Advanced Quantum Theory, AMATH 473/673, PHYS454 in Fall 2020

  • Term: Fall 2020.
  • Course codes: AMATH 473/673, PHYS454
  • Instructor: Achim Kempf
  • Teaching Assistants: Evan Peters and Basel Jayyusi
  • Prerequisite: AMATH 373 or PHYS 334, or consent of instructor.
  • Lecture times and location: 
    Videos will be posted Mondays, Wednesdays, Fridays by the end of the day, see below for the links.
    ​First lecture: Wednesday, 9 September 2020
  • Office hours with Prof: Fridays 1-2pm via Zoom
  • Office hours / Tutorial with the TAs (Evan or Basel): 
  • Grades (undergraduate): Homework 25%, Midterm 25%, Final 50%. 
  • Grades (graduate): Essay (see below) 1/3, remaining 2/3 as for undergraduate students.
  • Midterm and Final exam: time and logistics will be announced here. 
  • Graduate students (those who enrolled in AMATH673):
    Homework, midterm and final will be the same as for undergraduate students. Plus, graduate students are to hand in an approximately 10 page essay by 11:59pm on December 21st. The topic of the essay is: Summarize this new research paper: Essay-paper. The task is to discuss the general motivation, the specific questions raised in this paper and (some of) the results of the paper - all entirely in your own words. You can enhance your essay by calculating small examples. For general advice on writing an essay, see the bottom of this page.
  • Online discussion board for use by students, TAs and prof:  
    • The link is here: Piazza.  Please sign up, it is free.
    • Using Piazza is better than emailing the TAs or the instructor because by using Piazza, all can benefit from the discussion. If you wish, you can post anonymously. 
    • Particularly good answers from students to student questions may receive bonus points.
    • Of course, do not discuss the solutions to a homework exercise that is still due.  

Lecture videos, lecture notes and homework

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  

Special announcement video

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

Homework is to be submitted via Crowdmark

  • Homework 1 is due: 11:59am on Friday, 18 Sep. 2020
    Consists of all the exercises in Ch.2 of the lecture notes
  • Homework 2 is due: 11:59am on Friday, 25 Sep. 2020
    Consists of the exercises 3.1-3.14, which are here in the lecture notes: Ch.3.1-3.4.4
  • Homework 3 is due 11:59am on Monday, 5 October 2020
    Consists of the exercises 3.15-3.23 in the lecture notes.
  • Homework 4 is due 11:59am on Wednesday, 21 October 2020
    Consists of the exercises 3.24-5.1 in the Lecture notes

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).

General advice on what is expected in the essay (graduate students only)

  • Format: title and abstract page/motivation/main parts/summary (or conclusions)/bibliography.
  • Bibliography: List all of your sources explicitly. Of course you can use Wikipedia but you should not cite it - because it can change from day to day and because as it is not (yet) reliable enough to meet scientific standards. Instead, cite books and papers that you may have found via Wikipedia. Also, it is good style to list items in the bibliography in that sequence in which they are first referred to in the text.
  • At most about 10 pages.
  • 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.