Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry
We study the eigenvalue problem −u''+V(z)u=λu in the complex plane with the boundary condition that u(z) decays to zero as z tends to infinity along the two rays arg z=−π/2± 2π/(m+2), where V(z)=−(iz)m−P(iz) for complex-valued polynomials P of degree at most m−1≥2. We provide an asymptotic...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146153 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry / K.C. Shin // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707119635038208 |
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| author | Shin, K.C. |
| author_facet | Shin, K.C. |
| citation_txt | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry / K.C. Shin // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the eigenvalue problem −u''+V(z)u=λu in the complex plane with the boundary condition that u(z) decays to zero as z tends to infinity along the two rays arg z=−π/2± 2π/(m+2), where V(z)=−(iz)m−P(iz) for complex-valued polynomials P of degree at most m−1≥2. We provide an asymptotic formula for eigenvalues and a necessary and sufficient condition for the anharmonic oscillator to have infinitely many real eigenvalues.
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| first_indexed | 2025-12-07T17:03:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146153 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:03:50Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Shin, K.C. 2019-02-07T19:14:13Z 2019-02-07T19:14:13Z 2010 Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry / K.C. Shin // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34L20; 34L40 https://nasplib.isofts.kiev.ua/handle/123456789/146153 We study the eigenvalue problem −u''+V(z)u=λu in the complex plane with the boundary condition that u(z) decays to zero as z tends to infinity along the two rays arg z=−π/2± 2π/(m+2), where V(z)=−(iz)m−P(iz) for complex-valued polynomials P of degree at most m−1≥2. We provide an asymptotic formula for eigenvalues and a necessary and sufficient condition for the anharmonic oscillator to have infinitely many real eigenvalues. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry Article published earlier |
| spellingShingle | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry Shin, K.C. |
| title | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry |
| title_full | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry |
| title_fullStr | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry |
| title_full_unstemmed | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry |
| title_short | Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry |
| title_sort | anharmonic oscillators with infinitely many real eigenvalues and pt-symmetry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146153 |
| work_keys_str_mv | AT shinkc anharmonicoscillatorswithinfinitelymanyrealeigenvaluesandptsymmetry |