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 …