## Introduction¶

In this unit you will learn all of the **basic ingredients** of quantum mechanics — the theory that describes the universe at the smallest scales. By now you will undoubtedly heard about many of the **iconic** and **counter-intuitive** aspects of quantum mechanics, including particles being in **superposition**, the **uncertainty principle**, **discrete energy levels**, to name just a few. The aim of this course is to give you your **first solid grounding** in all of these aspects, and many more. Since quantum mechanics is a **huge departure** from all the came before it, we will keep the scope of this unit small, and focus exclusively on the **mechanics of a single particle in one dimension**. As you will see, this nevertheless gives a rich playground to study almost all of the key features of quantum mechanics.

As of **2023** I am trialing a HTML version of the lecture notes, which you are accessing here. If you spot any **typos** or **mistakes** which may have arisen from the conversion to HTML, **please let me know**, so that I can quickly fix them.

I have added links to the **lecture videos** at the appropriate points in the lecture notes. I hope this will make it easier to move back and forth quickly between the videos and the notes.

If you prefer a more traditional PDF version of the lecture notes, for instance in order to annotate, then please see the lecture notes on Blackboard.

## Table of Contents¶

- Chapter 1: History and Background
- Chapter 2: Basics of Quantum Mechanics
- Chapter 3: Separation of Variables & the Time-Independent Schrödinger Equation
- Chapter 4: The Free Particle
- Chapter 5: Momentum in Quantum Mechanics
- Chapter 6: Operators
- Chapter 7: Commutation and the Uncertainty Principle
- Chapter 8: The Infinite Square Well: Energy Eigenstates
- Chapter 9: The Infinite Square Well: Dynamics
- Chapter 10: The Finite Square Well
- Chapter 11: The Quantum Harmonic Oscillator
- Chapter 12: Scattering