Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
Mathematical Physics
2013-07-22 v2 High Energy Physics - Phenomenology
High Energy Physics - Theory
math.MP
Nuclear Theory
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1002.0742,
title = {Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity},
author = {A. A. Andrianov and F. Cannata and A. V. Sokolov},
journal= {arXiv preprint arXiv:1002.0742},
year = {2013}
}
Comments
25 pages, more refs added