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arXiv · 2609.03224

Optimal bounds for embedded eigenvalues of one-dimensional discrete Schr\"odinger operators with decaying potentials

Jifeng Chu·Wencai Liu·Kang Lyu
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Abstract

In this paper, we consider one-dimensional discrete Schr\"odinger operators \begin{align} Hu(n)=(\Delta+V)u(n)\nonumber \end{align} on $\ell^2(\mathbb{N})$ with a self-adjoint boundary condition at $n=0$, where $\Delta$ denotes the discrete Laplacian and $V(n)$ is a real-valued perturbation satisfying $$V(n)=\frac{O(1)}{1+n}.$$ We determine the sharp transition for the asymptotic coefficient of \(V\) governing the existence and nonexistence of embedded eigenvalues.

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Jifeng Chu, Wencai Liu, Kang Lyu. 2026-09-02. Optimal bounds for embedded eigenvalues of one-dimensional discrete Schr\"odinger operators with decaying potentials. https://arxiv.org/abs/2609.03224

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