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