Extended Krein-Adler theorem for the translationally shape invariant potentials

DOI10.1063/1.4871443zbMath1296.81023arXiv1309.3756OpenAlexW2054334871MaRDI QIDQ5171345

Robert Milson, Daivd Gómez-Ullate, Yves Grandati

Publication date: 26 July 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3756

zbMATH Keywords

exceptional orthogonal polynomialssolvable potentialsDarboux Backlund transformationextended Krein-Adler theoremharmonic and isotonic oscillationsTDPT and Morse potentialstransformation shape invariant potentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Other special orthogonal polynomials and functions (33C47) Initial value problems for second-order parabolic systems (35K45)

Related Items (21)

A short note on ``Group theoretic approach to rationally extended shape invariant potentials ⋮ Parametric symmetries in exactly solvable real and PT symmetric complex potentials ⋮ Exceptional orthogonal polynomials and generalized Schur polynomials ⋮ Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: Applications to ladder operators and superintegrability ⋮ Multi-indexed Jacobi polynomials and Maya diagrams ⋮ A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems ⋮ Infinite families of shape invariant potentials with \(n\) parameters subject to translation ⋮ A Bochner type characterization theorem for exceptional orthogonal polynomials ⋮ ABC of ladder operators for rationally extended quantum harmonic oscillator systems ⋮ Quasi-exactly solvable extensions of the Kepler-Coulomb potential on the sphere ⋮ The algebra of recurrence relations for exceptional Laguerre and Jacobi polynomials ⋮ Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger's equation ⋮ Deformed shape invariance symmetry and potentials in curved space with two known eigenstates ⋮ Families of quasi-exactly solvable extensions of the quantum oscillator in curved spaces ⋮ Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials ⋮ Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial ⋮ Trends in Supersymmetric Quantum Mechanics ⋮ Quantum oscillator and Kepler–Coulomb problems in curved spaces: Deformed shape invariance, point canonical transformations, and rational extensions ⋮ Generalized quantum nonlinear oscillators: Exact solutions and rational extensions ⋮ Rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials ⋮ Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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