Hydrogen atom confined to an ellipsoid

Abstract

We have analysed the properties of a hydrogen atom at the focus of a confining, prolate ellipsoid. This system is separable in terms of elliptic coordinates, and has the unusual property that the solution is a product of two identical functions of elliptic coordinates. We have obtained the energies for several states, for different positions of the foci and different values of the semi-major axis, and also developed simple model wavefunctions for some states, based on the cusp and boundary conditions. The model may provide a good representation of the distortions in the confining surface when the confined atom moves away from the centre.