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.

It gives a detailed and rigorous exposition of the WKB method in one dimension and its exact version, which includes nonperturbative effects in the Planck constant. This is illustrated in many examples, including the double-well potential. It also includes a description of the semiclassical quantization of higher-dimensional integrable systems, which are illustated by the Toda lattice.