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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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2010
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146153 |
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| 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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irk-123456789-1461532019-02-08T01:24:13Z Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry Shin, K.C. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146153 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Shin, K.C. |
| spellingShingle |
Shin, K.C. Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Shin, K.C. |
| author_sort |
Shin, K.C. |
| title |
Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry |
| title_short |
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_sort |
anharmonic oscillators with infinitely many real eigenvalues and pt-symmetry |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146153 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT shinkc anharmonicoscillatorswithinfinitelymanyrealeigenvaluesandptsymmetry |
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2025-07-10T23:18:06Z |
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2025-07-10T23:18:06Z |
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