Expand knowledge base, remove comments

1 files changed, 1 insertions, 6 deletions

diff --git a/content/know/concept/jellium/index.pdc b/content/know/concept/jellium/index.pdc
index 15c3308..9743514 100644
--- a/content/know/concept/jellium/index.pdc
+++ b/content/know/concept/jellium/index.pdc
@@ -5,6 +5,7 @@ publishDate: 2021-11-23
 categories:
 - Physics
 - Quantum mechanics
+- Perturbation
 
 date: 2021-10-15T20:31:12+02:00
 draft: false
@@ -363,17 +364,11 @@ $$\begin{aligned}
     &= \frac{- e^2 V}{4 \pi^4 \varepsilon_0} \int_0^{2 k_F}
     \bigg[ \frac{k_F^3}{3} x + \frac{|\vb{q}|^3}{48 \xi^2} \bigg]_{|\vb{q}| / (2 k_F)}^1 \dd{|\vb{q}|}
     \\
-    %&= \frac{- e^2 V}{4 \pi^4 \varepsilon_0} \int_0^{2 k_F}
-    %\bigg( \frac{k_F^3}{3} + \frac{|\vb{q}|^3}{48} - \frac{k_F^3}{3} \frac{|\vb{q}|}{2 k_F} - \frac{4 k_F^2 |\vb{q}|^3}{48 |\vb{q}|^2} \bigg)
-    %\dd{|\vb{q}|}
-    %\\
     &= \frac{- e^2 V}{4 \pi^4 \varepsilon_0} \int_0^{2 k_F}
     \bigg( \frac{k_F^3}{3} + \frac{|\vb{q}|^3}{48} - \frac{k_F^2 |\vb{q}|}{4} \bigg) \dd{|\vb{q}|}
     \\
     &= \frac{- e^2 V}{4 \pi^4 \varepsilon_0} \bigg[ \frac{k_F^3 |\vb{q}|}{3} + \frac{|\vb{q}|^4}{192} - \frac{k_F^2 |\vb{q}|^2}{8} \bigg]_0^{2 k_F}
     \\
-    %&= \frac{- e^2 V}{4 \pi^4 \varepsilon_0} \bigg( \frac{k_F^3}{3} 2 k_F + \frac{16 k_F^4}{192} - \frac{k_F^2 4 k_F^2}{8} \bigg)
-    %\\
     &= \frac{- e^2 V}{16 \pi^4 \varepsilon_0} k_F^4
     = \frac{- e^2 N}{16 \pi^4 \varepsilon_0 n} k_F^4
     = -\frac{3 e^2 N}{16 \pi^2 \varepsilon_0} k_F