The dynamical algebra of the generic superintegrable model on the two-sphere

Abstract

The rank two Jacobi algebra ${\mathfrak{J}}_2$ is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of this algebra is obtained from its embedding in $\mathfrak{su}(1,1{)}^{\otimes 3}$. The exact solution of the model is derived algebraically from this representation. The wavefunctions are found to be expressed in terms of two-variable Jacobi polynomials whose characterization is a by-product of the algebraic treatment of the model.

30 pages, Comments are welcome