# Schr\"odinger operators with $\delta$-potentials supported on unbounded Lipschitz hypersurfaces

@inproceedings{Behrndt2021SchrodingerOW, title={Schr\"odinger operators with \$\delta\$-potentials supported on unbounded Lipschitz hypersurfaces}, author={Jussi Behrndt and Vladimir Lotoreichik and Peter Schlosser}, year={2021} }

In this note we consider the self-adjoint Schrödinger operator Aα in L(R), d ≥ 2, with a δ-potential supported on a Lipschitz hypersurface Σ ⊆ R of strength α ∈ L(Σ) + L∞(Σ). We show the uniqueness of the ground state and, under some additional conditions on the coefficient α and the hypersurface Σ, we determine the essential spectrum of Aα. In the special case that Σ is a hyperplane we obtain a Birman-Schwinger principle with a relativistic Schrödinger operator as Birman-Schwinger operator. As…

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