For perturbed Stark operators $Hu=-u^{\prime\prime}-xu+qu$, the author has proved that $\limsup_{x\to \infty}{x}^{\frac{1}{2}}|q(x)|$ must be larger than $\frac{1}{\sqrt{2}}N^{\frac{1}{2}}$ in order to create $N$ linearly independent eigensolutions in $L^2(\mathbb{R}^+)$. In this paper, we apply generalized Wigner-von Neumann type functions to construct embedded eigenvalues for a class of Schrodinger operators, including a proof that the bound $\frac{1}{\sqrt{2}}N^{\frac{1}{2}}$ is sharp.

中文翻译：

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扰动 Stark 类型算子的有限多个嵌入特征值的锐界

对于扰动 Stark 算子 $Hu=-u^{\prime\prime}-xu+qu$，作者证明了 $\limsup_{x\to \infty}{x}^{\frac{1}{2} }|q(x)|$ 必须大于 $\frac{1}{\sqrt{2}}N^{\frac{1}{2}}$ 才能在 $ 中创建 $N$ 线性无关的特征解L^2(\mathbb{R}^+)$。在本文中，我们应用广义 Wigner-von Neumann 类型函数来构造一类薛定谔算子的嵌入特征值，包括证明有界 $\frac{1}{\sqrt{2}}N^{\frac{1 }{2}}$ 是尖锐的。