The existence and location of eigenvalues of the one particle discrete Schroedinger operators

2015/05/14 by Saidakhmat N. Lakaev, Lakaev, Saidakhmat N., Ender Ozdemir +1
Mathematics · Physics and Astronomy · #47N50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 81Q10 #Secondary: 35P20 #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35P20 #msc:47N50 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.1505.03645

11 pages, 1 figure

arxiv created 2015/05/14 · arxiv updated 2015/05/15

Abstract

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below the bottom of the essential spectrum, as well as above its top. Moreover, we show that the operator H can have two eigenvalues outside of the essential spectrum such that one of them is situated below the bottom of the essential spectrum, and other one above its top.

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