summaryrefslogtreecommitdiffstats log msg author committer range
path: root/physics
diff options
 context: 12345678910152025303540 space: includeignore mode: unifiedssdiffstat only
Diffstat (limited to 'physics')
-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: