No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators

Kota Ujino

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arXiv · 2301.05899

No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators

Kota Ujino

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Abstract

It is known that the spectrum of Schr\"odinger operators with sparse potentials consists of singular continuous spectrum. We give a sufficient condition so that the edge of the singular continuous spectrum is not an eigenvalue and construct examples with singular continuous spectrum which have no eigenvalues and which have a single negative eigenvalue.

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Kota Ujino. 2023-01-14. No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators. https://arxiv.org/abs/2301.05899

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