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Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions — R. K. Pathria
Physics — Statistical Mechanics · fermi-gas-mean-inverse-speed
Problem Show that for an ideal Fermi gas
⟨ u ⟩ ⟨ 1 u ⟩ = 4 π f 1 ( z ) f 2 ( z ) [ f 3 / 2 ( z ) ] 2 , \langle u \rangle \left\langle \frac{1}{u} \right\rangle = \frac{4}{\pi}\frac{f_1(z)f_2(z)}{[f_{3/2}(z)]^2}, ⟨ u ⟩ ⟨ u 1 ⟩ = π 4 [ f 3/2 ( z ) ] 2 f 1 ( z ) f 2 ( z ) , u u u ⟨ u ⟩ ⟨ 1 u ⟩ ≃ 9 8 [ 1 + π 2 12 ( k T ε F ) 2 ] ; \langle u \rangle \left\langle \frac{1}{u} \right\rangle \simeq \frac{9}{8}\left[1 + \frac{\pi^2}{12}\left(\frac{kT}{\varepsilon_F}\right)^2\right]; ⟨ u ⟩ ⟨ u 1 ⟩ ≃ 8 9 [ 1 + 12 π 2 ( ε F k T ) 2 ] ; Browse the problem library