# Schr\"odinger operators with oblique transmission conditions in $\mathbb{R}^2$

@inproceedings{Behrndt2022SchrodingerOW, title={Schr\"odinger operators with oblique transmission conditions in \$\mathbb\{R\}^2\$}, author={Jussi Behrndt and Markus Holzmann and Georg Stenzel}, year={2022} }

. In this paper we study the spectrum of self-adjoint Schr¨odinger operators in L 2 ( R 2 ) with a new type of transmission conditions along a smooth closed curve Σ ⊆ R 2 . Although these oblique transmission conditions are formally similar to δ ′ -conditions on Σ (instead of the normal derivative here the Wirtinger derivative is used) the spectral properties are signiﬁcantly diﬀerent: it turns out that for attractive interaction strengths the discrete spectrum is always unbounded from below…

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