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6 - The WKB Approximation. Electronic Properties of Solids

Published online by Cambridge University Press:  27 December 2025

Ana María Cetto
Affiliation:
Universidad Nacional Autónoma de México, Mexico
Luis de la Peña
Affiliation:
Universidad Nacional Autónoma de México, Mexico
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Summary

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.

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