Two-Dimensional Angular Momentum in the Presence of Long-Range Magnetic Flux

Abstract

It is shown that eigenvalues of two-dimensional angular momentum remain integer valued in the magnetic field of a solenoid, contrary to published assertions that they are modified by the flux. For a vortex, flux does contribute, and the angular momentum can fractionize, as asserted in the literature, provided phases of wave functions are chosen consistently with the solenoid problem. Long-range effects of flux, the distinction between orbital and canonical angular momentum, and interactions with Cooper pairs are essential to this argument.