Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
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abstract
In this paper, we consider the perturbed Stark operator \begin{equation*} Hu=H_0u+qu=-u^{primeprime}-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.
