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Ideal Fermi gas in two dimensions
Consider an ideal Fermi gas in two dimensions. It is contained in an area of dimensions L × L. The particle mass is m.
1. Calculate the density of states.
2. Using your result for the density of states, calculate the number of particles as a function of the chemical potential at zero temperature. (μ(T = 0) = ?F, the Fermi energy.)
3. Calculate the Fermi energy as a function of the number of particles.
4. Again using your result for the density of states, calculate the total energy of the system at zero temperature as a function of the Fermi energy, ?F.
5. Calculate the energy per particle as a function of the Fermi energy ?F.
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