N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N)

The $N$-dimensional Smorodinsky-Winternitz system is a maximally superintegrable and exactly solvable model, being subject of study from different approaches. model has been demonstrated to be multiseparable with wavefunctions given by Laguerre Jacobi polynomials. In this paper we present the complete symmetry algebra ${\cal SW}(N)$ system, which it higher-rank quadratic one containing recently discovered Racah R}(N)$ as subalgebra. substructures distinct Q}(3)$ algebras their related Casimirs are also studied. way, constraints on oscillator realizations these substructures, energy spectrum obtained. We show that allows set based R}({ N})$ can applied independently algebraically derive system.