Self-adjoint extensions of the Hamiltonian for a charged particle in the presence of a thread of magnetic flux

Self-adjoint extensions of the usual Hamiltonian are studied for a charged particle moving in the x-y plane in the presence of an infinitely thin thread of magnetic flux along the z axis. This is done by starting with a square-well potential and taking its zero-range limit. The wave function for such an extended Hamiltonian is, although square integrable, singular at the origin. There are interesting differences between the cases with and without the magnetic flux.