Interface response theory of composite systems

A short account of a new unified interface response theory of composite systems is given. This theory applies as well to discrete as to continuous d-dimensional spaces and enables one to calculate the response function for any composite system from a new simple and general equation. With the help of this response function all the properties associated to a given operator and a composite system can be obtained. A short review of a few physical properties obtained with the help of response functions will be given for vibrational, electronic, magnetic, electromagnetic problems associated with surfaces, interfaces, adsorbates, superlattices,… As an illustration, it will be shown how the interface response theory enables one to solve the Schrödinger equation for free electrons in any composite material, and in particular superlattices.