Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition, which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly under the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way.