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\sect{Electron gas in a magnetic field, Landau levels}

Calculate the partition function for electrons in a 3D box
subject to a homogeneous magnetic field in the $z$ direction. 
Use the known results for the Landua levels and their degeneracy. 
Assume the Boltzmann approximation. 

\Dn

Find the magnetization for arbitrary field, 
and the susceptibility at zero field. Distinguish 
the orbital (Landau) and spin (Pauli) contributions. 

\Dn

Disregarding the spin, explain why there is no magnetism in the classical limit.

\Dn

Note: The zero temperature case is treated in a different exercise, 
and requires to take the Pauli exclusion into account.

