Fermi wavevector ($k_F=p_F/\hslash$)

The Fermi wavevector is the radius of the occupied sphere in wavevector coordinates for an isotropic Fermi gas. In the uniform two-component electron model, $k_F=(3{\pi }^{2}n{)}^{1/3}$ and $E_F={\hslash }^2{k}_F^2/(2m_e)$ for nonrelativistic particles. Its units are inverse length, whereas the Fermi momentum has units of momentum.

The wavelength associated with a specified Fermi wavevector. A local-density response normally requires variation on a scale large compared with $k_F^{-1}$; numerical factors such as $2\pi$ must be kept explicit when comparing a variation scale with the full wavelength.