Complex WKB analysis of a PT-symmetric eigenvalue problem

Mark James Sorrel

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The spectra of a particular class of -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 quantization conditions obtained from the complex WKB method. In particular, we consider the relation of the quantization 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 (2001 J. Phys. A: Math. Gen. 34 5679 (Preprint hep-th/0103051), 2001 J. Phys. A: Math. Gen. 34 L391 (Preprint hep-th/0104119)). © 2007 IOP Publishing Ltd.

Original languageEnglish
Article number023
Pages (from-to)10319-10335
Number of pages17
JournalJournal of Physics A: Mathematical and Theoretical
Issue number33
Publication statusPublished - 17 Aug 2007


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