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

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

2002-12-15

arxiv.org/abs/math-ph/0212045v1

J.Math.Phys. 43 (2002) 5310-5324

Physics

Mathematical Physics

14 pages, 5 tables, LaTeX2e

Scientific paper

We have generated, using an sl(2,R) 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 problems 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.

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