From 08a1d77053372b310055ddde8621c6b8a206ef50 Mon Sep 17 00:00:00 2001
From: bnewbold
Date: Thu, 19 Mar 2009 14:32:23 -0400
Subject: corrections to fermi, TODO check second to last line
---
physics/quantum/fermigas | 11 +++++------
1 file changed, 5 insertions(+), 6 deletions(-)
(limited to 'physics/quantum')
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:`$$E_{F}=\frac{\hbar^{2}}{2m}|k_{F}|^{2}=\frac{\hbar^{2}}{2m}(3\rho \pi)^{2/3}$$`
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