2010/10/25 by Jun-Li Xin, J. -Q. Liang, Jiu-Qing Liang
Physics and Astronomy · #Angular momentum #Angular momentum coupling #Angular momentum operator #Anyon #Gauge symmetry #Gauge theory #Noncommutative and Quantum Gravity Theories #Orbital angular momentum of light #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Total angular momentum quantum number #Wave function #hep-th #quant-ph
paper · pdf · doi:10.1088/1674-1056/21/4/040303
6 pages, 5 figures
arxiv created 2010/10/25 · openalex publication_date 2012/04/01 · arxiv updated 2015/05/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 2π-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 2π-periodic.