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. ISSN 0305-4470. (Full text available)

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http://dx.doi.org/10.1088/0305-4470/34/28/305

Abstract

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
Uncontrolled keywords: ANHARMONIC-OSCILLATORS; SCHRODINGER-EQUATION; STOKES MULTIPLIERS; BOUND-STATES; SUPERSYMMETRY; EIGENVALUES; POTENTIALS; SYSTEMS; MODELS
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:26
Last Modified: 25 Jun 2012 09:36
Resource URI: http://kar.kent.ac.uk/id/eprint/707 (The current URI for this page, for reference purposes)
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