- 19-35 Pavel Exner and Sylwia Kondej
- Spectral optimization for strongly singular Schr dinger operators with a star-shaped interaction
Jun 2, 19
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Abstract. We discuss the spectral properties of singular Schr dinger 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 known as solutions of the closely related Thomson problem.