Equilibrium positions, shape invariance and Askey–Wilson polynomials

DOI10.1063/1.1927080zbMath1110.33012arXivhep-th/0410109OpenAlexW2104603154MaRDI QIDQ3438495

Satoru Odake, Ryu Sasaki

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/hep-th/0410109

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Groups and algebras in quantum theory and relations with integrable systems (81R12) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (11)

Unified theory of annihilation-creation operators for solvable (“discrete”) quantum mechanics ⋮ Shape invariance through Crum transformation ⋮ Properties of the zeros of generalized basic hypergeometric polynomials ⋮ Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials ⋮ \(q\)-oscillator from the \(q\)-Hermite polynomial ⋮ Deformed multivariable Fokker-Planck equations ⋮ Multiparticle quasiexactly solvable difference equations ⋮ Solutions of convex Bethe ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials ⋮ Gradient system for the roots of the Askey-Wilson polynomial ⋮ Perturbations around the zeros of classical orthogonal polynomials ⋮ Unified theory of exactly and quasiexactly solvable “discrete” quantum mechanics. I. Formalism

Cites Work

• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Difference Schrödinger operators with linear and exponential discrete spectra
• Polynomials associated with equilibrium positions in Calogero Moser systems
• Quantum versus classical integrability in Ruijsenaars–Schneider systems
• Equilibria of ‘discrete’ integrable systems and deformation of classical orthogonal polynomials
• Generalized coherent and intelligent states for exact solvable quantum systems
• Difference Calogero–Moser systems and finite Toda chains
• ASSOCIATED STURM-LIOUVILLE SYSTEMS

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