2007/03/31 by Mark Sorrell · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #msc:34L40 #msc:34M40 #msc:81Q20 #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/33/023
published as J.Phys.A40:10319-10336,2007 · 22 pages, 13 figures. Added references, minor revisions
arxiv created 2007/06/27 · openalex publication_date 2007/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
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)).