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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Bibliographic Details
Main Author: Kwang C. Shin
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2010-02-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Online Access:http://dx.doi.org/10.3842/SIGMA.2010.015