Advanced Quantum Theory, AMATH 473/673, PHYS454 in Fall 2023

  • Term: Fall 2023.
  • Course codes: AMATH 473/673, PHYS454
  • Instructor: Achim Kempf
  • Teaching Assistants: Matheus Zambianco (email: mhzambianco) and Christopher Pollack (email: cajpollack)
  • Prerequisite: AMATH 373 or PHYS 334, or consent of instructor.
  • Lecture times and location: Tue+Thu 4-5:20pm, in MC2035
    First lecture: Thu Sep 7
    Reading week: no lectures Tue Oct 10 and Thu Oct 12.
    Last lecture: Tue Dec 5
  • Health precautions (permanent):
    • If you have cold/flu/covid symptoms, do not come to class. Do the right thing, which is taking care of yourself and getting healthy first. 
      • For Lecture ​​​​​​​Videos (of my previous teaching), scroll down to the bottom of this page.
      • All important updates will always be posted here. 
  • Office hours with Prof: Wednesdays 12:30-1:30pm, MC6334, starting Sep 20
  • Office hour with a TA: Mondays 2-3pm in MC6334, starting Sep 18
  • Tutorials with a TA:  Fridays, 10:30-11:20am in MC2054, starting Sep 15
  • Midterm exam: Tue, November 7, at 4-5:20pm, Room: HH1101
  • Final exam:  Mon, December 18, 4:00-6:30pm, in PAC UPPER 10
  • Grades (undergraduate): Homework 10%, Midterm 40%, Final 50%. 
  • Grades (graduate): Essay (see below) 1/3, remaining 2/3 as for undergraduate students.
  • Graduate students (those who enroled 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: TBA
    • For general advice on writing an essay, see the bottom of this page.
  • For online discussions about this course, for use by students, TAs and Prof: Sign up here on Piazza

Lecture Notes

Here are the Lecture Notes.

  • Chapter 1 is a historical introduction which is not covered in the lectures and will not be examined. It is assigned reading.
  • The lecture notes will be updated continually with typo corrections etc. 
  • Therefore, best reload the lecture notes regularly.


The lectures start with Chapter 2. 

Lecture 1 (Thu Sep 7)

Lecture 2 (Tue Sep 12)

Lecture 3 (Thu Sep 14)

Lecture 4 (Tue Sep 19)  

Homework 1 is due: 11:30pm on Tue Sep 19.
Consists of all the exercises in Ch.2 of the lecture notes.

Lecture 5 (Thu Sep 21) 

Lecture 6 (Tue Sep 26)

Homework 2 is due: 11:30pm on Tue Sep 26. 
Consists of the exercises 3.1-3.14, in the lecture notes.

Lecture 7 (Thu Sep 28)

Lecture 8 (Tue Oct 3)

Homework 3 is due: 11:30pm on Tue Oct 3.
Consists of the exercises 3.15-3.23 in the lecture notes.

Lecture 9 (Thu Oct 5)

Tue 10: no class b/c reading week

Thu 12: no class b/c reading week

Lecture 10 (Tue Oct 17)

Lecture 11 (Thu Oct 19)

Homework 4 is due: 11:30pm on Thu Oct 19.
Consists of the exercises 3.24-5.1 in the lecture notes.

Lecture 12 (Tue Oct 24)

Lecture 13 (Thu Oct 26)

Lecture 14 (Tue Oct 31)

Homework 5 is due: 11:30pm on Tue Oct 31.
Consists of the exercises 5.2-7.2 in the lecture notes. 

Lecture 15 (Thu Nov 2)

*** Midterm on Tuesday Nov 7, at 4-5:20pm. Room: HH 1101 (in Hagey Hall) ***

Lecture 16 (Thu Nov 9)

Lecture 17 (Tue Nov 14)

Homework 6 is due: 11:30pm on Tue Nov 14.
Consists of the exercises 8.1-8.7 in the lecture notes. 

Lecture 18 (Thu Nov 16)

Lecture 19 (Tue Nov 21)

Lecture 20 (Thu Nov 23)

Homework 7 is due: 11:30pm on Thu Nov 23.
Consists of the exercises 8.8-10.4 in the lecture notes.

Lecture 21 (Tue Nov 28)

Lecture 22 (Thu Nov 30)

Lecture 23 (Tue Dec 5)

Homework 8 is due: 11:30pm on Tue Dec 5. 
Consists of the exercises 11.1 - 16.1 in the lecture notes. 

All homework is to be submitted via Crowdmark



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).


For those who can't make it to class, e.g., because illness, here are the lecture videos and lecture notes from teaching this course in 2020

Notice that this course was taught in 2020 in the format of 3 lectures of 50min each per week. Our course in 2023 is taught in the format of 2 lectures of 75min per week, hence we cover in 24 long lectures what in 2020 was covered in 36 short lectures. So, roughly, lectures 1,2 this year are lectures 1,2,3 in 2020 and lectures 14,15 this year are lectures 21,22,23 in 2020 etc.  

Here are the recordings of the lectures of 2020:

Caution: Listed below are the lecture notes from 2020. The text and exercises have slightly changed since. This means that for the purposes you should not use the lecture notes below. For homework, therefore always use the Current Lecture Notes

Lecture 1, Video 1, Notes Ch.2.1-2.3.3   

Lecture 2, Video 2, Notes Ch.2.33-2.5

Lecture 3, Video 3, Notes Ch.3.1-3.2

Lecture 4, Video 4, Notes Ch.3.2

Lecture 5, Video 5, Notes 3.4-3.4.4  

Lecture 6, Video 6, Ch.3.4.5

Lecture 7, Video 7, Ch.3.4.6-3.6

Lecture 8, Video 8, Lecture notes so far

Lecture 9, Video 9, Lecture notes so far

Lecture 10, Video 10, Lecture notes so far

Lecture 11, Video 11, Lecture notes so far

Lecture 12, Video 12, Lecture notes so far

Lecture 13, Video 13, Lecture notes so far

Lecture 14, Video 14, Lecture notes so far

Lecture 15, Video 15, Lecture notes so far

Lecture 16, Video 16, Lecture notes so far

Lecture 17, Video 17, Lecture notes so far

Lecture 18, Video 18, Lecture notes so far

Lecture 19, Video 19, Lecture notes so far

Lecture 20, Video 20, Lecture notes so far

Lecture 21, Video 21, Lecture notes so far

Lecture 22, Video 22, Lecture notes so far

Lecture 23, Video 23, Lecture notes so far

Lecture 24, Video 24, Lecture notes so far

Lecture 25, Video 25, Lecture notes so far

Lecture 26, Video 26, Lecture notes so far  

Lecture 27, Video 27, Lecture notes so far

Lecture 28, Video 28, Lecture notes so far

Lecture 29, Video 29, Lecture notes so far

Lecture 30, Video 30, Lecture notes so far

Lecture 31, Video 31, Lecture notes so far

Lecture 32, Video 32, Lecture notes so far

Lecture 33, Video 33, Lecture notes so far

Lecture 34, Video 34, Lecture notes so far

Lecture 35, Video 35Lecture notes so far

Lecture 36, Video 36, Full lecture notes


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 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! Show that you are thinking for yourself.