## Stuck “easily showing that…” in Modinos

I’m currently stuck on Modinos’ derivation of the the number of electrons when cross a unit area per unit time, with total energy between $E$ and $E+dE$ and normal energy between $W$ and $W+dW$.

$N(E,W) dE dW = \frac{m}{2 \pi^2 \hbar^3} n(E) dE dW$

where $n(E)$ is the Fermi-Dirac distribution.   The blocking issue is integrating over an unusual region or k-vector 3 space where {E,W} under the triple integral indicates only states with total energy between $E$ and $E+dE$ and normal energy between $W$ and $W+dW$ corresponding to $v_z>0$ included in the integration.