From 60f0df3df68ae7c56504b7450a3f5604bed7a2f7 Mon Sep 17 00:00:00 2001
From: Kevin Choi <k.choi-1@student.tudelft.nl>
Date: Tue, 5 Feb 2019 11:12:09 +0000
Subject: [PATCH] Added hint for exercise 1.1
---
src/8_many_atoms.md | 4 ++++
1 file changed, 4 insertions(+)
diff --git a/src/8_many_atoms.md b/src/8_many_atoms.md
index 0a168e5..77055ad 100644
--- a/src/8_many_atoms.md
+++ b/src/8_many_atoms.md
@@ -228,6 +228,10 @@ $\rightarrow \rho_{\rm R}(k)=\frac{L}{2\pi}$, which is lower than for the case o
Recall the eigenfrequencies of a diatomic vibrating chain in the lecture notes with 2 different masses (can be found below [here](#more-degrees-of-freedom-per-unit-cell)).
1. Find the magnitude of the group velocity near $k=0$ for the _acoustic_ branch.
+
+ ??? hint
+ Make use of Taylor series.
+
2. Show that the group velocity at $k=0$ for the _optical_ branch is zero.
3. Derive an expression for the density of states $g(\omega)$ for the _acoustic_ branch and small $ka$. Make use of your expression of the group velocity in 1.
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