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| -rw-r--r-- | physics/quantum/fermigas.page | 3 |
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: |