PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one-dimensional x²(ix)ⁿ for −1<n<0.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146116 |
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| Cite this: | PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues / E. Caliceti // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Caliceti, E. Cannata, F. Graffi, S. 2019-02-07T14:17:38Z 2019-02-07T14:17:38Z 2010 PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues / E. Caliceti // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 47A55; 47A75; 81Q15; 34L40; 35J10 https://nasplib.isofts.kiev.ua/handle/123456789/146116 We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one-dimensional x²(ix)ⁿ for −1<n<0. This paper is a contribution to the Proceedings of the 5-th Microconference “Analytic and Algebraic Methods V”. The full collection is available at http://www.emis.de/journals/SIGMA/Prague2009.html. We wish to thank R. Tateo for useful correspondence. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues |
| spellingShingle |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues Caliceti, E. Cannata, F. Graffi, S. |
| title_short |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues |
| title_full |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues |
| title_fullStr |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues |
| title_full_unstemmed |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues |
| title_sort |
pt symmetric schrödinger operators: reality of the perturbed eigenvalues |
| author |
Caliceti, E. Cannata, F. Graffi, S. |
| author_facet |
Caliceti, E. Cannata, F. Graffi, S. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one-dimensional x²(ix)ⁿ for −1<n<0.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146116 |
| citation_txt |
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues / E. Caliceti // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
| work_keys_str_mv |
AT calicetie ptsymmetricschrodingeroperatorsrealityoftheperturbedeigenvalues AT cannataf ptsymmetricschrodingeroperatorsrealityoftheperturbedeigenvalues AT graffis ptsymmetricschrodingeroperatorsrealityoftheperturbedeigenvalues |
| first_indexed |
2025-12-07T17:29:52Z |
| last_indexed |
2025-12-07T17:29:52Z |
| _version_ |
1850871478664298496 |