= Ground-state filling of two spin-degenerate Landau levels
{title2=$E=\hbar(eB/m)[3N-eBA/(\pi\hbar)]$}
For $2N$ noninteracting electrons in a planar sample of area $A$, neglecting Zeeman splitting leaves two spin states for each orbital. Each Landau level therefore holds $D=eBA/(\pi\hbar)$ electrons. When $N\le D\le2N$, fill the lowest level with $D$ electrons and the next with $2N-D$; summing their energies gives the displayed concave quadratic in $B$. The energies at the two integer-filling endpoints are equal.
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