The electronic states of a model Hamiltonian representing a single impurity atom adsorbed on the surface of a semi-infinite crystal are described in general terms. The model potential field is constructed by abruptly terminating the potential of the infinite crystal at the surface and by replacing the potential outside the crystal by a constant. The adsorbed atom is represented by a spherical potential of the muffin-tin type superimposed on the constant potential on the vacuum side of the metal–vacuum interface. A method for evaluating the eigenvalues and eigenfunctions of this model Hamiltonian is presented.