Abstract
In this paper, we consider the perturbed Stark operatorHu=H0u+qu=−u″−xu+qu, where q is the power-decaying perturbation. The criteria for q such that H=H0+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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