Schrödinger operators with singular interactions: a model of tunneling resonances

Abstract

We discuss a generalized Schrödinger operator in L2(Rd), 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 BirmanSchwinger method it is cast into a form similar to the Friedrichs model.

Cite this paper

@inproceedings{Exner2003SchrodingerOW, title={Schrödinger operators with singular interactions: a model of tunneling resonances}, author={Pavel Exner}, year={2003} }