ON THE ONE-DIMENSIONAL HELIUM ATOM

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.