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arXiv · 1809.04694

Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators

Wencai Liu
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Abstract

In this paper, we consider the perturbed Stark operator \begin{equation*} Hu=H_0u+qu=-u^{\prime\prime}-xu+qu, \end{equation*} where $q$ is the power-decaying perturbation. The criteria for $q$ such that $H=H_0+q$ has at most one eigenvalue (finitely many, infinitely many eigenvalues) are obtained. All the results are quantitative and are generalized to the perturbed Stark type operator.

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Wencai Liu. 2018-09-12. Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators. https://doi.org/10.1016/j.jfa.2018.11.010

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