On eigenfunction approximations for typical non-self-adjoint Schroedinger operators

Details On eigenfunction approximations for typical non-self-adjoint Schroedinger operators On eigenfunction approximations for typical non-self-adjoint Schroedinger operators

1999-04-19

arxiv.org/abs/math/9904093v1

Mathematics

Spectral Theory

17 pages, 11 figures

Scientific paper

10.1098/rspa.2000.0562

We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide accurate lobal approximations to them.

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