Fermi gasgrand canonical ensemblestatistical mechanicsThermal and Statistical Physics 2020
(K&K 7.11) Show for a single
orbital of a fermion system that \begin{align}
\left<(\Delta N)^2\right> = \left<N\right>(1+\left<N\right>)
\end{align} if \(\left<N\right>\) is the average number of fermions in
that orbital. Notice that the fluctuation vanishes for orbitals with
energies far enough from the chemical potential \(\mu\) so that
\(\left<N\right>=1\) or \(\left<N\right>=0\).

These notes from week 6 of Thermal and Statistical Physics cover the ideal gas from a grand canonical standpoint starting with the solutions to a particle in a three-dimensional box. They include a number of small group activities.

These lecture notes from week 7 of Thermal and Statistical Physics apply the grand canonical ensemble to fermion and bosons ideal gasses. They include a few small group activities.