Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

doi:10.1088/1674-1056/21/4/040303

Abstract We study quantum-classical correspondence in terms of the 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

ℏ

is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2

π

-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 well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2

π

-periodic.

Keywords: quantum-classical correspondence anyon rotational symmetry arbitrary quantization of angular momentum

Received: 22 June 2011
Revised: 10 October 2011
Accepted manuscript online:

PACS:	03.65.Vf	(Phases: geometric; dynamic or topological)
	05.30.Pr	(Fractional statistics systems)
	45.20.df	(Momentum conservation)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China(Grant No.11075099)

Corresponding Authors: Xin Jun-Li, E-mail:xinjunliycu@163.com
E-mail: xinjunliycu@163.com

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Xin Jun-Li(辛俊丽) and Liang Jiu-Qing(梁九卿) Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space 2012 Chin. Phys. B 21 040303

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