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arXiv · 0907.1543

Lower bound on the spectrum of the Schrödinger operator in the plane with delta-potential supported by a curve

Igor Lobanov·Vladimir Lotoreichik·Igor Popov
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Abstract

We consider the Schrödinger operator in the plane with delta-potential supported by a curve. For the cases of an infinite curve and a finite loop we give estimates on the lower bound of the spectrum expressed explicitly through the strength of the interaction and a parameter which characterizes geometry of the curve. Going further we cut the curve into finite number of pieces and estimate the bottom of the spectrum using the parameters for the pieces. As an application of the elaborated theory we consider a curve with a finite number of cusps and "leaky" quantum graphs.

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Igor Lobanov, Vladimir Lotoreichik, Igor Popov. 2009-07-09. Lower bound on the spectrum of the Schrödinger operator in the plane with delta-potential supported by a curve. https://arxiv.org/abs/0907.1543

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