From fb354c80404a1203c8ffdd59c605aeb48e890b59 Mon Sep 17 00:00:00 2001
From: Bowy La Riviere <b.m.lariviere@student.tudelft.nl>
Date: Fri, 8 Jan 2021 09:45:47 +0000
Subject: [PATCH] Added warm-up questions

---
 src/5_atoms_and_lcao.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/src/5_atoms_and_lcao.md b/src/5_atoms_and_lcao.md
index 5f643f6f..d5f5c1cd 100644
--- a/src/5_atoms_and_lcao.md
+++ b/src/5_atoms_and_lcao.md
@@ -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?
+
 
 ### Exercise 1: Shell-filling model of atoms
 1. Describe the shell-filling model of atoms.
-- 
GitLab