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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.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: