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Disconjugacy, regularity of multi-indexed rationally-extended potentials, and Laguerre exceptional polynomials

Abstract : The power of the disconjugacy properties of second-order differential equations of Schrödinger type to check the regularity of rationally-extended quantum potentials connected with exceptional orthogonal polynomials is illustrated by re-examining the extensions of the isotonic oscillator (or radial oscillator) potential derived in kth-order supersymmetric quantum mechanics or multistep Darboux-Bäcklund transformation method. The function arising in the potential denominator is proved to be a polynomial with a nonvanishing constant term, whose value is calculated by induction over k. The sign of this term being the same as that of the already known highest-degree term, the potential denominator has the same sign at both extremities of the definition interval, a property that is shared by the seed eigenfunction used in the potential construction. By virtue of disconjugacy, such a property implies the nodeless character of both the eigenfunction and the resulting potential.
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https://hal.archives-ouvertes.fr/hal-00755966
Contributor : Yves Grandati Connect in order to contact the contributor
Submitted on : Saturday, December 8, 2012 - 3:26:55 PM
Last modification on : Tuesday, October 19, 2021 - 12:55:34 PM
Long-term archiving on: : Monday, March 11, 2013 - 12:05:11 PM

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  • HAL Id : hal-00755966, version 2
  • ARXIV : 1211.5308

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Yves Grandati, Christiane Quesne. Disconjugacy, regularity of multi-indexed rationally-extended potentials, and Laguerre exceptional polynomials. 2012. ⟨hal-00755966v2⟩

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