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.