Eigenvalues of the discrete Schrödinger operator in the large coupling constant limit
Abstract
Let (λ−,λ+) be a spectral gap of a periodic Schrödinger operator A on the lattice Zd. Consider the operator A(α)=A−αV where V is a decaying positive potential on Zd. We study the asymptotic behavior of the number of eigenvalues of A(t) passing through a point λ∈(λ−,λ+) as t grows from 0 to α.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Applicable Analysis
- Publisher
- Informa UK Limited
- Pages
- 1–9
- Publication date
- 21 June 2026
- Language
- EN