New classes of quasi-solvable potentials, their exactly solvable limit, and related orthogonal polynomials

摘要

We have generated, using an sl(2,R) Lie-algebraic formalism, several new classes of quasi-solvable elliptic potentials, which in the appropriate limit go over to the exactly solvable forms. We have obtained exact solutions of the corresponding spectral problem for some real values of the potential parameters. We have also given explicit expressions of the families of associated orthogonal polynomials in the energy variable. (C) 2002 American Institute of Physics. [References: 23]