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author committer bnewbold 2010-01-24 09:48:25 +0000 User 2010-01-24 09:48:25 +0000 214bc7f402377bdafea60be508c7194e596ef238 (patch) f1950843062d75f5a2fcaf894402defe5160c135 /physics/quantum 7268485fbc18c538d58471806ba7b38b372249f1 (diff) knowledge-214bc7f402377bdafea60be508c7194e596ef238.tar.gzknowledge-214bc7f402377bdafea60be508c7194e596ef238.zip
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-rw-r--r--physics/quantum/fermigas.page3
1 files changed, 2 insertions, 1 deletions
 diff --git a/physics/quantum/fermigas.page b/physics/quantum/fermigas.pageindex 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: