Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators

Wencai Liu

Mathematische Nachrichten, 2020, vol. 293, issue 9, 1776-1790

Abstract: For perturbed Stark operators Hu=−u′′−xu+qu, the author has proved that lim supx→∞x12|q(x)| must be larger than 12N12 in order to create N linearly independent eigensolutions in L2(R+) [29]. In this paper, we apply generalized Wigner–von Neumann type functions to construct embedded eigenvalues for a class of Schrödinger operators, including a proof that the bound 12N12 is sharp.

Date: 2020
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https://doi.org/10.1002/mana.201800517

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