03-548 Pavel Exner and Sylwia Kondej

Schroedinger operators with singular interactions: a model of tunneling resonances (98K, LaTeX) Dec 22, 03

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Abstract. We discuss a generalized Schr\"odinger operator in $L^2(\mathbb{R}^d),\, d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky quantum wire and a family of quantum dots if $d=2$, or surface waves in presence of a finite number of impurities if $d=3$. We analyze the discrete spectrum, and furthermore, we show that the resonance problem in this setting can be explicitly solved; by Birman-Schwinger method it is cast into a form similar to the Friedrichs model.

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