Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

Abstract

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 Schrödinger, 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 so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on 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 Schrödinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n.

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Cited by in corpus (5)

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• Difference equations and pseudo-differential operators on ${\mathbb{Z}}^n$
• Hypercomplex Fock States for Discrete Electromagnetic Schrödinger Operators: A Bayesian Probability Perspective
• Ellipticity and Fredholmness of pseudo-differential operators on $\ell^2(\Zn)$
• Pseudo-differential operators on ${\mathbb{Z}}^n$ with applications to discrete fractional integral operators