Oleg Safronov
Absolutely continuous spectrum of the Schr\"odinger operator with a potential representable as a sum of three functions with special properties
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ABSTRACT.  We consider a family of Schr\"odinger operators depending on a real parameter and prove that the a.c. spectrum covers the positive half-line for almost every value of the parameter. The potentials in this model are neither fast decaying, nor they are oscillating or have derivatives with respect to the angular variable.