1307.1233 (Sylwia Kondej et al.)

Spectral analysis of a quantum system with a double line singular
interaction    [PDF]

Sylwia Kondej, David Krejcirik

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 find conditions which guarantee either the existence of discrete eigenvalues or Hardy-type inequalities. For a class of our models admitting a mirror symmetry, we also establish the existence of embedded eigenvalues and show that they turn into resonances after introducing a small perturbation.

View original: http://arxiv.org/abs/1307.1233