I Where did the extra 8 come from in the derivation for density of states?

[iampaul]

TL;DR Summary

I tried to follow the derivation, but I got a different result

I was looking for a derivation for the density of states and I came across this page: https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm

I followed the derivation and came up with:
g(E) = (¹/_L³)^dN/_dE
= (¹/_L³)^L3/_∏²*k² * ^dk/_dE
=^K2/_∏² * ^dk/_dE
=^K2/_∏² *
g(E) = (^∏√2/_h³)*m^3/2*√2but the book gives:
g(E) = (^8∏√2/_h³)*m^3/2*√2

where did the extra 8 come from?

 

[BvU]

Check your math. You miss some factors $\pi$.
The 8 comes from the $\ \hbar^3\$ and $\ \hbar = {h\over2\pi}$

 

[iampaul]

Check your math. You miss some factors $\pi$.
The 8 comes from the $\ \hbar^3\$ and $\ \hbar = {h\over2\pi}$

Thanks, I've been plugging in $\ \hbar = {h\over\pi}$.