The Aharonov–Bohm problem revisited Original Research Article

Explicit solutions are constructed, and their properties investigated, for a nonrelativistic charged particle in two dimensions in the presence of an arbitrary number of nonquantized magnetic vortices in free space as well as in a uniform magnetic field. After eliminating the gauge potential, the vortices are represented as branch points in one of the complex coordinates. Multivortex solutions in free space can be obtained only if the vortices are treated as dynamical objects. But all the solutions suffer from some unphysical properties. The formulas may be generalized to describe a system of anyons.