No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators
Spectral Theory
2023-01-18 v1
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.
Cite
@article{arxiv.2301.05899,
title = {No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators},
author = {Kota Ujino},
journal= {arXiv preprint arXiv:2301.05899},
year = {2023}
}