• Corpus ID: 250280153

# 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}
}
• Published 5 July 2022
• Mathematics
. 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…

## References

SHOWING 1-10 OF 28 REFERENCES

• Mathematics, Physics
• 2019
In this article, Dirac operators A η,τ coupled with combinations of electrostatic and Lorentz scalar δ - shell interactions of constant strength η and τ , respectively, supported on compact surfaces
• Mathematics
SIAM J. Math. Anal.
• 2015
An uncertainty principle is developed, and its relation to some eigenvectors of the coupling is shown, and a criterion for generating confinement is given.
• Mathematics
• 2022
In this article we develop a systematic approach to treat Dirac operators Aη,τ,λ with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths η, τ, λ ∈ R,
The aim of this review is to provide an overview of a recent work concerning leaky'' quantum graphs described by Hamiltonians given formally by the expression $-\Delta -\alpha \delta (x-\Gamma)$
• Physics
• 2017
References: • F.A.Berezin, M. Shubin: The Schrödinger equation. Mathematics and its Applications, Springer (1991). • M.Combescure, D.Robert: Coherent states and applications in Mathematical Physics,
• Mathematics
• 2015
We establish high energy $L^2$ estimates for the restriction of the free Green's function to hypersurfaces in $\mathbb{R}^d$. As an application, we estimate the size of a logarithmic resonance free