Three-dimensional parabolic interband joint density of states
= Three-dimensional parabolic interband joint density of states
{title2=$g_j(E)=\frac{(2m_r/\hbar^2)^{3/2}}{2\pi^2}\sqrt{E-E_g}$}
For isotropic direct-gap parabolic bands, $m_r^{-1}=m_e^{*-1}+m_h^{*-1}$ and transition <energy> is $E_g+\hbar^2k^2/(2m_r)$. Differentiating the two-spin state count $k^3/(3\pi^2)$ per volume gives the displayed density for $E>E_g$, and zero below. Density per <angular frequency> is $\hbar g_j(\hbar\omega)$, not the same dimensioned quantity.