Advanced Quantum Theory, AMATH 473/673, PHYS454 in F17

  • Term: Fall 2017.
  • Course codes: AMATH 473/673, PHYS454
  • Instructor: Achim Kempf
  • Prerequisite: AMATH 373 or PHYS 334, or consent of instructor.
  • Lecture times and location: 
    Tue + Thu 10:00-11:20am, in room ML 349
    ​First lecture: Thursday, 7 September 2017
    Last lecture: Thursday, 30 November 2017
  • Office hours with Prof: Thursdays 11:30am-12:30pm in MC6322.
  • Office hours with the TAs (Maria or Kai): Wednesdays 4:30-5:30pm in MC6334.
  • Grades (undergraduate): Homework 25%, Midterm 25%, Final 50%. 
  • Grades (graduate): Essay (see below) 1/3, remaining 2/3 as for undergraduate students.
  • 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 a 10 page essay on the topic of the "Berry phase" by 11:59pm on December 1st. For advice on writing an essay, see the bottom of this page.
  • Midterm exam: Thu. 26 Oct. in class (extra office hours Wed. 25 Oct. 10am-12pm) in MC4059.
  • Final exam: Saturday, December 9, 2017 12:30 PM to 3:00 PM. Room: MC4020
  • Anonymous feedback form (very helpful - please fill in any time, I keep reading it): here

Lecture notes and exercises

Here are the complete Lecture notes with many typos fixed - special thanks to Daniel Wong for pointing out a long list of typos!
Note: Chapter 14 and the Appendix are not examinable and the exercises need not be handed in.  

The exercises 2.1-2.6 are due on Thursday, Sep. 14, in class. 

The exercises 2.7-3.5 are due on Thursday, Sep. 21, in class. 

The exercises 3.6-3.22 are due on Thursday, Sep. 28, in class.

The exercise 3.23,3.24 are due on Thursday, Oct. 5, in class. 

The exercises 3.25-5.2 are due on Thursday, Oct. 12, in class. 

The exercises 5.3-5.7 are due on Thursday, Oct. 19, in class.

The exercises of Chapters 6,7,8 are due on Tuesday, Oct. 31, in class.

The exercises of Chapters 9,10 are due on Thursday, Nov. 9, in class.

The exercises of Chapter 11 are due on Thursday, Nov.16, in class.  

The exercises 12.1-13.2 are due on Thursday, Nov. 23, in class.

The exercises 13.2-13.9 are due on Thursday, Nov. 30, in class. 

Final exam: Saturday, December 9, 2017 12:30 PM to 3:00 PM. Room: MC4020

Office hours in the week before the final:

  • With Maria: Wednesday 6 Dec: 3:30-5:00pm in MC6334.
  • With Kai: Friday 8 Dec. 11am-noon in MC6334.
  • With Prof (Achim): Friday 8 Dec: 9-11am and 3-5pm in MC6334.



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-live 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.