Self-consistent field approximation for the plasma frequencies of an electron gas in a layered thin film

The dispersion relation for plasma oscillations in a thin layered film is calculated in the SCF approximation for a model in which the electron motion along the film thickness is described like a tunnelling process between adjacent planes. For a semi-infinite medium the linear term in the dispersion relation of the surface plasmon is obtained. This is done using an appropriate expansion technique and in the limit of a 'create' separation between adjacent planes.