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Spectral singularities for non-Hermitian one-dimensional Hamiltonians : Puzzles with resolution of identity. / Andrianov, A. A.; Cannata, F.; Sokolov, A. V.

In: Journal of Mathematical Physics, Vol. 51, No. 5, 036005JMP, 05.2010.

Research output: Contribution to journal › Article › peer-review

Harvard

Andrianov, AA, Cannata, F & Sokolov, AV 2010, 'Spectral singularities for non-Hermitian one-dimensional Hamiltonians: Puzzles with resolution of identity', Journal of Mathematical Physics, vol. 51, no. 5, 036005JMP. https://doi.org/10.1063/1.3422523

APA

Andrianov, A. A., Cannata, F., & Sokolov, A. V. (2010). Spectral singularities for non-Hermitian one-dimensional Hamiltonians: Puzzles with resolution of identity. Journal of Mathematical Physics, 51(5), [036005JMP]. https://doi.org/10.1063/1.3422523

Vancouver

Andrianov AA, Cannata F, Sokolov AV. Spectral singularities for non-Hermitian one-dimensional Hamiltonians: Puzzles with resolution of identity. Journal of Mathematical Physics. 2010 May;51(5). 036005JMP. https://doi.org/10.1063/1.3422523

Author

Andrianov, A. A. ; Cannata, F. ; Sokolov, A. V. / Spectral singularities for non-Hermitian one-dimensional Hamiltonians : Puzzles with resolution of identity. In: Journal of Mathematical Physics. 2010 ; Vol. 51, No. 5.

BibTeX

@article{2230448e13f848f3a93280749c26db5a,
title = "Spectral singularities for non-Hermitian one-dimensional Hamiltonians: Puzzles with resolution of identity",
abstract = "We examine the completeness of biorthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for deltalike 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.",
author = "Andrianov, {A. A.} and F. Cannata and Sokolov, {A. V.}",
note = "Funding Information: The work of A.A. and A.S. was supported by RFBR Grant No. 09-01-00145-a. A.A. was supported in part by CUR Generalitat de Catalunya under Project No. 2009SGR502.",
year = "2010",
month = may,
doi = "10.1063/1.3422523",
language = "English",
volume = "51",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "5",

}

RIS

TY - JOUR

T1 - Spectral singularities for non-Hermitian one-dimensional Hamiltonians

T2 - Puzzles with resolution of identity

AU - Andrianov, A. A.

AU - Cannata, F.

AU - Sokolov, A. V.

N1 - Funding Information: The work of A.A. and A.S. was supported by RFBR Grant No. 09-01-00145-a. A.A. was supported in part by CUR Generalitat de Catalunya under Project No. 2009SGR502.

PY - 2010/5

Y1 - 2010/5

N2 - We examine the completeness of biorthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for deltalike 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.

AB - We examine the completeness of biorthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for deltalike 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.

UR - http://www.scopus.com/inward/record.url?scp=77955240459&partnerID=8YFLogxK

U2 - 10.1063/1.3422523

DO - 10.1063/1.3422523

M3 - Article

AN - SCOPUS:77955240459

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

M1 - 036005JMP

ER -

ID: 98658847