DYNAMICAL SYMMETRIES IN A SPHERICAL GEOMETRY .2.

For pt.I see ibid., vol.12 (1979). The quantum mechanical Coulomb and isotropic oscillator problems in an N-dimensional spherical geometry, which were shown in the previous paper to possess the dynamical symmetry groups SO(N+1) and SU(N) respectively as classical systems, are analysed by the method used by Pauli to find the energy eigenvalues of the hydrogen atom. This analysis is carried through completely for N=3 to obtain energy eigenvalues and recurrence relations among energy eigenfunctions. It is shown that Pauli's method is equivalent to Schrodinger's method of solving the radial Schrodinger equation by factorisation of the second order differential operator. The latter method is used to find the energy eigenvalues in N dimensions, and the corresponding eigenfunctions are obtained in closed form.