We consider the quantum mechanical description of electrons that are confined to D-dimensional spheres. In the physically interesting cases of a ring (D = 1), a normal sphere (D = 2) and a glome (D = 3), we show that accurate wave functions and energies can be obtained when the electron density (i.e. the ratio of the number of electrons to the volume of the sphere) is high or low. Intermediate densities are more difficult but smooth interpolations appear to yield satisfactory results. (For more information see: PF Loos and PMW Gill, Phys Rev Lett 103 (2009) 241101 & PMW Gill and PF Loos, Theor Chem Acc, 131 (2012) 1069).