TABLE OF CONTENTS As I have mentioned before, phonons represent lattice vibrations just as photons represent electromagnetic vibrations. In this section I will try to elaborate on this statement and clarify what I mean. At low temperatures, the atoms that make up a molecule or a solid are frozen in their positions on the lattice and this frozen atomic potential is used in calculating the energy levels for the electrons, starting from the Schr dinger equation. As the temperature is raised these vibrations increase in amplitude and exchange energy with the electrons through the electron phonon interaction. To understand how we describe these vibrations, let us start with a simple example, namely a hydrogen molecule.
As we discussed in Chapter 3, we could describe the vibrations of this molecule in terms of a mass and spring system (Fig. 10.4.1). The mass M is just that of the two hydrogen atoms, while the spring constant K is equal to the second derivative of the potential energy with respect to the interatomic distance. We know from freshman physics that such a system behaves like an oscillator with a resonant frequency 
. Experimentalists have measured this frequency to be approximately ? = 2 ?(10 14/s). Knowing M we could calculate K and compare against theory, but that is a different story. The question we wish to address is the following. As we raise the temperature we expect the molecule to vibrate with increasing amplitude due to the...
