2004/07/31 by Alberto Enciso, A. Enciso, Federico Finkel +5
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th
paper · pdf · doi:10.1016/j.physletb.2004.11.031
published as Phys.Lett. B605 (2005) 214-222 · 10 pages, LaTeX. Minor typos corrected
arxiv created 2004/09/02 · openalex publication_date 2004/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass frame, while the rational models are shown to possess an equally spaced infinite algebraic spectrum. For the trigonometric and one of the rational models, the corresponding eigenfunctions are explicitly computed. We also study the scalar reductions of the models, some of which had already appeared in the literature, and compute their algebraic eigenfunctions in closed form. In the rational cases, for which only partial results were available, we give concise expressions of the eigenfunctions in terms of generalized Laguerre and Jacobi polynomials.