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Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Інший ID:
2010 Mathematics Subject Classification: 81Q60; 81R15; 47B15
DOI: http://dx.doi.org/10.3842/SIGMA.2011.112
DOI: http://dx.doi.org/10.3842/SIGMA.2011.112
Посилання:
Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs / A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 4 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
This work was supported by Grant RFBR 09-01-00145-a and by the SPbSU project 11.0.64.2010.
Дата:
2011
Переглядів:
438
Завантажень:
241
Анотація:
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.
