add learning goals to the first week

src/lecture_1.md

@@ -14,14 +14,13 @@ configure_plotting()
 _(based on chapter 2 of the book)_  
 Exercises: 2.3, 2.4, 2.5, 2.6, 2.8
 
-In this lecture we will:
+!!! summary "Learning goals"
 
-- discuss specific heat of a solid based on atomic vibrations (_phonons_)
-- disregard periodic lattice $\Rightarrow$ consider homogeneous medium
-    - _(chapter 9: discuss phonons in terms of atomic masses and springs)_
-- discuss the Einstein model
-- discuss the Debye model
-- introduce reciprocal space, periodic boundary conditions and _density of states_
+    After this lecture you will be able to:
+
+    - Explain quantum mechanical effects on the heat capacity of solids (Einstein model)
+    - Compute occupation number, energy and heat capacity of a bosonic particle
+    - Write down the total thermal energy of a material
 
 ### Einstein model
 Before solid state physics: heat capacity per atom $C=3k_{\rm B}$ (Dulong-Petit). Each atom is (classical) harmonic oscillator in three directions. Experiments showed that this law breaks down at low temperatures, where $C$ reduces to zero ($C\propto T^3$).
@@ -128,6 +127,13 @@ $$E=\int\limits_0^\infty\left(\frac{1}{2}\hbar\omega+\frac{\hbar\omega}{ {\rm e}
 
 $g(\omega)$ is the _density of states_: the number of normal modes found at each position along the $\omega$-axis. How do we calculate $g(\omega)$?
 
+!!! summary "Learning goals"
+
+    After this lecture you will be able to:
+
+    - Describe the concept of reciprocal space and allowed momenta
+    - Write down the total energy of phonons given the temperature and the dispersion relation
+    - Estimate heat capacity due to phonons in high temperature and low temperature regimes
 
 #### Reciprocal space, periodic boundary conditions
 Each normal mode can be described by a _wave vector_ ${\bf k}$. A wave vector represents a point in _reciprocal space_ or _k-space_. We can find $g(\omega)$ by counting the number of normal modes in k-space and then converting those to $\omega$.