Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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dc.contributor.author	Shin, K.C.
dc.date.accessioned	2019-02-07T19:14:13Z
dc.date.available	2019-02-07T19:14:13Z
dc.date.issued	2010
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 34L20; 34L40
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146153
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA