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