2009/11/18 by Satoru Odake, Ryu Sasaki · 161 citations
Mathematics · Physics and Astronomy · #Invariant (physics) #Julia set #Laguerre polynomials #Limiting #Mathematical functions and polynomials #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.CA #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1016/j.physletb.2009.12.062
published in Physics Letters B 684(2-3), 173-176 (Elsevier BV) · 4 pages
arxiv created 2009/11/18 · openalex publication_date 2010/01/07 · arxiv updated 2010/11/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (Xℓ) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one-dimensional quantum mechanics and the corresponding Xℓ Laguerre and Jacobi polynomials [S. Odake, R. Sasaki, Phys. Lett. B 679 (2009) 414]. The new Xℓ Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known Xℓ Jacobi polynomials and the potentials, whereas the known Xℓ Laguerre polynomials and the potentials are obtained in the same manner from the mirror image of the known Xℓ Jacobi polynomials and the potentials.