@@ -223,6 +223,13 @@ If each atom has 0 or 2 electrons in the outermost shell, the net electron force
## Exercises
### Warm-up questions
1. Is the assumption that the atomic orbitals are orthogonal always a reasonable assumption?
2. What happens if the hopping $t$ is chosen to be negative?
3. How does the size of the Hamiltonian matrix change with the number of atoms?
4. How does the size of the Hamiltonian matrix change if each atom now has two orbitals?
5. Assuming that we have two atoms with each a single orbital, what is the size of the Hamiltonian matrix if we also consider the spin of the electron?
