FormulaFree electron gas in 3d (density of states) $$ D(W) ~=~ \frac{V}{2\pi^2} \, \left(\frac{2m}{\hbar^2}\right)^{3/2} \, \sqrt{W} $$
FormulaFree electron gas in 1d (density of states) $$ D(W) ~=~ \frac{L}{\pi} \, \left(\frac{2m}{\hbar^2}\right)^{1/2} \, \frac{1}{\sqrt{W}} $$
