Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

2008/07/31 by C. Quesne, C Quesne · 10 citations
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/39/392001

published as J. Phys. A: Math. Theor. 41 (2008) 392001 (6pp) · 10 pages, no figure, published version (http://stacks.iop.org/1751-8121/41/392001)

openalex publication_date 2008/08/29 · arxiv created 2008/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schr"odinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type X₁ exceptional orthogonal polynomials. These potentials, extending either the radial oscillator or the Scarf I potential by the addition of some rational terms, turn out to be translationally shape invariant as their standard counterparts and isospectral to them.

Citations

• Supersymmetry and Quantum Mechanics

Cited by

• Supersymmetry, shape invariance and the Legendre equations
• Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
• Information entropy of conditionally exactly solvable potentials
• Exactness of semiclassical quantization rule for broken supersymmetry
• Moment representations of the exceptional X1‐Laguerre orthogonal polynomials
• Another set of infinitely many exceptional (Xℓ) Laguerre polynomials
• Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians
• Schrödinger potentials solvable in terms of the general Heun functions
• Exactly solvable discrete quantum mechanical systems and multi-indexed orthogonal polynomials of the continuous Hahn and Meixner–Pollaczek types
• Rational Extension of Quantum Anisotropic Oscillator Potentials with Linear and/or Quadratic Perturbations

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