Theory of atoms in strong, pulsed electromagnetic fields: 2, A free electron and a harmonically bound electron

Multiple scale methods are used to treat several ingredients of the theory of atoms in strong electromagnetic fields. First, a focused electromagnetic field is expanded. Second, a classical electron is described giving the ponderomotive potential. Third, the quantum electron is treated in the WKB approximation. Fourth, the one dimensional quantum harmonic oscillator is solved; and last the one dimensional square well, showing the low intensity limit of the theory