= Filling fraction of an independent cosine band
{title2=$k_Fa=\pi f\quad(t<0)$}
For a <dispersion relation> $E(k)=E_0+t\cos(ka)$, $t<0$, occupied states at zero <temperature> form the interval $|k|<k_F$ in the first <Brillouin zone>. Its occupied fraction is $f=2k_F/(2\pi/a)=k_Fa/\pi$. A spin-degenerate band therefore holds $2f$ <electrons> per site. If the band is independent of the other two wavevector coordinates, its <Fermi surface> consists of two planes. For $t>0$ the occupied region is instead near the zone edges, bounded by $|k|=\pi(1-f)/a$.
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