Publication details for Patrick DoreyDorey, Patrick, Millican-Slater, Adam & Tateo, Roberto (2005). Beyond the WKB approximation in PT-symmetric quantum mechanics. Journal of Physics A 38(6): 1305-1332.
- Publication type: Journal Article
- ISSN/ISBN: 1751-8113, 1751-8121
- DOI: 10.1088/0305-4470/38/6/010
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
The mergings of energy levels associated with the breaking of symmetry in the model of Bender and Boettcher, and in its generalization to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrödinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero