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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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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| _version_ | 1862711291834007552 |
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| author | Caliceti, E. Cannata, F. Graffi, S. |
| author_facet | Caliceti, E. Cannata, F. Graffi, S. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:29:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146116 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:29:52Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues Caliceti, E. Cannata, F. Graffi, S. |
| title | 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_short | PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues |
| title_sort | pt symmetric schrödinger operators: reality of the perturbed eigenvalues |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146116 |
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