Note on the spectrum of discrete Schrödinger operators

Abstract

The spectrum of discrete Schrödinger operator L + V on the d-dimensional lattice is considered, where L denotes the discrete Laplacian and V a delta function with mass at a single point. Eigenvalues of L + V are specified and the absence of singular continuous spectrum is proven. In particular it is shown that an embedded eigenvalue does appear for d ≥ 5 but does not for 1 ≤ d ≤ 4.