. H.
Wiese, U. -J.
##### Description
We consider a particle moving on a cone and bound to its tip by $1/r$ or harmonic oscillator potentials. When the deficit angle of the cone divided by $2 \pi$ is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional spin'' and unusual degeneracies.
Comment: 26 pages, 7 figures
##### Keywords
Quantum Physics, High Energy Physics - Theory, Mathematical Physics