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Eigenvalues of Šeba billiards with localization of low-energy eigenfunctions
We study the localization of eigenfunctions produced by a point scatterer on a thin rectangle. We find an explicit set of eigenfunctions localized to part of the rectangle by showing that the one-dimensional Schr\"odinger operator with a Dirac delta potential asymptotically governs the spectral properties of the two-dimensional point scatterer. …