1.1 Introduction

In the popular mind the electron lives as something very small that has something to do with electricity. Studying electromagnetism does not change the picture appreciably. You learn that the electron can be regarded as a negative point charge and it duly obeys the laws of mechanics and electromagnetism. It is a particle that can be accelerated or decelerated but cannot be taken to bits.

Is this picture likely to benefit an engineer? Yes, if it helps him to produce a device. Is it a correct picture? Well, an engineer is not concerned with the truth; that is left to philosophers and theologians: the prime concern of an engineer is the utility of the final product. If this physical picture makes possible the birth of the vacuum tube, we must deem it useful; but if it fails to account for the properties of the transistor then we must regard its appeal as less alluring. There is no doubt, however, that we can go quite far by regarding the electron as a particle even in a solid the subject of our study.

What does a solid look like? It consists of atoms. This idea originated a few thousand years ago in Greece, and has had some ups and downs in history, but today its truth is universally accepted. Now if matter consists of atoms, they must be somehow piled upon each...