paper

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

arXiv:1809.04694 · doi:10.1016/j.jfa.2018.11.010

Abstract

In this paper, we consider the perturbed Stark operator \begin{equation*} Hu=H_0u+qu=-u^{\prime\prime}-xu+qu, \end{equation*} where is the power-decaying perturbation. The criteria for such that 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.

J. Funct. Anal. to appear

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