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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Дата:2010
Автор: Shin, K.C.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2010
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/146153
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
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spelling 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
first_indexed 2023-05-20T17:23:58Z
last_indexed 2023-05-20T17:23:58Z
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