From 5e1ed099963c4e2367926bbca5b38f16be196198 Mon Sep 17 00:00:00 2001
From: Lars kleyn Winkel <l.kleynwinkel@student.tudelft.nl>
Date: Mon, 10 Feb 2020 17:04:36 +0000
Subject: [PATCH] Update src/7_tight_binding_model_sol.md

---
 src/7_tight_binding_model_sol.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/7_tight_binding_model_sol.md b/src/7_tight_binding_model_sol.md
index dbbee22e..5cf60831 100644
--- a/src/7_tight_binding_model_sol.md
+++ b/src/7_tight_binding_model_sol.md
@@ -29,7 +29,7 @@ Hint: What kind of particles obey Bose-Einstein statistics? What kind of 'partic
 
 ### Subquestion 2
 
-Group velocity is given as $v=\hbar^{-1}\frac{\partial E}{\partial k}$ with $E=\hbar\omega$ and $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$. So we find: $$ v(k) = \frac{a}{2}\sqrt{\frac{2\kappa}{m}}\frac{\sin(ka)}{\sqrt{1-\cos(ka)}}$$ $$ g(\omega) = \frac{L}{2\pi}\frac{d}{d\omega} \bigg [\frac{2}{a}\sin^{-1}\bigg(\sqrt{\frac{m}{\kappa}}\frac{\omega}{2} \bigg) \bigg ] = \frac{L}{2\pi a} \sqrt{\frac{m}{\kappa}} \frac{1}{\sqrt{1-\frac{m\omega^2}{4\kappa}}}$$
+Group velocity is given as $v=\hbar^{-1}\frac{\partial E}{\partial k}$ with $E=\hbar\omega$ and $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$. So we find: $$ v(k) = \frac{a}{2}\sqrt{\frac{2\kappa}{m}}\frac{\sin(ka)}{\sqrt{1-\cos(ka)}}$$ $$ g(\omega) = \frac{L}{2\pi}\frac{d}{d\omega} \bigg [\frac{2}{a}\sin^{-1}\bigg(\sqrt{\frac{m}{\kappa}}\frac{\omega}{2} \bigg) \bigg ] = \frac{L}{\pi a} \frac{1}{\sqrt{\frac{4\kappa}{m}-\omega^2}}$$
 
 ### Subquestion 3
 
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