M. Christ and A. Kiselev
Scattering and wave operators for 
one-dimensional Schr\"odinger operators with slowly 
decaying nonsmooth potentials
(150K, LaTeX)

ABSTRACT.  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.