1st major update to lecture note 4

src/4_vector_spaces_QM.md

@@ -244,7 +244,7 @@ cannot represent physical states. We show below an explicit example of a normali
      $$
      as required to ensure the probabilistic description of the state vector.
 
-## Problems
+## 4.5. Problems
 
 **1)** [:grinning:] *The inner product*