00-259 Jaouad Sahbani
On the absolutely continuous spectrum of Stark Hamiltonians (183K, PS) Jun 7, 00
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Abstract. We study the spectral properties of the Schr\H{o}dinger operator with a constant electric field perturbed by a bounded potential. It is shown that if the derivative of the potential in the direction of the electric field is smaller at infinity than the electric field then the spectrum of the corresponding Stark operator operator is purely absolutely continuous. In one dimension the absolute continuity of the spectrum is implied by just the boundedness of the derivative of the potential. The sharpness of our criterion for higher dimensions is illustrated by constructing smooth potentials with bounded partial derivatives for which the corresponding Stark operators have a dense point spectrum.

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