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arXiv · 2601.10523

Some Eigenvalue Inequalities for the Schrödinger Operator on Integer Lattices

Wentao Liu
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Abstract

In this paper, we establish analogues of the Payne-Pólya-Weinberger, Hile-Protter, and Yang eigenvalue inequalities for the Schrödinger operator on arbitrary finite subsets of the integer lattice $\mathbb{Z}^n$. The results extend known inequalities for the discrete Laplacian to a more general class of Schrödinger operators with nonnegative potentials and weighted eigenvalue problems.

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Wentao Liu. 2026-01-15. Some Eigenvalue Inequalities for the Schrödinger Operator on Integer Lattices. https://arxiv.org/abs/2601.10523

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