Pavel Exner and Sylwia Kondej
Schroedinger operators with singular interactions:
a model of tunneling resonances
(98K, LaTeX)

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.