Generalized spheroidal wave equations from an image-potential method for surface effects on impurity states

Based on the hydrogenic effective-mass approximation, an image-potential method is developed for the treatment of impurities in semiconductors with a boundary surface. The Schr\"odinger equation is separable in prolate spheroidal coordinates (ξ, η, φ). Generalized spheroidal wave equations of ξ and η resulting from the separation constitute the basic equations for the study of surface effects on impurity states.