From 6e70f28ccbd5afc1506f71f013278a9d157ef03a Mon Sep 17 00:00:00 2001 From: Prefetch Date: Thu, 27 Oct 2022 20:40:09 +0200 Subject: Optimize last images, add proof template, improve CSS --- source/know/concept/lindhard-function/index.md | 23 +++++++++-------------- 1 file changed, 9 insertions(+), 14 deletions(-) (limited to 'source/know/concept/lindhard-function') diff --git a/source/know/concept/lindhard-function/index.md b/source/know/concept/lindhard-function/index.md index 4033148..fd620df 100644 --- a/source/know/concept/lindhard-function/index.md +++ b/source/know/concept/lindhard-function/index.md @@ -149,11 +149,8 @@ $$\begin{aligned} = \hat{n}^\dagger(\vb{q}) \end{aligned}$$ -
- - - -
+{% include proof/end.html id="proof-density" %} + When neglecting interactions, it is tradition to rename $$\chi$$ to $$\chi_0$$. We insert $$\hat{n}$$, suppressing spin: @@ -290,12 +287,10 @@ $$\begin{aligned} = \hat{c}_{\vb{k}}^\dagger \hat{c}_{\vb{k}} - \hat{c}_{\vb{k} + \vb{q}}^\dagger \hat{c}_{\vb{k} + \vb{q}} \end{aligned}$$ -
- - - -
+{% include proof/end.html id="proof-commutator" %} + We substitute this result into $$\chi_0$$, and reintroduce the spin index $$\sigma$$ associated with $$\vb{k}$$: -- cgit v1.2.3