ABSTRACT
This chapter presents an introduction to the basics of electron energy structure and the theory of optical functions of nanomaterials and focuses on the physical nature of phenomena. It considers a few relevant examples of the electron energy structure in quantum-confined systems in order to illustrate their specific features in optics and modifications of optical functions of nanoparticles due to the confinement. The tight binding method has existed for many years as a convenient and transparent model for the description of electronic structure in molecules and solids. Electrons in silicon thin slabs are confined in one dimension and thus show two-dimensional quantum behavior. The confinement of electrons at the nanometer scale is one of the central goals of graphene-based electronics and has attracted increasing attention. The conduction and valence states in graphene are degenerate at the K point of the Brillouin zone which gives rise to a linear dispersion of the electronic bands.
