Publications of the Research Institute for Mathematical Sciences

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Volume 49, Issue 4, 2013, pp. 831–859
DOI: 10.4171/PRIMS/121

Spectral Analysis of a Quantum System with a Double Line Singular Interaction

Sylwia Kondej[1] and David Krejčiřík[2]

(1) Institute of Physics, University of Zielona Góra, ul. Szafrana 4a, 65246, ZIELONA GORA, POLAND
(2) Department of Mathematics, Czech Technical University in Prague, Trojanova 13, 12000, PRAGUE 2, CZECH REPUBLIC

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically approaches a constant value, and nd conditions which guarantee either the existence of discrete eigenvalues or Hardy-type inequalities. For a class of our models admitting mirror symmetry, we also establish the existence of embedded eigenvalues and show that they turn into resonances after introducing a small perturbation.

Keywords: Schrödinger operator, singular perturbation, spectral analysis, Hardy inequality, resonance

Kondej Sylwia, Krejčiřík David: Spectral Analysis of a Quantum System with a Double Line Singular Interaction. Publ. Res. Inst. Math. Sci. 49 (2013), 831-859. doi: 10.4171/PRIMS/121