ABSTRACT
In the preceding chapter, we showed that, under commonly prevalent conditions, a crystal behaves dynamically like a set of independent harmonic oscillators [see equation (7.65)]. The quantized form of these oscillators are phonons. The generalized coordinates of the oscillators are, in general, not atomic coordinates, but rather collective coordinates involving all the atoms of the crystal [see equations (7.37), (7.50) and (7.51)]. The normal mode frequencies !~k, equation (7.66), are obtainable classically if the force constants are known, and we have shown [equations (7.12), (7.18), (7.38), (7.46) and (7.48)] how to derive them under the approximations of Chapter 7 from the quantum-mechanical state of the electrons in the crystal.
