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

Dorey, P. and Dunning, C. and 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). pp. 5679-5704.

Abstract

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.

Item Type:Article
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1088/0305-4470/34/28/305
Record Created:26 Feb 2008
Last Modified:29 Apr 2009 14:44

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