Quantisation of the multidimensional rotor

We reconsider the problem of quantising a particle on the D-dimensional sph ere. Adopting a Lagrangian method of reducing the degrees of freedom, the q uantum Hamiltonian is found to be the usual Schrodinger operator without an y curvature term. The equivalence with the Dirac Hamiltonian approach is de monstrated, either in the cartesian or in the curvilinear basis. We also br iefly comment on the path integral approach.