2012/11/22 by Yves Grandati, Grandati, Yves, C. Quesne +2 · 1 citation
Mathematics · Physics and Astronomy · #Eigenfunction #Eigenvalues and eigenvectors #FOS: Physical sciences #Function (biology) #Laguerre polynomials #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Order (exchange) #Orthogonal polynomials #Physics #Polynomial #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum mechanics #Sign (mathematics) #Term (time) #math-ph #math.MP #quant-ph
paper · pdf · open access · doi:10.48550/arxiv.1211.5308
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2012/11/22 · arxiv created 2012/12/09 · arxiv updated 2012/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
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.