reformulations of learning goals

src/lecture_1.md

@@ -19,7 +19,7 @@ Exercises: 2.3, 2.4, 2.5, 2.6, 2.8
     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
+    - Compute the expected particle number, energy, and heat capacity of a quantum harmonic oscillator (a single boson)
     - Write down the total thermal energy of a material
 
 ### Einstein model
@@ -133,7 +133,7 @@ $g(\omega)$ is the _density of states_: the number of normal modes found at each
 
     - 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
+    - Estimate heat capacity due to phonons in high temperature and low temperature regimes of the Debye model
 
 #### 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 $\omega$.

src/lecture_3.md

@@ -149,7 +149,7 @@ Therefore if each atom has a single electron in the outermost shell, these atoms
 
     - Explain the origins of interatomic forces
     - Compute vibrational spectra of small molecules in 1D
-    - Write down Hamiltonians and equations of motion of bulk materials (but not yet solve them)
+    - Formulate Hamiltonians and equations of motion of bulk materials (but not yet solve them)
 
 ## Adding repulsion