Asymptotics of the S-Matrix for Perturbed Hill Operators

摘要

We consider the Schr?dinger operator with a periodic potential p plus a compactly supported potential q on the real line. We assume that both p and q have m ≥ 0 derivatives. For generic p, the essential spectrum of the operator has an infinite sequence of open gaps. We determine the asymptotics of the S-matrix at high energy.