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

0524196 - ÚJF 2021 RIV NL eng J - Journal Article
Exner, Pavel - Kondej, S.
Spectral optimization for strongly singular Schrodinger operators with a star-shaped interaction.
Letters in Mathematical Physics. Roč. 110, č. 4 (2020), s. 735-751. ISSN 0377-9017. E-ISSN 1573-0530
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : singular Schrodinger operator * three dimensions * spectral optimization * star-shaped interaction
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.550, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s11005-019-01237-0

We discuss the spectral properties of singular Schrodinger 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.
Permanent Link: http://hdl.handle.net/11104/0308578