# Rational extensions of solvable potentials and exceptional orthogonal polynomials

@article{Grandati2012RationalEO, title={Rational extensions of solvable potentials and exceptional orthogonal polynomials}, author={Yves Grandati}, journal={Journal of Physics: Conference Series}, year={2012}, volume={343}, pages={012041} }

We present a generalized SUSY QM partnership in which the DBT are built on the excited states Riccati-Schrödinger (RS) functions regularized via specific discrete symmetries of translationally shape invariant potentials. Applied to the isotonic oscillator, this scheme allows to generate the solvable rational extensions the spectrum of which is associated to the recently discovered exceptional Laguerre polynomials

## 10 Citations

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Ladder operators for the hyperbolic Rosen–Morse (RMII) potential are realized using the shape invariance property appearing, in particular, using supersymmetric quantum mechanics. The extension of…

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In this paper, we construct isospectral Hamiltonians without shape-invariant potentials for the relativistic quantum mechanical potentials such as the Dirac oscillator and hydrogen-like atom.

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The $X_m$ exceptional orthogonal polynomials (XOP) form a complete set of eigenpolynomials to a differential equation. Despite being complete, the XOP set does not contain polynomials of every…

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It was recently conjectured that every system of exceptional orthogonal polynomials is related to classical orthogonal polynomials by a sequence of Darboux transformations. In this paper we prove…

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