Eigenvalues of the discrete Schrödinger operator in the large coupling constant limit

2025/02/16 by Gao, Siyu
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2502.11257

Abstract

Let (λ_-,λ₊) be a spectral gap of a periodic Schrödinger operator A on the lattice \mathbb Z^d. Consider the operator A(α)=A-αV where V is a decaying positive potential on \mathbb Z^d. 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.

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