Quantum physics II

Chapter 1: Recap of the basics 

1.1 The qubit  

1.3 Evolution 

1.4 Measurement

Useful textbooks: Chpts 1.1,1.2 of Nielson & Chuang (recap of basics). Chpts 1 and 2 of Townsend (recap of basics + superposition and interference). 

Chapter 2 continued...

• Non-locality and Bell inequalities
• Entanglement (Part 3) Formal derivation of Bell inequalities
• Contextuality 

Useful textbooks: Nielson & Chuang, Chpt.2.4.

• 3.1 Density operators 
• 3.1.1 Pure states and mixed states
• 3.3 - Reduced states
• 3.4 - General properties of density operators 
• 3.5 - Evolution of density operators 

• 4.1 Statement of the measurement problem
• 4.2 Simple resolutions to the measurement problem and why they don't work 
• 4.3 Simple models of decoherence 

Reading week 

Introduction to groups and representations

-Introduction

- Motivational example on spatial translations and degeneracies 

- Introduction to groups 

- Finite group examples

- Continuous group examples

-Basic definitions and properties of groups 

-Basic definitions and properties of representations 

Groups and reps continued... 

Equivalence/conjugacy classes 
Grand / Petit orthogonality theorems
Group mixing
A bit on characters

The final bit on groups and reps:

Small orthogonality theorem + characters 

A physicists introduction to Lie Algebras (via angular momentum). 

The most important take away from this section for the exam is that you know how to compute: A representation of the basis of a Lie-Algebra from either i. the structure constant that define the algebra or ii. a representation of the corresponding Lie group.  

The most important take away from this section for the exam is that you:

1) Understand the link between finding irreducible representations and addition of angular momentum

2) Can compute Clebsch–Gordan coefficients for simple cases 

The final bit on Lie Algebras and Angular Momentum

- Addition of angular momentum 

Fermions and Bosons 

• 5.1 Two identical particles
• 5.2 Multiple identical particles 
  • 5.2.1 Bosons
  • 5.2.2 Fermions 
• 5.3 Distinguishing identical particles 
• 5.4 Second Quantization: 
• 5.5 The Hong-Ou-Mandel Effect and Bosonic Bunching 

Useful textbooks: Binney & Skinner Chpt 10.1, Townsend Chpt 12, Cohen-Tannoudji Diu Laloe (Volume 2 for identical particles, Volume 3 for distinguishing identical particles)

The Variational Principle:

8.1 - The general Idea

Time independent Perturbation Theory

6.1 Non-degenerate Time-Independent Perturbation Theory

    6.1.1 Examples

6.2 Degenerate Time-Independent Perturbation Theory

    6.2.1 Examples

    7.1 Dyson series

    7.2 Interaction Representation

Here are some rules to follow for the exam.

Cheat sheet and other material:  You are allowed a cheatsheet ("formulaire") written on two A4 sheets. This means four sides in total. These notes can be handwritten or typed. No official version of these notes is provided: it is the responsibility of each student to prepare their own notes. Once in the exam room, it will be forbidden to ask for another student's notes. No other documents are admitted.

Calculator and electronic devices:  No electronic device connected to the internet, or having significant storage and data visualization capabilities, is allowed. The use of scientific calculators is permitted, even those with graphic functionality. You will be able to leave your phones in your bags at the back of the room (see below).