Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

Details Complex WKB Analysis of a PT Symmetric Eigenvalue Problem Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

2007-03-09

arxiv.org/abs/math-ph/0703030v2

J.Phys.A40:10319-10336,2007

Physics

Mathematical Physics

22 pages, 13 figures. Added references, minor revisions

Scientific paper

10.1088/1751-8113/40/33/023

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].

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