Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?

Avinash Khare; Bhabani Prasad Mandal

doi:10.1016/S0375-9601(97)00897-9

Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?

Mathematical Physics 2009-10-30 v1 High Energy Physics - Theory math.MP Quantum Physics

Authors: Avinash Khare , Bhabani Prasad Mandal

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Abstract

We consider two quasi-exactly solvable problems in one dimension for which the Schr\"odinger equation can be converted to Heun's equation. We show that in neither case the Bender-Dunne polynomials form an orthogonal set. Using the anti-isopectral transformation we also discover a new quasi-exactly solvable problem and show that even in this case the polynomials do not form an orthogonal set.

Keywords

painlevé equations and orthogonal polynomials

Cite

@article{arxiv.physics/9709043,
  title  = {Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?},
  author = {Avinash Khare and Bhabani Prasad Mandal},
  journal= {arXiv preprint arXiv:physics/9709043},
  year   = {2009}
}