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arXiv · 1010.4352

Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space

Jun-Li Xin·J. -Q. Liang
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Abstract

We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level-space of angular momentum being greater or less than $\hbar$ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily $2\pi$-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The quantum mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144) becomes a special case of the arbitrary-quantization.

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Jun-Li Xin, J. -Q. Liang. 2010-10-21. Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space. https://doi.org/10.1088/1674-1056/21/4/040303

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