HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS
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Publication:2861608
DOI10.1142/S0217732311036383zbMath1274.81113arXiv1106.1990OpenAlexW2078203229MaRDI QIDQ2861608
Publication date: 11 November 2013
Published in: Modern Physics Letters A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1106.1990
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Exactly and quasi-solvable systems arising in quantum theory (81U15) Supersymmetry and quantum mechanics (81Q60) Special quantum systems, such as solvable systems (81Q80)
Related Items (33)
A short note on ``Group theoretic approach to rationally extended shape invariant potentials ⋮ A family of fourth-order superintegrable systems with rational potentials related to Painlevé VI ⋮ Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials ⋮ Group theoretic approach to rationally extended shape invariant potentials ⋮ Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials ⋮ RATIONALLY-EXTENDED RADIAL OSCILLATORS AND LAGUERRE EXCEPTIONAL ORTHOGONAL POLYNOMIALS IN kTH-ORDER SUSYQM ⋮ REVISITING (QUASI-)EXACTLY SOLVABLE RATIONAL EXTENSIONS OF THE MORSE POTENTIAL ⋮ An affine Weyl group characterization of polynomial Heisenberg algebras ⋮ Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: Applications to ladder operators and superintegrability ⋮ Extensions of a class of similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries ⋮ A conjecture on exceptional orthogonal polynomials ⋮ Infinite families of shape invariant potentials with \(n\) parameters subject to translation ⋮ A Bochner type characterization theorem for exceptional orthogonal polynomials ⋮ New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization ⋮ Convergence rates of exceptional zeros of exceptional orthogonal polynomials ⋮ Analytical solution of two-dimensional Scarf II model by means of SUSY methods ⋮ Higher order supersymmetric truncated oscillators ⋮ Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator ⋮ New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials ⋮ Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials ⋮ Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials ⋮ Extending Romanovski polynomials in quantum mechanics ⋮ Comments on the generalized SUSY QM partnership for Darboux-Pöschl-Teller potential and exceptional Jacobi polynomials ⋮ Extended Krein-Adler theorem for the translationally shape invariant potentials ⋮ Multistep DBT and regular rational extensions of the isotonic oscillator ⋮ Solvable potentials with exceptional orthogonal 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 ⋮ Generalized quantum nonlinear oscillators: Exact solutions and rational extensions ⋮ Superintegrable systems with position dependent mass ⋮ COHERENT STATE OF THE EXTENDED SCARF I POTENTIAL AND SOME OF ITS PROPERTIES ⋮ GENERALIZED RAYLEIGH AND JACOBI PROCESSES AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS ⋮ Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties
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