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

• URL: http://arxiv.org/abs/2308.10256v1
• Date: Sun, 20 Aug 2023 12:49:30 GMT
• Title: Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence
• Authors: Jun-Li Xin, Jiu-Qing Liang
• Abstract summary: 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. A non-Abelian anyon-model emerges in a natural way.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 at 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.

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