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Spectral equivalences, Bethe ansatz equations, and reality properties in PT-symmetric quantum mechanics

Dorey, Patrick, Dunning, Clare, Tateo, Roberto (2001) Spectral equivalences, Bethe ansatz equations, and reality properties in PT-symmetric quantum mechanics. Journal of Physics A: Mathematical and General, 34 (28). pp. 5679-5704. ISSN 0305-4470. (doi:10.1088/0305-4470/34/28/305) (KAR id:707)


The one-dimensional Schrodinger equation for the potential x(6)+alphax(2)+l (l+1)/x(2) has many interesting properties. For certain values of the parameters I and a 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 PT-symmetric quantum mechanical systems.

Item Type: Article
DOI/Identification number: 10.1088/0305-4470/34/28/305
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:26 UTC
Last Modified: 16 Nov 2021 09:39 UTC
Resource URI: (The current URI for this page, for reference purposes)

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