# Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction

@article{Exner2019SpectralOF, title={Spectral optimization for strongly singular Schr{\"o}dinger operators with a star-shaped interaction}, author={Pavel Exner and Sylwia Kondej}, journal={Letters in Mathematical Physics}, year={2019}, volume={110}, pages={735-751} }

We discuss the spectral properties of singular Schrödinger operators in three dimensions with the interaction supported by an equilateral star, finite or infinite. In the finite case, the discrete spectrum is nonempty if the star arms are long enough. Our main result concerns spectral optimization: we show that the principal eigenvalue is uniquely maximized when the arms are arranged in one of the known five sharp configurations.

## 2 Citations

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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…

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