On the Duality of Quasi-Exactly Solvable Problems
  It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This transformation helps one to reveal some new features of quasi-exactly solvable models and associated orthogonal polynomials. 
A. Krajewska, A. Ushveridze, Z. Walczak