(If you are registered for the course, see myCourses for the detailed syllabus)
Prof. Andrew Cumming, Rutherford Physics Building 310, email andrew.cumming-at-mcgill.ca
This is an advanced course in quantum mechanics. The goal is to build on earlier courses in quantum mechanics to expose you to some of the concepts, tools, and outstanding questions in quantum mechanics research today and how quantum mechanics is applied to complex systems.
The course will cover the following general areas, with an emphasis on the basic physics and illustrative applications. Particular sub-topics may change, depending on the time available.
Fundamentals - Dirac notation, matrix representation, change of basis, measurement and observables, entanglement and composite states, density matrices, purity, coherence, quantum gates and quantum computing
Quantum dynamics - time-evolution and the Hamiltonian, Schrodinger and Heisenberg pictures, transitions and Fermis Golden Rule, time-dependent perturbation theory, coupling to the electromagnetic field, Landau levels and the Quantum Hall Effect, radiative transitions, scattering
Multiparticle systems - identical particles, helium atom, symmetry breaking, second quantization, Cooper pairs and superfluidity
Relativistic quantum mechanics - Klein-Gordon and Dirac equations, the need for quantum field theory
You should have already taken one year of undergraduate quantum mechanics, at the level of the books Introduction to Quantum Mechanics by Griffiths or A Modern Approach to Quantum Mechanics by Townsend, or their equivalent. At McGill, this means the courses PHYS 446/447 or PHYS 357/457.
The recommended textbook for the course will be Sakurai & Napolitano Modern Quantum Mechanics, which is now in its 3rd Edition. This is the classic book on this subject at this level, and covers most of the topics in the course. Note that the first edition is substantially different from the 2nd and 3rd, but may still be useful.
Sakurai and Napolitano is unfortunately not available as an ebook from the library. An excellent alternative text which is available as an ebook from the McGill library is Principles of Quantum Mechanics by Shankar (2nd edition).
I will also make my lecture notes available on myCourses.
Otherwise, it is worthwhile to read as widely as you can to see different treatments of the various topics we will cover in the course. There are many books and lecture notes available online that you can look at. Here are some suggestions:
MW 1.05-2.25PM, RPHYS 114. The first lecture is on Wednesday September 1st.
Your grade will be based on weekly reading questions (5%), homework assignments (25%), a term paper (20%) and open book midterm and final exams (20% midterm, 30% final, or 0% midterm, 50% final, whichever gives you the best grade).
Term paper: write an article that reports on a recent paper in the literature on research in quantum mechanics, what the result/experiment is and why it is important, the background and how it relates to the course. It should be at the level of a Nature News & Views article (these are articles in the journal Nature that give the background to one of the research papers and explain why the result is important). The length should be 3 pages when set in a similar format to News & Views. Work in a group of 2-3. Topic will be due mid-October; the paper will be due in the third week of November. I will post interesting papers that I come across in a discussion forum on myCourses to give you ideas; I encourage you to do the same.
McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (more information). In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded. In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change. Additional policies governing academic issues which affect students can be found in the McGill Charter of Students' Rights.