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

A. Aslanyan; E. B. Davies

doi:10.1098/rspa.2000.0562

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

A. Aslanyan·E. B. Davies

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Abstract

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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A. Aslanyan, E. B. Davies. 1999-04-19. On eigenfunction approximations for typical non-self-adjoint Schroedinger operators. https://doi.org/10.1098/rspa.2000.0562

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