Advanced Quantum Mechanics

This is the homepage for 3rd year advanced stream quantum mechanics.

Teaching assistants

The teaching assistant for this course is Alistair Milne.

Quizzes, assignments, exam

There will be 4 quizzes to be held during Lectures 5, 11, 14, 16 (all on Thursdays). There will be 2 assignments and 1 final exam. The marks will be apportioned to 35% of the total module mark according to: 5/35 1st Assignment, 3.33/35 2nd Assignment (QP section), 10/35 Quizzes, and 16.66/35 Exam.

Textbooks

Main text: A Modern Approach to Quantum Mechanics, 2nd Edition, by John S. Townsend.

Secondary texts: Quantum Mechanics: A Paradigms Approach, by David McIntyre, Corinne A Manogue, and Janet Tate.

Quantum Mechanics with Applications to Nanotechnology and Information Science, by Yehuda B. Band and Yshai Avishai.

Lecture notes

I will post lecture notes here as I finish them. I will try to post them before each class, but no promises.

• Week 1 Reading: Townsend 1.3, 1.6, 2.3, 2.4, 3.2, 4.1, 4.2, 6.1, 6.2, 6.3, 6.4, 6.9
• Pre-lecture / Lecture 01. Review of Dirac notation, operators, expectation values, and observables.
• Pre-lecture / Lecture 02. Time evolution and the Schroedinger equation. The Hamiltonian as the generator of time translations. Wavefunctions in infinite-dimensional Hilbert spaces; Position and Momentum Operators.
• Pre-lecture / Lecture 03. Uncertainty relations; Time-independent Schrödinger equation; Particle in a box.
• Week 2 Reading: Townsend 2.2, 3.1, 3.3, 3.4, 3.5, 3.6, 9.3, 9.5, 9.6
• Pre-lecture / Lecture 04. Introduction to wave mechanics in 3D; The generator of rotations; Angular momentum.
• Pre-lecture / Lecture 05. Angular momentum eigenstates; Ladder operators; Spin-1/2 systems.
• Pre-lecture / Lecture 06. Angular momentum in a 3D spherical system.
• Week 3 Reading: Townsend 9.8, 9.9, 10.1, 10.2, 11.1
• Pre-lecture / Lecture 07. Solving the Schrödinger Equation in a 3D radially symmetric potential; the spherical harmonics.
• Pre-lecture / Lecture 08. The Hydrogen atom; Radial wavefunctions; Hydrogenic wavefunctions; Hydrogen spectroscopy.
• Pre-lecture / Lecture 09. Nondegenerate Perturbation Theory.
• Week 4 Reading: Townsend 5.1, 5.2, 5.3, 11.2, 11.3, 11.5, 11.7, Appendix B.
• Pre-lecture / Lecture 10. Degenerate perturbation theory; The Stark effect.
• Pre-lecture / Lecture 11. Spin-orbit coupling; Fine structure.
• Pre-lecture / Lecture 12. Hyperfine structure; Addition of angular momentum; Clebsch-Gordan coefficients.
• Week 5 Reading: Townsend 12.1, 12.2, 14.1, 14.2, 14.4, 14.5.
• Pre-lecture / Lecture 13. Identical particles; Spin-statistics theorem; Helium atom; Exchange interaction.
• Pre-lecture / Lecture 14. The quantum Hamiltonian for classical EM fields; Zeeman splitting; Aharonov-Bohm effect.
• Pre-lecture / Lecture 15. Time-dependent perturbation theory; The interaction picture.
• Week 6 Reading: Townsend 14.6, 14.7, 14.9.
• Pre-lecture / Lecture 16. Fermi's golden rule.
• Pre-lecture / Lecture 17. Electric dipole approximation; Einstein A and B coefficients; Spontaneous Emission; Selection Rules.
• Week 7 Reading: Townsend 7.8, 14.8.
• Pre-lecture / Lecture 18. Harmonic oscillator redux: Coherent states, Quantum phase space.
• Pre-lecture / Lecture 19. Cat states; Cat codes (non-examinable).