Department of Mathematics
University of Kentucky
Lexington, KY 490506-0027 USA
email: hislop@ms.uky.edu
P. D. Hislop
Abstract:
We review various results on the exponential decay of the
eigenfunctions of two-body Schrödinger operators. The
exponential, isotropic bound results of Slaggie and
Wichmann for eigenfunctions
of Schrödinger operators corresponding to
eigenvalues below the bottom of the essential spectrum are proved.
The exponential, isotropic bounds on eigenfunctions
for nonthreshold eigenvalues due to Froese and Herbst
are reviewed.
The exponential, nonisotropic bounds of Agmon for eigenfunctions
corresponding to eigenvalues below the bottom of the essential spectrum
are developed, beginning with a discussion of the Agmon metric.
The analytic method of Combes and Thomas, with improvements
due to Barbaroux, Combes, and Hislop,
for proving exponential decay of the resolvent, at energies
outside of the spectrum of the operator and localized between
two disjoint regions, is presented in detail.
The results are applied to prove the exponential
decay of eigenfunctions corresponding
to isolated eigenvalues of Schrödinger and Dirac operators.
Published November November 3,, 2000.
Mathematics Subject Classifications: 81Q10.
Key words: Schrodinger operator, eigenfunction, exponential decay, Dirac operator.
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Peter D. Hislop Department of Mathematics University of Kentucky Lexington, KY 490506-0027 USA email: hislop@ms.uky.edu |
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