Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials

Details Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials

2001-10-13

arxiv.org/abs/math/0110140v1

Mathematics

Spectral Theory

46 pages

Scientific paper

We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. 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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