From 214bc7f402377bdafea60be508c7194e596ef238 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Sun, 24 Jan 2010 09:48:25 +0000 Subject: fixes --- physics/quantum/fermigas.page | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) (limited to 'physics') diff --git a/physics/quantum/fermigas.page b/physics/quantum/fermigas.page index de66ee1..38398d5 100644 --- a/physics/quantum/fermigas.page +++ b/physics/quantum/fermigas.page @@ -43,7 +43,8 @@ excited states in the gas. The radius can be derived by calculating the total volume enclosed: each block has volume $\frac{\pi^3}{l_x l_y l_z}=\frac{\pi^3}{V}$ and there are N/2 blocks occupied by N fermions, so: -$$\frac{1}{8}(\frac{4\pi}{3} |k_{F}|^{3})&=&\frac{Nq}{2}(\frac{\pi^{3}}{V})\\|k_{F}|&=&\sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$ +$$\frac{1}{8}(\frac{4\pi}{3} |k_{F}|^{3}) = \frac{Nq}{2}(\frac{\pi^{3}}{V})$$ +$$|k_{F}| = \sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$ $\rho$ is the "free fermion density". The corresponding energy is: -- cgit v1.2.1