Extended Krein-Adler theorem for the translationally shape invariant potentials

Abstract

Considering successive extensions of primary translationally shape invariant potentials, we enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux-Bäcklund transformations. It allows us to establish novel bilinear Wronskian and determinantal identities for classical orthogonal polynomials.

32 pages, typed in AMS-LaTeX

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• Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
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• A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
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• Quantization of rationally deformed Morse potentials by Wronskian transforms of Romanovski-Bessel polynomials
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• Infinite families of shape invariant potentials with n parameters subject to translation
• Deformed Shape Invariant Superpotentials in Quantum Mechanics and Expansions in Powers of $\hslash$
• Survey of Nodeless Regular Almost-Everywhere Holomorphic Solutions for Exactly Solvable Gauss-Reference Liouville Potentials on the Line I.Subsets of Nodeless Jacobi-Seed Solutions Co-Existent with Discrete Energy Spectrum