Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Fax: 519-746-4319
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Wed 9 Sep: Lecture 1, Video 1, Notes Ch.2.1-2.3.3
Fri 11 Sep: Lecture 2, Video 2, Notes Ch.2.33-2.5
Mon 14 Sep: Lecture 3, Video 3, Notes Ch.3.1-3.2
Wed 16 Sep: Lecture 4, Video 4, Notes Ch.3.2
Fri 18 Sep: Lecture 5, Video 5, Notes 3.4-3.4.4
Mon 21 Sep: Lecture 6, Video 6, Ch.3.4.5
Wed 23 Sep: Lecture 7, Video 7, Ch.3.4.6-3.6
Fri 25 Sep: Lecture 8, Video 8, Lecture notes so far
Mon 28 Sep: Lecture 9, Video 9, Lecture notes so far
Wed 30 Sep: Lecture 10, Video 10, Lecture notes so far
Fri 2 Oct: Lecture 11, Video 11, Lecture notes so far
Mon 5 Oct: Lecture 12, Video 12, Lecture notes so far
Wed 7 Oct: Lecture 13, Video 13, Lecture notes so far
Fri 9 Oct: Lecture 14, Video 14, Lecture notes so far
Mon 19 Oct: Lecture 15, Video 15, Lecture notes so far
Wed 21 Oct: Lecture 16, Video 16, Lecture notes so far
Fri 23 Oct: Lecture 17, Video 17, Lecture notes so far
Mon 26 Oct: Lecture 18, Video 18, Lecture notes so far
Wed 28 Oct: Lecture 19, Video 19, Lecture notes so far
Fri 30 Oct: Lecture 20, Video 20, Lecture notes so far
Mon 2 Nov: Lecture 21, Video 21, Lecture notes so far
Wed 4 Nov: Lecture 22, Video 22, Lecture notes so far
Fri 6 Nov: Lecture 23, Video 23, Lecture notes so far
Mon 9 Nov: Lecture 24, Video 24, Lecture notes so far
Wed 11 Nov: Lecture 25, Video 25, Lecture notes so far
Fri 13 Nov: Lecture 26, Video 26, Lecture notes so far
Mon 16 Nov: Lecture 27, Video 27, Lecture notes so far
Wed 18 Nov: Lecture 28, Video 28, Lecture notes so far
Fri 20 Nov: Lecture 29, Video 29, Lecture notes so far
Mon 23 Nov: Lecture 30, Video 30, Lecture notes so far
Wed 25 Nov: Lecture 31, Video 31, Lecture notes so far
Fri 27 Nov: Lecture 32, Video 32, Lecture notes so far
Mon 30 Nov: Lecture 33, Video 33, Lecture notes so far
Wed 2 Dec: Lecture 34, Video 34, Lecture notes so far
Fri 4 Dec: Lecture 35, Video 35, Lecture notes so far
Mon 7 Dec: Lecture 36, Video 36, Lecture notes
Extended lecture notes with non-examinable bonus: Noether's theorem
Homework is to be submitted via Crowdmark:
The homework with your lowest percentage will not count.
The aim of AMATH 473 / PHYS 454 is to give a solid understanding of the mathematical structure and physical principles which underlie quantum theory. The course should provide a basis from which interested students can proceed, for example, to studies of quantum technologies, or to studies of the quantum theory of fields, which can then lead, for example, to particle physics and to quantum gravity and cosmology.
In AMATH 473 / PHYS 454, we will, therefore, study the internal workings of quantum mechanics, in its abstract formulations by Heisenberg, Schroedinger, Dirac and Feynman, as well as practical perturbative tools for applying quantum mechanics to real-life systems. We will investigate the relation between Bose-Einstein and Fermi statistics, symmetries and conservation laws, and we will cover Bell's paradox, open quantum systems, decoherence and thermal states.
Textbooks: Recommended are the modern texts by Griffiths, Cohen-Tannoudji, Shankar and Sakurai, as well as the classics by Feynman Hibbs (path integral, ingenious) and Messiah (operator formalism, very comprehensive: >1000 pages). The two classics are now very cheap (from Dover).
An essay should be a review of existing literature on a given topic. The sources can be textbooks, lecture notes or review articles or original articles or some of each. All and everything that is used needs to be cited. Most articles are now available online and for example "Google Scholar" can get you there quickly. Try for example searching for a few key words along with the words "review" or "introduction". Most electronic journals require a subscription, which the university library usually has. For the license to be recognized you may need to browse either from a university computer (the domain is what counts) or you log into the library website from home and go to an electronic journal through the library's electronic journal search engine.
In the essay, your task is to show that you have understood and critically reflected upon the material by making it your own. You make it your own by coming up with an original way for presenting the material that you are bringing together. Try to give it your own angle or spin. Wherever possible, try to put things into a larger context. Sometimes (hopefully very rarely) it may be necessary to stick quite closely to a source, e.g., when a calculation is to be presented and the source does it in a way that is just hard to improve upon. In this case, you can make it your own for example by filling in a few steps in the calculation that the author omitted. In this case, it is important that you point out at that place that you do so. Filling in steps obviously proves that you understood that calculation.
A good essay describes. An excellent essay explains.
No original research is expected. But, you are encouraged to make educated speculations about what interesting things could be done in this area. You have been a regurgitating undergraduate for a long time. This is an opportunity to show that you still have some creativity left in you! Don't worry, you are not expected to solve the problem of quantum gravity here. Just show that you are thinking for yourself.
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.