Ground state of a spin-½ charged particle in a two-dimensional magnetic field

We prove that a spin-{} charged particle moving in a plane under the influence of a perpendicular magnetic field has (N-1) zero-energy states, where N is the closest integer to the total flux in units of the flux quantum. The (N-1) independent wave functions are calculated explicitly. The result, which is extremely simple to prove, is an example of the Atiyah-Singer index theorem when applied to the Euclidean two-dimensional Dirac equation.