The interaction between atoms and surfaces may be probed by bound stat
e resonance spectroscopy. The experiments are usually interpreted with
in the free particle picture which assumes that the energy-momentum re
lation of atoms adsorbed onto a surface is described by 2D parabolic b
ands. We calculate and analyze the band structure of an atom adsorbed
on a model corrugated surface and follow its behavior as the interacti
on potential evolves from weakly to strongly corrugated. Besides the e
xpected reduction of degeneracy and development of gaps, we obtained a
sizable correction to the bound state energies. We employ our results
to reanalyze the available experiments on the system He-NaCl(001).