Inadequacy of Perfect-Reflector Models in Cavity QED for Systems with Low-Frequency Excitations

It is shown that the model of perfectly reflecting boundaries widely employed in cavity QED is unsuitable for systems that have long-wavelength excitations. A prime example is a free charged particle near a reflecting wall. Modeling the wall as perfectly reflecting from the outset ignores evanescent waves that couple to the particle through virtual excitations at low energies, which can lead to errors in order of magnitude and even sign. The example of a free electron near an imperfectly reflecting wall characterized by a constant frequency-independent refractive index $n$ is investigated in detail by determining its energy shift relative to an electron in vacuum through both nonrelativistic and relativistic calculations.