Note on the spectrum of discrete Schrödinger operators [article]

Fumio Hiroshima, Itaru Sasaki, Tomoyuki Shirai, Akito Suzuki
2012 arXiv   pre-print
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.
arXiv:1209.0522v1 fatcat:z4aafe6nizb6xmofg3lyey7poa