\(\mathcal{N}\)-fold supersymmetry and quasi-solvability associated with \(X_2\)-Laguerre polynomials. (English) Zbl 1309.81102
Summary: We construct a new family of quasi-solvable and \(\mathcal{N}\)-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 \(\mathcal{N}\)-fold supercharge.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 81Q60 | Supersymmetry and quantum mechanics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
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