diff --git a/src/8_many_atoms.md b/src/8_many_atoms.md index 0a168e551760959618ec89b800649f0b99186f3d..77055ad8b0518436f41b9a807ab781b1edbd9214 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.