The hydrogen atom in a semi-infinite space limited by a hyperboloidal boundary

The hydrogen atom in a semi-infinite space limited by a hyperboloidal boundary, with the nucleus at a focus. is investigated as a model of an atom on the surface of a solid. The energy eigenvalues, hyperfine structure and electric dipole moment of the system are evaluated for different focal distances and eccentricities of the boundary. It is shown that the system tends to become infinitely degenerate at the ionization threshhold as the boundary closes in approaching the nucleus. This model includes as special cases the corresponding models in the literature with plane and paraboloidal boundaries. 5 figs., 2 tabs