Professor Patrick Dorey p.e.dorey@durham.ac.uk
Professor
Beyond the WKB approximation in PT-symmetric quantum mechanics
Dorey, Patrick; Millican-Slater, Adam; Tateo, Roberto
Authors
Adam Millican-Slater
Roberto Tateo
Abstract
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.
Citation
Dorey, P., Millican-Slater, A., & Tateo, R. (2005). Beyond the WKB approximation in PT-symmetric quantum mechanics. Journal of Physics A: Mathematical and General, 38(6), 1305-1332. https://doi.org/10.1088/0305-4470/38/6/010
Journal Article Type | Article |
---|---|
Publication Date | 2005-02 |
Deposit Date | Feb 26, 2008 |
Journal | Journal of Physics A: Mathematical and General |
Print ISSN | 0305-4470 |
Electronic ISSN | 1361-6447 |
Publisher | IOP Publishing |
Peer Reviewed | Peer Reviewed |
Volume | 38 |
Issue | 6 |
Pages | 1305-1332 |
DOI | https://doi.org/10.1088/0305-4470/38/6/010 |
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