Interaction between Electron and One-Dimensional Electromagnetic Field

For a single electron interacting with the quantized transverse electromagnetic field it is found that, in the one-dimensional case, the Schrödinger equation can be put into a form like that of a system of coupled harmonic oscillators. From the classical frequencies of the normal modes of oscillation of such a system the quantal energy can be determined. While the perturbation method gives a logarithmic divergence in the interaction energy, one finds by the present method that the energy diverges like the square root of a logarithm.