2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185528In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.10 pages, LaTeXHigh Energy Physics - Theorytext