Quantum Theory of Metallic Reflection

In the classical (Drude) theory of the reflection and transmission of light at a metal surface, the component of electric intensity perpendicular to the surface is discontinuous there, the remaining components of the field vectors being continuous. In a more detailed description the interaction of the light with the metal is expressed as scattering by the conduction electrons according to quantum theory. Those components of the field vectors which were continuous in the classical theory retain very approximately their values in that theory. The electric intensity perpendicular to the surface, though given approximately elsewhere by the classical theory, fluctuates widely within a few electron wavelengths of the surface. If this fluctuating field is used to calculate the surface photoelectric effect by Mitchell's method, the agreement of his result for a clean potassium surface with observation is improved. To a first approximation, the new theory predicts that the frequency at the peak of the spectral distribution curve for a clean surface of a metal depends only on the number $N$ of free electrons per unit volume and for different metals varies approximately as $N^{\frac{5}{9}}$; although the experimental results are uncertain, this is roughly the case. No calculations have been made for sensitized surfaces, but arguments based on the use of the Drude form seem to be precarious.