Born-Oppenheimer Approximation

The full interaction Hamiltonian raises the first question why our previous models could give sensible results in many cases. The physical reason for that is since the mass of just one nucleon is about 1800 times larger than the electronic mass the electrons can react on a certain configuration of the ions nearly instantanously; so from the electrons' point of view the ions are immobile whereas from the ions' point of view the electrons react and produce a charge distribution depending only on the configuration of the ions, but not on their dynamics. These considerations suggest a two step procedure:

• Solve the electronic problem for a fixed, arbitrary ionic configuration.
• Solve the ionic problem by treating the influence of the electrons only through the dependence of their charge distribution on the ionic configuration; the action of the electrons is therefore reduced to an effective potential.