Wannier excitons in a thin crystal film

Energy levels and wave functions of Wannier excitons in a crystal film whose thickness is smaller than the size of the exciton are calculated. The exciton is found to behave like a two-dimensional hydrogenic atom when projected onto a plane parallel to the film surface; it behaves like an independent particle and hole in a potential well in the direction normal to the film. The effect of the finite thickness of the film is calculated perturbatively. The energy-level scheme is plotted for a numerical example.