03-383 A. Laptev, S. Naboko, O. Safronov

Absolutely continuous spectrum of Schr\"odinger operators with slowly decaying and oscillating potentials (233K, Postscript) Aug 25, 03

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Abstract. The aim of this paper is to extend a class of potentials for which the absolutely continuous spectrum of the corresponding multidimensional Schr\"odinger operator is essentially supported by $[0,\infty)$. Our main theorem states that this property is preserved for slowly decaying potentials provided that there are some oscillations with respect to one of the variables.

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