Two-dimensional joint density of states ($J_{2D}$)

For two isotropic parabolic subbands, the joint density of states per area and per independent channel is $\mu /(2\pi {\hslash }^2)\Theta (\hslash \omega -E_{\mathrm{edge}})$. The constant is a two-dimensional phase-space effect. Degeneracy and optical matrix elements determine the actual step weights.