While doing the problems for the Einstein model I was surprised to see that in some of the questions we use the energy E and in others we use \left\langle E \right\rangle. For example in the last problem about diatomic materials, why do we use the energy instead of averaging? I don’t really understand when you are supposed to average over the energy and when we can just leave it. I suppose one should take statistical averages when there are many fluctuations, but in the case of the diatomic material, wouldn’t the energies fluctuate? So why no \left\langle E \right\rangle there?
The angular brackets are frequently omitted for brevity when talking about macroscopic quantities—that is quite common.
In practice, it should be mostly clear from the context what is meant. However if there is a specific place where the meaning is confusing—let us know and we’ll fix it right away.
So in the question about diatomic materials from this lecture there should be angular brackets? Isn’t the energy of the individual Lithium atoms microscopic?
Whenever the temperature is being mentioned, you can assume <E> is being talked about. So in this case, exercise 3.3 and 3.4 refers to the statistical average. On the other hand, 3.2 refers to the simple total energy E since it explicitly tells what modes are occupied and thus there are no thermal fluctuations.