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For a scattering problem of tight-binding Bloch electrons by a weak randomsurface potential, a generalized Levinson theorem is put forward showing theequality of the total density of surface states and the density of the totaltime delay. The proof uses explicit formulas for the wave operators in the newrescaled energy and interaction (REI) representation, as well as an indextheorem for adequate associated operator algebras.

The density of surface states as the total time delay