Scattering theory for Schrödinger operators with L∞ potentials and distorted Bloch waves

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Abstract
We prove that, if q 1 ε C 0 (R 3 )∩L ∞ (R 3 ) and q 2 ε L 1 (R 3 )∩L 2 (R 3 ) are real‐valued functions, the wave operators associated with the self‐adjoint operators H 1=−Δ+q 1 and H 2=−Δ+q 1+q 2 in L 2(R 3) exist and are complete. We also prove that, if q 1 is periodic and q 2 is in a certain weighted L 2 space X , the absolutely continuous part of H 2 possesses two sets of generalized eigenfunctions which belong to the dual space X * of X and are solutions of linear equations involving the generalized eigenfunctions of H 1.

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