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A set of integral equations for the transverse and longitudinal electromagnetic fields is obtained, which describes the evolution of an incoming free field on a spatially dispersive metal. Boundary conditions are discussed when a plasmonic mode too is propagating.

The coupling between the ionic and electronic motion is analysed in an unidimensional exact chemisorption problem. The influence of the ionic motion on the electron resonance and the modification of the bound-state equation of the ion are studied.

The cross-section and the scattering amplitude from an impurity in a crystal are expressed, through formulae which are similar to the classical ones, in terms of quantities which present many ianalogies and some differences with respect to the usual phase shifts. The relations between these phase shifts and the poles of the Green’s function of the total Hamiltonian and other properties are also discussed.