Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
by Mark Sorrell
Abstract: There has recently been much interest in Hamiltonians that are non-Hermitian, but instead possess PT Symmetry, and may be found to still have an entirely real spectrum. The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied by Dorey et al., and found to have an extremely rich structure. In this talk I present an explanation for these spec- tral properties in terms of quantisation conditions obtained from the complex WKB (Wentzel-Kramers-Brillouin) method. In particular, we consider the re- lation of the quantisation conditions to the reality and positivity properties of the eigenvalues as well as give an explanation of the previously observed pattern of eigenvalue degeneracies.
For More Information: contact: Iwan Jensen. email: I.Jensen@ms.unimelb.edu.au