  Surface bound states in a discrete-lattice model of a $d_{x^2 - y^2}$ cuprate
superconductor are shown to be, in general, coherent superpositions of an
incoming excitation and more than one outgoing excitation, and a simple
graphical construction based on a surface Brillouin zone is developed to
describe their nature. In addition, a momentum-dependent lifetime contribution
to the width of these bound states as observed in tunneling experiments is
derived and elucidated in physical terms.
