A. Kiselev
Imbedded Singular Continuous Spectrum for Schr\"odinger Operators
(406K, Postscript)
ABSTRACT. We construct examples of potentials $V(x)$ satisfying
$|V(x)| \leq \frac{h(x)}{1+x},$
where the function $h(x)$ is growing arbitrarily slowly, such that
the corresponding Schr\"odinger
operator has imbedded singular continuous spectrum. This solves
one of the fifteen ``twenty-first century"
problems for Schr\"odinger operators posed
by Barry Simon. The construction also provides the
first example of a Schr\"odinger operator for
which M\"oller wave operators exist but are not asymptotically
complete due to the presence of singular continuous spectrum.