Fundamentals of Electron-Photon Interaction in Nanostructures

We describe the fundamental equations for description of electron-photon interactions in insulating nanostructures. Since the theory for the nanostructures are based on the theory for the bulk crystals, we shall describe elements of the theory for the bulk crystals \cite{knox}-\cite{b2} in the first three subsections. It is important in discussions on optical phenomena that both the envelope function and the Wannier functions (or, equivalently, cell-periodic parts of the Bloch functions) should be taken into account. The theory for the nanostructure is discussed in the fourth subsection. In the final subsection, we briefly mention quantum optics in nanostructures.