Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials. (Q1811211)

Using the asymptotic behavior of generalized eigenfunctions studied in their earlier paper [J. Funct. Anal. 179, 426--447 (2001; Zbl 0985.34078)], the authors prove the existence of modified wave operators for one-dimensional Schrödinger equations with potentials belonging to \(L^{p}(\mathbb R)\) for \(1<p<2.\) The asymptotic completeness of these wave operators is proved for some classes of random potentials.