Free electron model
= Free electron model
{title2=$\epsilon_{\mathbf k}=\hbar^2|\mathbf k|^2/(2m)$}
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The <free electron model> approximates conduction <Electrons> by noninteracting particles with the displayed parabolic <dispersion relation>, filling one-particle states according to <Fermi-Dirac distribution>. A uniform positive background supplies <charge neutrality>. <Periodic boundary conditions> give one spatial state per $k$-space volume $(2\pi)^d/V_d$ in $d$ dimensions; the physical <spin> degeneracy is two. The model captures basic state counting and degeneracy but omits the periodic lattice potential, interaction corrections and detailed <electronic band structure>.