typo and added Sommerfeld question labeling

docs/3_drude_model.md

@@ -17,7 +17,7 @@ _(based on chapter 3 of the book)_
 
     - Write down the equation describing the Lorentz force
     - Formulate Newton's equation of motion for a particle subject to a force, including a damping term
-    - Discuss the concepts of voltage, current, resitivity, and conductivity
+    - Discuss the concepts of voltage, current, resistivity, and conductivity
 
 !!! summary "Learning goals"
 
@@ -277,7 +277,7 @@ While most materials have $R_H < 0$, interestingly some materials are found to h
 
 ## Exercises
 
-### Warm-up questions
+### Warm-up questions*
 
 1. Write down the Drude equation of motion for the average velocity of electrons in a material subject to an electric field. Discuss the scaling of the drag force with $\tau$ and $m$.
 2. From solving this equation in the steady state, we found the Drude conductivity $\sigma = \frac{ne^2\tau}{m}$. Discuss if its scaling with the electron density, charge, mass, and scattering time is reasonable.
@@ -285,7 +285,7 @@ While most materials have $R_H < 0$, interestingly some materials are found to h
    (Checking units is one of the fastest ways to see if an equation is incorrect!)
 4. Explain why the scattering times due to different types of scattering events add up in a reciprocal way. 
 
-### Exercise 1: Extracting quantities from basic Hall measurements
+### Exercise 1*: Extracting quantities from basic Hall measurements
 Hall-voltage measurements in an applied magnetic field are a powerful tool for determining the free charge density in a material. Conversely, knowledge of the charge density enables measurements of magnetic fields, which is used in [Hall sensors](https://en.wikipedia.org/wiki/Hall_effect_sensor). Here we analyze how to extract such quantities from Hall measurements.
 
 We consider a planar (two-dimensional) sample that sits in the $xy$ plane. The sample has width $W$ in the $y$-direction and length $L$ in the $x$-direction. We apply a current $I$ along the $x$-direction and a magnetic field $\bf B$ along the $z$-direction.

docs/4_sommerfeld_model.md

@@ -435,7 +435,7 @@ Thus the total energy is proportional to $T \times T^2$ and the heat capacity $C
 
 ## Exercises
 
-### Warm-up questions
+### Warm-up questions*
 
 1. List the differences between electrons and phonons from your memory.
 2. Write down the dispersion of free electrons.
@@ -452,7 +452,7 @@ What is the density of $\mathbf{k}$-points in 1, 2, and 3 dimensions?
 3. Express the number of states between energies $0<\varepsilon<\varepsilon_0$ as an integral over k-space. Do so for 1D, 2D and 3D. Do not forget spin degeneracy.
 4. Transform these integrals into integrals over energy for 1D, 2D and 3D. What relation do you need to do so? Indicate the integral boundaries. Extract the density of states. Are the integral boundaries important for the result?
 
-### Exercise 2: Applying the free electron model to potassium
+### Exercise 2*: Applying the free electron model to potassium
 The Sommerfeld model provides a good description of free electrons in alkali metals such as potassium (element K), which has a Fermi energy of $\varepsilon_{F} =  2.12$ eV (data from Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Saunders, 1976.).
 
 1. Check the [Fermi surface database](http://www.phys.ufl.edu/fermisurface/). Explain why potassium and (most) other alkali metals can be described well with the Sommerfeld model.
@@ -460,7 +460,7 @@ The Sommerfeld model provides a good description of free electrons in alkali met
 3. Calculate the free electron density $n$ in potassium.
 4. Compare this with the actual electron density of potassium, which can be calculated by using the density, atomic mass and atomic number of potassium. What can you conclude from this?
 
-### Exercise 3*: graphene
+### Exercise 3: graphene
 One of the most famous recently discovered materials is [graphene](https://en.wikipedia.org/wiki/Graphene). It consists of carbon atoms arranged in a 2D honeycomb structure. 
 Unlike in metals, electrons in graphene cannot be treated as 'free'. Instead, close to the Fermi level, the dispersion relation can be approximated by a linear relation:
 $ \varepsilon(\mathbf{k}) = \pm c|\mathbf{k}|.$ Note that the $\pm$ here means that there are two energy levels at a specified $\mathbf{k}$.