Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 42, Issue 38, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/42/38/385207
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This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z(n) which are discrete analogs of the Schrodinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of pseudodifference operators (i.e., pseudodifferential operators on the group Z(n) with analytic symbols), and the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schrodinger operators on Z(n), Dirac operators on Z(3) and square root Klein-Gordon operators on Z(n).
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