2D ideal Fermi gas.

2D ideal Fermi gas
Consider an ideal Fermi gas in 2D. It is contained in an area of dimensions L x L. The particle mass is m

  1. Find the density of states D(∈)
  2. Find the Fermi energy as a function of the particle density n = N/L2 
  3. Find the total energy as a function of the Fermi energy ∈F
  4. Find the chemical potential µ as a function of n and T

Note that

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