Quantum–classical correspondence for motion on a plane with deficit angle

A particle constrained to move on a cone and bound to its tip by harmonic oscillator and Coulomb–Kepler potentials is considered both in the classical as well as in the quantum formulations. The SU(2) coherent states are formally derived for the former model and used for showing some relations between closed classical orbits and quantum probability densities. Similar relations are shown for the Coulomb–Kepler problem. In both cases a perfect localization of the densities on the classical solutions is obtained even for low values of quantum numbers.