N-fold Supersymmetry and Quasi-solvability Associated with X_2-Laguerre Polynomials

Details N-fold Supersymmetry and Quasi-solvability Associated with X_2-Laguerre Polynomials N-fold Supersymmetry and Quasi-solvability Associated with X_2-Laguerre Polynomials

2009-10-02

arxiv.org/abs/0910.0328v2

J. Math. Phys.51:032101, 2010

Physics

Mathematical Physics

22 pages, no figures; minor corrections, to appear in Journal of Mathematical Physics

Scientific paper

10.1063/1.3332378

We construct a new family of quasi-solvable and N-fold supersymmetric quantum systems where each Hamiltonian preserves an exceptional polynomial subspace of codimension 2. We show that the family includes as a particular case the recently reported rational radial oscillator potential whose eigenfunctions are expressed in terms of the X_2-Laguerre polynomials of the second kind. In addition, we find that the two kinds of the X_2-Laguerre polynomials are ingeniously connected with each other by the N-fold supercharge.

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