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

    • Tutorial 5 - your concept maps from Padlet
  • 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

    • Submit your HW2 here!

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

    • Submit your HW3 here!

    • 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