Anti-isospectral Transformations, Orthogonal Polynomials and Quasi-Exactly Solvable Problems
量子物理
2015-06-26 v1 高能物理 - 理论
数学物理
math.MP
摘要
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.
引用
@article{arxiv.quant-ph/9711001,
title = {Anti-isospectral Transformations, Orthogonal Polynomials and Quasi-Exactly Solvable Problems},
author = {Avinash Khare and Bhabani Prasad Mandal},
journal= {arXiv preprint arXiv:quant-ph/9711001},
year = {2015}
}
备注
Revtex, 19 pages, No figure