Some Eigenvalue Inequalities for the Schrödinger Operator on Integer Lattices
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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Mathematical Inequalities and Applications
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 January 2026
- Document type
- Preprint