Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
数学物理
2008-11-26 v2 高能物理 - 理论
math.MP
量子物理
摘要
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].
引用
@article{arxiv.math-ph/0703030,
title = {Complex WKB Analysis of a PT Symmetric Eigenvalue Problem},
author = {Mark Sorrell},
journal= {arXiv preprint arXiv:math-ph/0703030},
year = {2008}
}
备注
22 pages, 13 figures. Added references, minor revisions