A system consists of two identical particles. Each particle can occupy only two energy levels : E1 = ε and E2 = 2ε. If the particles satisfy Fermi-Dirac statistics, the partition function would be \(\left(\beta=\frac{1}{K_B \tau}\right)\) :

1
z = e-2β​ε + e-3β​ε + e-4β​ε
2
\(z=\frac{1}{2}\left(e^{-\beta \varepsilon}+e^{-2 \beta \varepsilon}\right)^2\)
3
z = e-3β​ε
4
z = 2(e-β​ε + e-2β​ε)

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