%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\sect{Fermions in magnetic field - Landau}
Consider $N$ spinless electrons that have mass $m$ and charge $e$
in a 2D box that has an area $A$ at zero temperature.
A perpendicular magnetic field $B$ is applied. The purpose
of this question is to find the magnetization of the system.
\Dn
(1) What are the threshold value $B_{n}$
for which there are exactly $n$ filled Landau levels.
\Dn
(2) Find the energy $E(B)$ and the magnetization $M(B)$
for strong field $B>B_1$. Give an optional semicalssical
derivation to the result assuming that each electron is doing
a cyclotron motion with minimal one-particle energy.
\Dn
(3) Find the energy $E(B)$ and the magnetization $M(B)$ for $B_{n+1}