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

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Abstract

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice 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 pseudodifference operators (i.e., pseudodifferential operators on the group 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 Schrödinger operators on , Dirac operators on and square root Klein-Gordon operators on . © 2009 IOP Publishing Ltd.
Original languageAmerican English
JournalJournal of Physics A: Mathematical and Theoretical
DOIs
StatePublished - 20 Nov 2009

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Quantum theory
Essential Spectrum
Eigenvalues and eigenfunctions
Quantum Mechanics
Eigenfunctions
quantum mechanics
eigenvectors
operators
estimates
Operator
Estimate
Discrete Spectrum
Exponential Decay
Square root
Operator Matrix
Difference Operator
Dirac Operator
Pseudodifferential Operators
Paul Adrien Maurice Dirac
Calculus

Cite this

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abstract = "This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice which are discrete analogs of the Schr{\"o}dinger, 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 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 Schr{\"o}dinger operators on , Dirac operators on and square root Klein-Gordon operators on . {\circledC} 2009 IOP Publishing Ltd.",
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Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics. / Rabinovich, Vladimir S.; Roch, Steffen.

In: Journal of Physics A: Mathematical and Theoretical, 20.11.2009.

Research output: Contribution to journalArticleResearchpeer-review

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