Merge branch '75-add-warm-up-exercises-for-debye-model' into 'master'

Resolve "Add warm-up exercises for Debye model"

Closes #75

See merge request !63

src/2_debye_model.md

@@ -289,6 +289,15 @@ ax.legend(loc='lower right');
 
 ## Exercises
 
+### Quick warm-up exercises
+
+1. Express the three-dimensional density of states in terms of $\omega_D$.
+2. Express the heat capacity for low $T$ in terms of $T_D$. 
+3. Make a sketch of the heat capacity in the low $T$ for two different Debye temperatures. 
+4. Why are there only 3 polarizations when there are 6 degrees of freedom in three-dimensions for an oscillator?
+5. Convert the two-dimensional integral $\int\mathrm{d}k_x\mathrm{d}k_y$ to a one-dimensional integral.
+6. Einstein model has the free fitting parammeter $\omega$, but Debye model doesn't require any fitting parameters to properly describe the low temperature limit? There is, however, a material dependent parameter in the Debye model. Which one is it?
+
 ### Exercise 1: Debye model: concepts
 
 Consider the probability to find an atom of a 1D solid that originally had a position $x$ at a displacement $\delta x$ shown below: