add prior knowledge to w3

src/5_atoms_and_lcao.md

@@ -13,6 +13,14 @@ pi = np.pi
 # Atoms and bonds
 _(based on chapters 5 and 6.2 of the book)_  
 
+!!! success "Expected prior knowledge"
+
+    Before the start of this lecture, you should be able to:
+
+    - Write down the Schrödinger equation
+    - Compute eigenvectors and eigenvalues of a matrix
+    - Find a state bound at a $δ$-function potential in 1D (for the exercises)
+
 !!! summary "Learning goals"
 
     After this lecture you will be able to:

src/6_bonds_and_spectra.md

@@ -13,6 +13,14 @@ pi = np.pi
 # interatomic interaction and molecular spectra
 _(based on chapters 6.1, 6.3, 8 of the book)_  
 
+!!! success "Expected prior knowledge"
+
+    Before the start of this lecture, you should be able to:
+
+    - Apply Taylor expansion
+    - Write down Newton's equations of motion of masses on springs
+    - Define and diagonalize matrices numerically (for the exercises)
+
 !!! summary "Learning goals"
 
     After this lecture you will be able to:
@@ -227,7 +235,7 @@ Consider carbon dioxide (C0$_2$) which is a linear triatomic molecule shown belo
 2. For simplicity, we only consider 1D motion of the atoms. Write down Newton's equations of motion for the atoms.
 3. Consider a *symmetric* mode, for which the displacements of the oxygen atoms are equal in magnitude and have an opposite direction. Find the eigenfrequency of this mode.
 4. Now consider the antisymmetric mode when the oxygen atoms move in phase and have the same displacement. Find the ratio between the displacements of the carbon and oxygen atoms that keeps the center of mass at rest.
-5. Compute the eigenfrequency of the antisymmetric mode. 
+5. Compute the eigenfrequency of the antisymmetric mode.
 
 ??? hint