Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• ISSN: 1815-0659
• Main Author: Shin, K.C.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146153
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...