Scattering and wave operators for onedimensional Schrödinger operators with slowly decaying nonsmooth potentials
Abstract
We prove existence of modified wave operators for onedimensional Schrödinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual Möller 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110140
 Bibcode:
 2001math.....10140C
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 34L40;
 35P25;
 42B20;
 81Q10
 EPrint:
 46 pages