corrections to fermi, TODO check second to last line

1 files changed, 5 insertions, 6 deletions

diff --git a/physics/quantum/fermigas b/physics/quantum/fermigas
index b91c67c..0114b43 100644
--- a/physics/quantum/fermigas
+++ b/physics/quantum/fermigas
@@ -39,14 +39,13 @@ correction can be important. There will then be a second correction due to
 removing the states along the individual axes twice (once for each
 side-surface), u.s.w.
 
-The surface of this shell is called the Fermi surface
-and represents the most excited states in the gas. The radius can be derived
-by calculating the total volume enclosed: each block has volume 
-:m:`$\frac{\pi^3}{l_x l_y l_z}=\frac{pi^3}{V}$` and there are N/2 blocks occupied by N 
-fermions, so:
+The surface of this shell is called the Fermi surface and represents the most
+excited states in the gas. The radius can be derived by calculating the total
+volume enclosed: each block has volume :m:`$\frac{\pi^3}{l_x l_y
+l_z}=\frac{\pi^3}{V}$` and there are N/2 blocks occupied by N fermions, so:
 
 :m:`$$\frac{1}{8}(\frac{4\pi}{3} |k_{F}|^{3})&=&\frac{Nq}{2}(\frac{\pi^{3}}{V})\\|k_{F}|&=&\sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$`
 
 :m:`$\rho$` is the "free fermion density". The corresponding energy is:
 
-:m:`$$E_{F}=\frac{\hbar^{2}}{2m}|k_{F}|^{2}=\frac{\hbar^{2}}{2m}\sqrt{3\rho \pi}^3$$`
+:m:`$$E_{F}=\frac{\hbar^{2}}{2m}|k_{F}|^{2}=\frac{\hbar^{2}}{2m}(3\rho \pi)^{2/3}$$`