Blundell Thermal Physics · Problem 30.3

Quantum gases and condensates

Physics — Statistical Mechanics · fermi-gas-chemical-potential

Problem

Show that for a gas of fermions with density of states

g(E)

, the chemical potential is given by

\mu(T) = E_{\rm F} - \frac{\pi^2}{6}(k_{\rm B}T)^2\frac{g'(E_{\rm F})}{g(E_{\rm F})} + \ldots \tag{30.64}