Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

DOI10.1063/1.4949470zbMath1375.81100arXiv1511.01992OpenAlexW2262673394MaRDI QIDQ2814206

Ian Marquette, Christiane Quesne

Publication date: 20 June 2016

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

Full work available at URL: https://arxiv.org/abs/1511.01992

zbMATH Keywords

fourth Painlevé transcendent\(k\)-step rational extensions of the harmonic oscillator

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Supersymmetry and quantum mechanics (81Q60) Generalized hypergeometric series, ({}_pF_q) (33C20) Special quantum systems, such as solvable systems (81Q80)

Related Items (15)

Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials ⋮ A family of fourth-order superintegrable systems with rational potentials related to Painlevé VI ⋮ An affine Weyl group characterization of polynomial Heisenberg algebras ⋮ Poles of Painlevé IV rationals and their distribution ⋮ Fifth-order superintegrable quantum systems separating in Cartesian coordinates: Doubly exotic potentials ⋮ Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials ⋮ Exceptional Orthogonal Polynomials and Rational Solutions to Painlevé Equations ⋮ On integrable Ermakov-Painlevé IV systems ⋮ Complete classification of rational solutions of \(A_{2n}\)-Painlevé systems ⋮ Trends in Supersymmetric Quantum Mechanics ⋮ Higher Order Quantum Superintegrability: A New “Painlevé Conjecture” ⋮ Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method ⋮ On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials ⋮ A fourth-order superintegrable system with a rational potential related to Painlevé VI ⋮ Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians

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