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.
| PDF (Spectral Equivalences) | ||
|
Download (350Kb)
|
![[img]](http://kar.kent.ac.uk/style/images/fileicons/application_pdf.png)
|
|
| Official URL 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) |
- Depositors only (login required):
