2004/07/16 by Mourad E. H. Ismail, M. E. H. Ismail, S. S. Lin +6 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #math.QA #msc:33C45 #msc:33D45 #msc:39A13
paper · pdf · doi:10.48550/arxiv.math-ph/0407033
Latex 23 pages
arxiv created 2004/07/16 · arxiv updated 2009/12/01
In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin s XXZ model of a finite size and the q-Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz equations give rise to the polynomial solutions of a second order q-difference equation in terms of Askey-Wilson operator. The more general form of Bethe Ansatz equations and the mathematical problems relevant to the physics of XXZ model are discussed. Furthermore, the similar correspondence between Bethe Ansatz equations of XXX model and the Sturm-Liouville type difference equation in terms of Wilson operator has also been found.