  The semiclassical Kepler-Coulomb problem and the quantum-mechanical
Schr\"odinger-Coulomb problem are compared for their predictions of quadrupole
E2 transitions. The semiclassical treatment involves an extension of previous
work for the electric dipole transitions (Physical Review A 71, 020501), and
rates are derived for $\Delta \ell= 0, \pm 2$ transitions on the basis of the
multipolar properties of the emitted radiation. For the quantum case a
derivation is presented within the Schr\"odinger framework without reference to
spin. Comparison of the E2 rates shows reasonable agreement, but not as good as
was found for the electric dipole case.
