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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July 2013
Research Article|
July 25 2013
Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials
Y. Grandati;
Y. Grandati
a)
1Equipe BioPhysStat, LCP A2MC,
Université de Lorraine-Site de Metz
, 1 bvd D. F. Arago, F-57070 Metz, France
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J. Math. Phys. 54, 073512 (2013)
Article history
Received:
December 04 2012
Accepted:
July 04 2013
Citation
Y. Grandati, C. Quesne; Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials. J. Math. Phys. 1 July 2013; 54 (7): 073512. https://doi.org/10.1063/1.4815997
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