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Multistep DBT and regular rational extensions of the isotonic oscillator

Abstract : In some recent articles we developed a new systematic approach to generate solvable rational extensions of primary translationally shape invariant potentials. In this generalized SUSY QM partnership, the DBT are built on the excited states Riccati-Schrödinger (RS) functions regularized via specific discrete symmetries of the considered potential. In the present paper, we prove that this scheme can be extended in a multistep formulation. Applying this scheme to the isotonic oscillator, we obtain new towers of regular rational extensions of this potential which are strictly isospectral to it. We give explicit expressions for their eigenstates which are associated to the recently discovered exceptional Laguerre polynomials and show explicitely that these extensions inherit of the shape invariance properties of the original potential.
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Contributor : Yves Grandati Connect in order to contact the contributor
Submitted on : Friday, November 18, 2011 - 7:09:51 PM
Last modification on : Thursday, January 11, 2018 - 6:19:47 AM
Long-term archiving on: : Sunday, February 19, 2012 - 2:31:03 AM


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  • HAL Id : hal-00614879, version 2
  • ARXIV : 1108.4503



Yves Grandati. Multistep DBT and regular rational extensions of the isotonic oscillator. 2011. ⟨hal-00614879v2⟩



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