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

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

1997-09-30

arxiv.org/abs/physics/9709043v1

Phys.Lett. A239 (1998) 197-200

Physics

Mathematical Physics

Revtex, 7 pages, No figure

Scientific paper

10.1016/S0375-9601(97)00897-9

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.

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