Electrons confined on the surface of a sphere in a magnetic field

We derive an analytic expression for the quantum-mechanical spectrum of noninteracting electrons restricted to move on the surface of a sphere in a uniform external magnetic field. The field dependence of the energy levels leads to a complex level crossing structure which is manifested in the magnetic properties. For a fixed number of electrons, the magnetization exhibits irregular discontinuities at low fields while aperiodic oscillations occur at higher field values. The magnetic susceptibility exhibits sharp spikes and ``jumps,'' as the chemical potential crosses the energy gaps between adjacent energy levels.