Scattering and wave operators for one-dimensional Schr\"odinger operators with slowly decaying nonsmooth potentials
Abstract
We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in Lp(), p<2. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We also prove asymptotic completeness of these wave operators for some classes of random potentials, and for almost every boundary condition for any given potential.
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