Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
By Christiane Quesne. 2008
267 citations recorded by the source corpus.
We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schrödinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type X1 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.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/16b9e938aa7204b342833aa107496287e5e7f2e5
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials (2013, background): “Shortly after, Quesne [21, 22] showed the relation between exceptional orthogonal polynomials and the Darboux transformation, which enabled her to obtain examples of codimension two.”
- An extended class of orthogonal polynomials defined by a Sturm-Liouville problem (2008, background): “By way of conclusion, we mention that since our paper was posted in preprint form on the arXiv, the Schrödinger operators and potentials for which our new orthogonal polynomials appear as eigenfunctions (when multiplied by the corresponding weight) have been determined and studied [20].”