Quantum physics II

PHYS-314

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Chapter 1: Recap of the basics 

1.1 The qubit  

1.3 Evolution 

1.4 Measurement


Chapter 2: Composite systems and entanglement (part 1)

2.1 State Space for Many Particles

2.2 Operators

2.3 Measurements 


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). 

A little bit more on many body quantum systems:

- Measurements 
- Product states
- Entanglement

Chapter 2: What makes quantum different

  • Quantum eraser 
  • No signalling
  • Non-locality and Bell inequalities


Additional references: Chapter 5 Townsend, Chapter 6 Binney & Skinner.


Chapter 2 continued...

- Entanglement (Part 3) Formal derivation of Bell inequalities

- Contextuality 

Chapter 3 (part 1): Reduced and mixed quantum states 

4.1 Density operators 

4.1.1 Pure states and mixed states


Useful textbooks: Nielson & Chuang, Chpt.2.4.


Chapter 3 (part 2): Reduced and mixed quantum states 

3.3 - Reduced states

3.4 - General properties of density operators 

3.5 - Evolution of density operators 


The measurement problem and decoherence 

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 


I highly recommend going and reading Bell's account of the measurement problem, and Zurek's writing on decoherence. See papers attached. 

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)



Reading week 

Time independent Perturbation Theory

8.1 Non-degenerate Time-Independent Perturbation Theory

    8.1.1 Examples

8.2 Degenerate Time-Independent Perturbation Theory

    8.2.1 Examples


I quite like Binney and Skinner (https://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf) as a textbook covering peturbation theory. 

Time-dependent Hamiltonians 

    9.1 Dyson series

    9.2 Interaction Representation


I quite like Binney and Skinner (https://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf) as a textbook covering peturbation theory. 

11 November - 17 November

Time Dependent Perturbation Theory

- Transition Probabilities


18 November - 24 November

The variational Principle 

- Statement

- Simple examples 


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 





25 November - 1 December

Irreducible Representations 

- Introduction to irreps
-Schur's lemmas

2 December - 8 December

Groups and reps continued... 

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

9 December - 15 December

The final bit on groups and reps:

Small orthogonality theorem + characters 


A physicists introduction to Lie Algebras (via angular momentum)

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).