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

Abstract

We consider two quasi-exactly solvable problems in one dimension for which the Schrödinger 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.

Revtex, 7 pages, No figure

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