A careful discussion of the interaction of the inner electron with the
nucleus of the helium atom allows for the reduction to a one-dimensio
nal Hamiltonian describing the frozen planetary atom configuration. Th
is is obtained by cancelling the angular momentum of each electron, ev
en though it is only their sum which is guaranteed to be constant. The
true oscillatory nature of the angular momenta in the full two-dimens
ional Hamiltonian can be included in a time-periodic model that correc
tly accounts for the finite lifetime of the frozen planetary atom. Thi
s system can be Further simplified by averaging over the motion of the
inner electron so as to define an oscillatory Hamiltonian with a sing
le degree of freedom.