Generalized interactions supported on hypersurfaces

Abstract

We analyze a family of singular Schrödinger operators with local singular interactions supported by a hypersurface $\Sigma \subset {\mathbb{R}}^n,n\ge 2$, being the boundary of a Lipschitz domain, bounded or unbounded, not necessarily connected. At each point of $\Sigma$ the interaction is characterized by four real parameters, the earlier studied case of $\delta$- and ${\delta }^{\prime }$-interactions being particular cases. We discuss spectral properties of these operators and derive operator inequalities between those referring to the same hypersurface but different couplings and describe their implications for spectral properties.

References in corpus (4)

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• Schrödinger operators with $\delta$-interactions supported on conical surfaces
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• Scattering properties of two singularly interacting particles on the half-line
• On Schrödinger operators with ${\delta }^{\prime }$-potentials supported on star graphs
• Trace Hardy inequality for the Euclidean space with a cut and its applications
• A non-degeneracy theorem for interacting fermions in one dimension