Scattering Theory for the Perturbations of Periodic Schrr Odinger Operators
نویسنده
چکیده
In this article, we study the short-and long-range perturbations of periodic Schrr odinger operators. The asymptotic completeness is proved in the short-range case by referring to known results on the stationary approach and more explicitly with the time-dependent approach. In the long-range case, one is able to construct modiied wave operators. In both cases, the asymptotic observables can be deened as elements of a commutative C algebra of which the spectrum equals or is contained in the Bloch variety. Especially, the expression of the mean velocity as the gradient of the Bloch eigenvalues is completely justiied in this framework, even when the Bloch variety presents singularities.
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