diff --git a/src/8_many_atoms.md b/src/8_many_atoms.md index 8bff514acb99df2d5faa3acd664a423a4f134ac4..0a168e551760959618ec89b800649f0b99186f3d 100644 --- a/src/8_many_atoms.md +++ b/src/8_many_atoms.md @@ -229,8 +229,7 @@ Recall the eigenfrequencies of a diatomic vibrating chain in the lecture notes w 1. Find the magnitude of the group velocity near $k=0$ for the _acoustic_ branch. 2. Show that the group velocity at $k=0$ for the _optical_ branch is zero. -3. Derive an expression for the density of states $g(\omega)$ in the _optical_ branch. -4. Make a plot of your expression of $g(\omega)$ found in 3. Does the plot look like the bar diagram of the density of states of the optical branch in the lecture notes? +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. #### Exercise 2: atomic chain with 3 different spring constants Suppose we have a vibrating 1D atomic chain with 3 different spring constants alternating like $\kappa_ 1$, $\kappa_2$, $\kappa_3$, $\kappa_1$, etc. All the the atoms in the chain have an equal mass $m$.