Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Mathematical Physics
2011-12-06 v3 High Energy Physics - Theory
math.MP
Nuclear Theory
Quantum Physics
Abstract
This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.
Keywords
Cite
@article{arxiv.1107.5916,
title = {Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs},
author = {Andrey V. Sokolov},
journal= {arXiv preprint arXiv:1107.5916},
year = {2011}
}