Derive equations (8.4.3) through (8.4.5) for a Fermi gas in a harmonic trap. Evaluate equations (8.3.4) and (8.3.5) numerically to reproduce the theoretical curves shown in Figures 8.9 and 8.10.

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E/3kT 2.0 1.8 1.6 1.4 1.2- classical 1.0 0.0 0.2 0.4 0.6 0.8 1.0 TITF FIGURE 8.10 Experimental results for the mean energy per particle divided by the equipartition value of 3kT vs. scaled temperature (T/TF) for ultracold 40K atoms in a harmonic trap compared with the theoretical Fermi gas value from equations (4) and (5). This shows the development of the Fermi degeneracy of the gas at low temperatures. From Jin (2002). Figure courtesy of the IOP. Reprinted with permission; copyright 2002 American Institute of Physics.