Chapter 6 begins with an exposition of the WKB approximation technique developed in 1926 by Wentzel. Kramers and Brillouin. The WKB method is discussed in detail, and it is shown that it is particularly suitable when the particle is in a sufficiently energetic state that its behavior can be considered to be almost classical, for which reason it is called a semiclassical approximation. The method is applied specifically to the study of the nuclear alpha decay and the calculation of the tunneling time delay. The rest of the chapter is devoted to a discussion of the basic electronic properties of solids and some important applications of these properties, which are easily explained using the results obtained in the first part of the chapter. Starting with the free electron gas model, it concludes with a discussion of semiconductors based on the Kronig and Penney model.

Basic concepts of electromagnetic theory; Coulomb gauge; intensity of electromagnetic field. Electrons in an electromagnetic field: from the Lagrangian to the Hamiltonian; canonical momentum. Interaction Hamiltonian. Semiclassical approximation; weak-field limit. Electric dipole approximation. Calculation of the optical susceptibility by using the density matrix approach. From optical susceptibility to absorption coefficient. Momentum of an electron in a periodic crystal.

Starting from a detailed explanation of Klein paradox of relativistic quantum mechanics, we consider a motion of massless Dirac fermions through potential barriers. It is shown that chiral properties of these particles guarantee a penetration through arbitrarily high and broad potential barriers. The role of this phenomenon (chiral tunneling) for graphene physics and technology is explained. We discuss analogy between electronic optics of graphene and optical properties of metamaterials, especially, Veselago lensing effect for massless Dirac fermions. Chiral tunneling in bilayer graphene is discussed.