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This article is cited in 14 scientific papers (total in 14 papers)
Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
Alexander A. Andrianovab, Andrey V. Sokolova a V. A. Fock Department of Theoretical Physics, Sankt-Petersburg State University, 198504 St. Petersburg, Russia
b ICCUB, Universitat de Barcelona, 08028 Barcelona, Spain
Abstract:
Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their
eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration possess the continuous spectrum and the following peculiarities are
investigated: (1) the case when there is an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum; (2) the case when there is an exceptional point situated inside of continuous spectrum. The reductions of the derived resolutions of identity under narrowing of the classes of employed test functions are revealed. It is shown that in the case (1) some of associated functions included into the resolution of identity are normalizable and some of them may be not and in the case (2) the bounded associated
function corresponding to the exceptional point does not belong to the physical state space. Spectral properties of a SUSY partner Hamiltonian for the Hamiltonian with an exceptional point are examined.
Keywords:
non-Hermitian quantum mechanics, supersymmetry, exceptional points, resolution of identity.
Received: August 6, 2011; in final form November 25, 2011; Published online December 5, 2011
Citation:
Alexander A. Andrianov, Andrey V. Sokolov, “Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum”, SIGMA, 7 (2011), 111, 19 pp.
Linking options:
https://www.mathnet.ru/eng/sigma669 https://www.mathnet.ru/eng/sigma/v7/p111
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Abstract page: | 261 | Full-text PDF : | 57 | References: | 51 |
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