Geodesic
Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SIGMA_2011_7_a111,
     author = {Andrey V. Sokolov},
     title = {Resolutions of {Identity} for {Some} {Non-Hermitian} {Hamiltonians.} {II.~Proofs}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a111/}
}
TY  - JOUR
AU  - Andrey V. Sokolov
TI  - Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2011
VL  - 7
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a111/
LA  - en
ID  - SIGMA_2011_7_a111
ER  - 
%0 Journal Article
%A Andrey V. Sokolov
%T Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
%J Symmetry, integrability and geometry: methods and applications
%D 2011
%V 7
%U http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a111/
%G en
%F SIGMA_2011_7_a111
Andrey V. Sokolov. Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a111/

[1] Andrianov A.A., Sokolov A.V., “Resolutions of identity for some non-Hermitian Hamiltonians. I. Exceptional point in continuous spectrum”, SIGMA, 7 (2011), 111, 19 pp. ; arXiv: 1107.5911 | DOI

[2] Gel'fand I.M., Vilenkin N.J., Generalized functions, v. 4, Some applications of harmonic analysis, Academic Press, New York, 1964

[3] Sokolov A.V., Andrianov A.A., Cannata F., “Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians: puzzles with self-orthogonal states”, J. Phys. A: Math. Gen., 39 (2006), 10207–10227 ; arXiv: quant-ph/0602207 | DOI | MR | Zbl

[4] Andrianov A.A., Cannata F., Sokolov A.V., “Spectral singularities for non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity”, J. Math. Phys., 51 (2010), 052104, 22 pp. ; arXiv: 1002.0742 | DOI | MR