Joseph Conlon
Homepage for A3 Quantum Mechanics (Michaelmas 2024 and Hilary 2025)
Lecturers: Joseph Conlon (Quantum: Michaelmas + Hilary), Siddharth Parameswaran (Further Quantum: Hilary, Trinity),
Aims and Objectives of the Course
This is a first course in quantum mechanics, the most important scientific discovery of the twentieth century.
Lecture Notes
Lecture notes for my part of the course will appear here. Lecture notes are precisely that -- they are not a textbook and they are not a replacement for
attending the lectures. The primary delivery of the course material is via the lectures; the lecture notes are supplementary and exist to support the lectures.
The lecture notes will therefore appear gradually and track the lectures. Respecting causality, they will only appear after the lectures they relate to.
There will be 27 lectures in total, and currently lecture notes for lectures 1-23 as well as lectures 24 - 27 can be found here: Lecture notes.
Note that as well as including lecture 24, I still intend to do some tweaking of these notes to include various images.
Rough schedule of the course lectures:
1. Introduction; quantum ideas and 2-slit experiment; amplitudes
2. Complex vector spaces; bras and ket; operators
3. Hermitian operators; amplitudes and phases
4. Observables; measurement in quantum mechanics
5. Commutators and compatibility of observables
6. General form of uncertainty principle; Schrodinger equation
7. Evolution of general eigenstates; Ehrenfest's theorem
8. Wavefunctions; normalisation, position and momentum operators
9. Particle in an infinite square well
10. The free particle in quantum mechanics
11. Probability density current, matching conditions
12. Scattering problems, the step potential, finite potential well
13. Quantum harmonic oscillator: introduction, raising and lower operators
14. Quantum harmonic oscillator: spectrum, wavefunctions, uncertainty principle
15. Active and passive transformation, unitary transformations, translations
16. Translations, rotations, relations to linear and angular momentum
17. Time evolution, Heisenberg picture, angular momentum
18. More angular momentum: general representations
19. Angular momentum, matrix elements, position space description
20. Spherical harmonics; first discussion of spin
21. Composite systems; spin examples; entangled states
22. Composition of two general angular momentum states
23. Magnetic moments; Stern-Gerlach experiment
24. Bell Inequalities
25. Spherically symmetric systems; general properties
26. Hydrogen Atom I
27. Hydrogen Atom II
Problem Sheets
The first problem sheet for MT 2024 is Problem Sheet 1 .
The second problem sheet for MT 2024 is Problem Sheet 2 .
The third problem sheet for the Christmas vacation 2024 is Problem Sheet 3 .
The fourth problem sheet (for approx week 2 Hilary 2025) is Problem Sheet 4 .
The fifth problem sheet (for approx week 3 Hilary 2025) is Problem Sheet 5 .
The sixth problem sheet (for approx week 4 Hilary 2025) is Problem Sheet 6 .
The seventh problem sheet (Hydrogen atom, for approx week 5/6 Hilary 2025) is Problem Sheet 7 .