Editorial Board

JMI2012B-4 Note on the spectrum of discrete Schrödinger operators (pp.105-108)

Author(s): Fumio Hiroshima, Itaru Sasaki, Tomoyuki Shirai and Akito Suzuki

J. Math-for-Ind. 4B (2012) 105-108.

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 $d\geq5$ but does not for $1\leq d\leq 4$.

Keyword(s).  discrete Schrodinger operator, rank-one perturbation