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... KW(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 timeevolution pictures

Thursday  Tutorial 3  Pictures of timeevolution

Thursday  Submit your Tutorial 3  Pictures of timeevolution

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  Semiclassical 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


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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... (KW)L chart [Note: K is for Know, W is for Want, L is for Learnt]

Tutorial 8  solutions


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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


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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, Spacetime approach to nonrelativistic 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
