Update 2_debye_model.md - typo

src/2_debye_model.md

@@ -129,7 +129,7 @@ Periodic boundary conditions imply that the atomic displacement $\mathbf{\delta
 $$
 \mathbf{\delta r}(\mathbf{r} + L\mathbf{\hat{x}}) = \mathbf{\delta r}(\mathbf{r})
 $$
-To satisfy this equation, we arrive at the condition $k_x=p 2 \pi/L$]$, with $p= ..., -2, -1, 0, 1, 2$ in $\mathbb{Z}$.
+To satisfy this equation, we arrive at the condition $k_x=p 2 \pi/L]$, with $p= ..., -2, -1, 0, 1, 2$ in $\mathbb{Z}$.
 
 We see that periodicity implies that not all the points in $k$-space are allowed.
 Instead only waves for which each component $k_x, k_y, k_z$ of the $\mathbf{k}$-vector belongs to the set
@@ -140,7 +140,7 @@ In 3D the allowed $k$-vectors form a regular grid:
 
 ![](figures/DOS_periodic.svg)
 
-There is therefore exactly one allowed ${\bf k}$ per volume $\left(\frac{2\pi}{L}\right)^3$ in reciprocal space.
+There is therefore exactly one allowed ${\bf k}$-value per volume $\left(\frac{2\pi}{L}\right)^3$ in reciprocal space.
 
 When we consider larger and larger box sizes $L→∞$, the volume per allowed mode becomes smaller and smaller, and eventually we obtain an integral:
 $$
@@ -150,7 +150,7 @@ $$
 
 ## Density of states
 
-Continuing with our calculation of the total energy, we get:
+Let's use this knowledge and continue our calculation of the total energy:
 $$
 \begin{align}
 E &= \frac{L^3}{(2\pi)^3}\iiint\limits_{-∞}^{∞}dk_x dk_y dk_z × 3×\left(\frac{1}{2}\hbar\omega(\mathbf{k})+\frac{\hbar\omega(\mathbf{k})}{ {\rm e}^{\hbar\omega(\mathbf{k})/{k_{\rm B}T}}-1}\right),\\