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

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

2010-02-03

arxiv.org/abs/1002.0742v2

Physics

Mathematical Physics

25 pages, more refs added

Scientific paper

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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