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 representable as a sum of three terms. This sum is neither fast decaying, nor it rapidly changes its sign or has derivatives with respect to the angular variables.