The Bannai-Ito algebra and a superintegrable system with reflections on the 2-sphere

2014/01/31 by Vincent X. Genest, Luc Vinet, Alexei Zhedanov · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/47/20/205202

published as J. Phys. A: Math. Theor. 47 (2014) 205202 · 16 pp; Added references and comments

arxiv created 2014/04/02 · arxiv updated 2015/06/18

Abstract

A quantum superintegrable model with reflections on the 2-sphere is introduced. Its two algebraically independent constants of motion generate a central extension of the Bannai--Ito algebra. The Schrodinger equation separates in spherical coordinates and its exact solutions are presented. It is further observed that the Hamiltonian of the system arises in the addition of three representations of the sl_-1(2) algebra (the dynamical algebra of the one-dimensional parabosonic oscillator). The contraction from the two-sphere to the Euclidean plane yields the Dunkl oscillator in two dimensions and its Schwinger-Dunkl symmetry algebra sd(2).

Cited by

• Verma modules and finite-dimensional irreducible modules of the universal Askey–Wilson algebra at roots of unity

Related

• Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid
• Bannai-Ito algebras and the osp(1,2) superalgebra
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D