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

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 $\hslash$ 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.

6 pages, 5 figures

References in corpus (6)

• Hidden supersymmetry in quantum bosonic systems
• Bosons, fermions and anyons in the plane, and supersymmetry
• The origin of the hidden supersymmetry
• Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• Fidelity susceptibility and geometric phase in critical phenomenon