Professor Patrick Dorey p.e.dorey@durham.ac.uk
Professor
The one-dimensional Schrödinger equation for the potential x6 + αx2 + l(l + 1)/x2 has many interesting properties. For certain values of the parameters l and α the equation is in turn supersymmetric (Witten) and quasi-exactly solvable (Turbiner), and it also appears in Lipatov's approach to high-energy QCD. In this paper we signal some further curious features of these theories, namely novel spectral equivalences with particular second- and third-order differential equations. These relationships are obtained via a recently observed connection between the theories of ordinary differential equations and integrable models. Generalized supersymmetry transformations acting at the quasi-exactly solvable points are also pointed out, and an efficient numerical procedure for the study of these and related problems is described. Finally we generalize slightly and then prove a conjecture due to Bessis, Zinn-Justin, Bender and Boettcher, concerning the reality of the spectra of certain -symmetric quantum mechanical systems.
Dorey, P., Dunning, C., & Tateo, R. (2001). Spectral equivalences, Bethe ansatz equations, and reality properties in PT-symmetric quantum mechanics. Journal of Physics A: Mathematical and General, 34(28), 5679-5704. https://doi.org/10.1088/0305-4470/34/28/305
Journal Article Type | Article |
---|---|
Publication Date | Jul 1, 2001 |
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 | 34 |
Issue | 28 |
Pages | 5679-5704 |
DOI | https://doi.org/10.1088/0305-4470/34/28/305 |
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