Imbedded Singular Continuous Spectrum for Schrödinger Operators
نویسنده
چکیده
We construct examples of potentials V (x) satisfying |V (x)| ≤ h(x) 1+x , where the function h(x) is growing arbitrarily slowly, such that the corresponding Schrödinger operator has imbedded singular continuous spectrum. This solves one of the fifteen “twenty-first century” problems for Schrödinger operators posed by Barry Simon in [22]. The construction also provides the first example of a Schrödinger operator for which Möller wave operators exist but are not asymptotically complete due to the presence of singular continuous spectrum.
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