Anti-isospectral transformations, orthogonal polynomials, and quasi-exactly solvable problems

Khare, Avinash ; Mandal, Bhabani Prasad (1998) Anti-isospectral transformations, orthogonal polynomials, and quasi-exactly solvable problems Journal of Mathematical Physics, 39 (6). pp. 3476-3486. ISSN 0022-2488

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Official URL: http://jmp.aip.org/resource/1/jmapaq/v39/i6/p3476_...

Related URL: http://dx.doi.org/10.1063/1.532442

Abstract

We consider the double sinh-Gordon potential which is a quasi-exactly solvable problem and show that in this case one has two sets of Bender-Dunne orthogonal polynomials. We study in some detail the various properties of these polynomials and the corresponding quotient polynomials. In particular, we show that the weight functions for these polynomials are not always positive. We also study the orthogonal polynomials of the double sine-Gordon potential which is related to the double sinh-Gordon case by an anti-isospectral transformation. Finally we discover a new quasi-exactly solvable problem by making use of the anti-isospectral transformation.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Polynomials; Quantum Theory
ID Code:82059
Deposited On:09 Feb 2012 05:11
Last Modified:18 May 2016 23:24

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