Wednesday, September 5, 2012

1209.0522 (Fumio Hiroshima et al.)

Note on the spectrum of discrete Schrödinger operators    [PDF]

Fumio Hiroshima, Itaru Sasaki, Tomoyuki Shirai, Akito Suzuki
The spectrum of discrete Schr\"odinger 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 $1\leq d\leq 4$.
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