Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

Details Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

2008-07-25

arxiv.org/abs/0807.4087v3

J. Phys. A: Math. Theor. 41 (2008) 392001 (6pp)

Physics

Quantum Physics

10 pages, no figure, published version (http://stacks.iop.org/1751-8121/41/392001)

Scientific paper

10.1088/1751-8113/41/39/392001

We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schr\"odinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials, extending either the radial oscillator or the Scarf I potential by the addition of some rational terms, turn out to be translationally shape invariant as their standard counterparts and isospectral to them.

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