Teaching

I am lecturing the second part of the Level III (third year) Quantum Mechanics course given by the maths department at the University of Bristol.

I will make my hand-written lecture notes available on this page, sometime after I have given the corresponding lecture. I will also put up the question sheets and solution sheets, sometime after they've been set and marked, respectively.

However, in my opinion relying on the lecture notes alone is a very poor substitute for attending the lectures and taking your own notes. You miss out on the oportunity to ask questions during the lectures about anything that's not clear to you. You don't hear the less formal explanations I tend to give verbally during the lecture. You're forced to rely on notes that were only ever intended as an aid to myself when giving the lecture. And, if you're still not convinced, I find that the act of writing notes during lectures is surprisingly helpful when it comes to digesting and understanding the material later; you often find that you've already partially absorbed the material already, for free, when you took the notes in the first place.

(If you're looking for the old material I prepared for classical mechanics and electrodynamics courses taught by Prof. Weise at the TUM, it's available here.)

Lecture Notes

Lectures 1 and 2
Section 1: Angular Momentum and Spin
Lectures 3 to 5
Section 2: Representations of Angular Momentum
Bonus Lecture
Section 3: Orbital Anglular Momentum (non-examinable)
Lecture 6
Section 4: Measurement
Lectures 7 and 8
Section 5: Multiple Particles and Tensor Products
Lectures 9 and 10
Section 6: Non-Locality and Bell Inequalities

Problem Sheets

Problem sheets 7 and 8 correspond to my section of the course. I will make solutions available after the corresponding question sheets have been handed in and marked.

Problem Sheet 7
sheet 7    solution 7
Problem Sheet 8
sheet 8    solution 8: Q1-3    Q4-5    Q6-7

Recommended books

Angular momentum

(lectures 1 to 5)

The main text book for this part of the course is the book by Hannabuss. But any good text book on quantum mechanics will cover this material. A sample of ones I like is listed below, but if you find one that presents the material in a way that you find easier, you should by all means make use of it.

  • "An Introduction to Quantum Theory", Hannabuss
    The angular momentum section of the course closely follows chapter 8.
  • "Modern Quantum Mechanics", Sakurai
  • "Quantum Mechanics", Cohen-Tannoudji
  • "Group Theory in Physics", Cornwell
    Chapter 12, Volume 2. For interest only; well beyond the level of the course.
  • "Feynman Lectures vol. 3", Feynman, Leighton, Sands
    As an accompaniement to the other books, volume 3 of Feynman's famous lecture series contains a presentation of quantum mechanics with a different and somewhat less mathematical flavour, which some may find helpful or interesting.

Measurement, tensor products, non-locality, entanglement and Bell inequalities

(lectures 5 to 10)

There is no single ideal text book covering this part of the course. The books and references listed below cover parts of it in a way that's not too far removed from the course, but serve more as an accompaniement to the lecture notes than an alternate source for the material.

  • "Quantum Computation and Quantum Information", Nielsen & Chuang
    Chapter 2 gives a concise but excellent treatment of measurement, tensor products and entanglement, though at a level a little above the course. Bell inequalities are also covered in this chapter, but this is not the focus of the book and the proof they give obscures some of the subtleties.
  • "Quantum Theory: Concepts and Methods", Asher Peres
    A delightful text book that contains a good treatement of the Bell experiment and much more.
  • "Bell Inequalities and Entanglement", Werner and Wolf, arXiv:quant-ph/0107093
    This review article gives a careful and rigorous discussion of Bell inequalities.
  • "Speakable and Unspeakable in Quantum Mechanics", John Bell
    A collection of insightful essays and papers by John Bell of Bell experiment fame.

Exam-Related

The following summary lists the examinable material from my part of the course. Anything not explicitly mentioned should be considered part of the general understanding of quantum mechanics you are expected to have obtained, and is therefore examinable in that sense.

Summary of examinable material, final 10 lectures.

Below is a set of notes I wrote a while ago for first year undergraduates, giving general tips on revision technique for maths exams. Since a number of people have been asking me how they should revise for this course, I've put it here in case you find it useful. It's purely my personal view on how to revise for exams, and you are of course welcome to ignore it if you have your own approach to revision that works well for you.

Toby's Tips on Revision Technique