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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 112, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.112 (Mi sigma670) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs

Andrey V. Sokolov

V. A. Fock Department of Theoretical Physics, Sankt-Petersburg State University, 198504 St. Petersburg, Russia
Full-text PDF (345 kB) Citations (7)
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DOI: https://doi.org/10.3842/SIGMA.2011.112
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: 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
Bibliographic databases:
Document Type: Article
MSC: 81Q60; 81R15; 47B15
Language: English
Citation: Andrey V. Sokolov, “Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs”, SIGMA, 7 (2011), 112, 16 pp.
Citation in format AMSBIB
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