A. Chahrour et J. Sahbani, On the spectral and scattering theory of the Schrodinger operator with surface potential, REV MATH PH, 12(4), 2000, pp. 561-573
We consider a discrete Schrodinger operator H = -Delta + V acting in l(2)(Z
(d+1)), with potential V supported by the subspace Z(d) X {0}. We prove tha
t sigma(-Delta) = [-2(d + 1), 2(d + 1)] is contained in the absolutely cont
inuous spectrum of H. For this we develop a scattering theory for H. We emp
hasize the fact that this result applies to arbitrary potentials, so it dep
ends on the structure of the problem rather than on a particular choice of
the potential.