2011/05/03 by Luc Vinet, Vinet, Luc, Alexei Zhedanov +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Optical and Acousto-Optic Technologies #Quantum Mechanics and Non-Hermitian Physics #Quantum optics and atomic interactions #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1105.0701
33 pages
arxiv created 2011/05/03 · openalex publication_date 2011/05/03 · arxiv updated 2011/05/05 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The representations of the Schrödinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural formulas (recurrence relations, difference equations, Rodrigues' formula etc.) that these matrix orthogonal polynomials satisfy.