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arXiv · 1002.0742

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

A. A. Andrianov·F. Cannata·A. V. Sokolov
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Abstract

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.

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A. A. Andrianov, F. Cannata, A. V. Sokolov. 2010-02-07. Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity. https://doi.org/10.1063/1.3422523

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