## Course curriculum

• 1

### Welcome to the course!

• A message from your QT instructor - Maïté

• A message from your QT TA - Tomas

• How to use this course

• Course outline

• Before we begin... K-W-(L) chart [Note: K is for Know, W is for Want, L is for Learnt]

• 2

### Week 1 - Lie group, Lie algebras and representation theory

• Welcome to the 1st week of this course!

• Lecture notes for week 1

• Tuesday - Lecture 1.1 - Groups, Lie groups and representation theory

• Wednesday - Tutorial 1 - Some fun with discrete groups

• Wednesday - submit your Tutorial 1 - Some fun with discrete groups

• Thursday - Lecture 1.2 - Group representation theory and Quantum Theory

• Friday - Lecture 1.3 - Lie algebras and Lie groups

• Friday - Time to test your learning! - And this is part of HW1! (and you are allowed to take it several times if needed)

• Friday - any questions? feedback?

• Tutorial 1 - solutions (with the participation of Hikari and Neel for Pb 3.6!)

• 3

### Week 2 - Canonical Quantization

• Welcome to the 2nd week for the Quantum Theory course!

• Lecture notes for week 2

• Monday - Quiz 2.1 - What do you know about vector spaces and linear operators?

• Monday - review on vector spaces and linear operators

• Tuesday - Lecture 2.1 - From classical mechanics to Quantum Mechanics

• Tuesday - Tutorial 2 - Harmonic Oscillator (first level) [+Optional problem on Poincaré group]

• Tuesday - Submit your Tutorial 2 - Harmonic Oscillator (first level) [+Optional problem on Poincaré group]

• Wednesday - Lecture 2.2 - Time evolution operator and time-evolution pictures

• Thursday - Tutorial 3 - Pictures of time-evolution

• Thursday - Submit your Tutorial 3 - Pictures of time-evolution

• Thursday - Quiz 2.2 - Time to review what you learnt! (part of HW1)

• Any question? Feedback?

• Tutorial 2 - solutions

• Tutorial 3 - solutions

• 4

### Week 3 - Group representation in Quantum Theory

• Welcome to the third week of the Quantum Theory course

• Lecture notes for week 3

• Monday - Lecture 3.1 - Coordinate and momentum representations for the free particle

• Tuesday - Lecture 3.2 - The Heisenberg group and the free particle

• Tuesday - Tutorial 4 - The holomorphic representation and more about the Heisenberg group

• Tuesday - submit your Tutorial 4 - The holomorphic representation and more about the Heisenberg group

• Wednesday - Lecture 3.3 - The Quantum Free particle as a representation of the Euclidean group

• Thursday -Tutorial 5 - Concept map!

• Friday - time to test your learning (HW1)!

• Tutorial 4 - solutions

• Tutorial 5 - solutions

• 5

### Week 4 - Path Integral

• Welcome to the 4th week of the Quantum Theory course!

• Lecture notes for week 4

• Monday (because I forgot last Friday!) - any question, feedback on Week 3?

• Monday - Lecture 4.1 - The propagator as path integral

• Tuesday - Tutorial 6 - Complex analysis and path integral

• Tuesday - submit your tutorial 6 - Complex analysis and path integral

• Wednesday - Lecture 4.2 - Semi-classical expansion and path integral

• Thursday - Lecture 4.3 - Partition function

• Thursday - Tutorial 7 - Path integral

• Thursday - submit your tutorial 7 - Path integral

• Friday - test what you've learnt! (HW1)

• Tutorial 6 - solutions

• Tutorial 7 - solutions

• 6

### Week 5 - Perturbation theory in the Path Integral formalism

• Welcome to the last week of the Quantum Theory course!

• Lecture notes for week 5

• Monday (because I forgot again last Friday!) - any question, feedback on week 4?

• Monday - Lecture 5.1 - Perturbative expansion

• Tuesday - Tutorial 8 - Interview practise and some perturbation theory in the path integral formalism.

• Tuesday - submit your tutorial 8 - Perturbation theory in the path integral formalism

• Tuesday - Lecture 5.2 - Correlation function and generating functional

• Wednesday - it's time to test your learning! (HW1) - Note: questions on Week 4 and Week 5 content

• Time to reflect... (K-W)-L chart [Note: K is for Know, W is for Want, L is for Learnt]

• Tutorial 8 - solutions

• 7

### Homeworks

• HW1 - continuous assessment

• HW2 - Everything about $\mathrm{SU}(2)$ - due date Sept. 23rd

• HW3 - Energy levels of the anharmonic oscillator - due date Oct. 9th

• Interview questions

• 8

### Resources

• References for lecture notes

• Quantum Theory, Groups and Representations: an introduction, by Peter WOIT.

• P. Dirac, On the Analogy between Classical and Quantum Mechanics (1945)

• R. Feynman, Space-time approach to non-relativistic Quantum Mechanics (1948)

• E. Wigner, The Unreasonable Effectiveness of Mathematics in Natural Sciences (1960)

• L Hardy, R. Spekkens, Why physics needs Quantum Foundations (2010)

• M. Sotne, P. Goldbart, Mathematics for Physics