Advanced Quantum Theory, AMATH 473/673, PHYS454 in Fall 2024

  • Term: Fall 2024
  • Course codes:ÌýAMATH 473/673,ÌýPHYS454
  • Instructor: Achim Kempf
  • Teaching Assistants:ÌýBoris Ragula,ÌýAdam Teixido-Bonfill
  • Prerequisite: AMATH 373 or PHYS 334, or consent of instructor.
  • Lecture times and location:ÌýTue+Thu 2:30-3:50pm. Room: AL-211
    First lecture:ÌýThuÌýSep 5. Caution: See revised Schedule below!
    Reading week: no lectures on TueÌýOct 15Ìýand Thu Oct 17.
    Last lecture: TueÌýDec 3
  • Office hours with Prof: Thursdays 4:00-6:00pm
  • Office hours with aÌýTA:ÌýTuesdays 4:00-5:00pm in MC6334, starting SepÌý17
  • Tutorials with aÌýTA:Ìý Thursdays, 11:30am-12:20pm in E2-1732, starting Sep 19
  • Homework:ÌýviaÌýCrowdmark
  • Midterm exam:ÌýThursday Nov 7,Ìý11:30am-12:20pm in RCH301
  • Final exam:ÌýÌýFriday, Dec. 13, 12:30-3pm, room MC1085
  • Grades (undergraduate): Homework 10%, Midterm 30%, Final 60%.Ìý
  • Grades (graduate): Essay (see below) 1/3, remaining 2/3 as for undergraduate students.
  • Graduate students (those who enroled in AMATH673):
    Ìý
    • Homework, midterm and final will be the same as for undergraduate students.
    • Plus, graduate students are to hand in an approximately 10 page essay byÌý11:59pm on December 21st.
    • The topic of the essay is: The Berry Phase
    • 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 onÌý .ÌýÌýÌý
  • HealthÌýprecautions (permanent):ÌýIf youÌýhave cold/flu/covidÌýsymptoms, do not come to class. Do the right thing, which is taking care of yourself and getting healthy first.ÌýFor Lecture Videos (of my previous teaching), scroll downÌýto the bottom of this page..In any case, all important updates willÌýalways be postedÌýhere.
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Lecture Notes

Here are the Lecture Notes.
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  • Chapter 1 is a historical introduction which is not covered in the lectures and willÌýnot be examined. It is assigned reading.
  • The lecture notes will beÌýupdated continually. Some updates are mere corrections of typos but corrections can also affectÌýassignments.Ìý
  • Therefore, bestÌýreload the lecture notes regularly, especially before doing homework.
  • Caution: at the bottom of this page, you can find the video recordings of a prior teaching of this course, along with the lecture notes, as they were at the time. Since the homework in the lecture notes hasÌýslightly changed since then, do not use these old lecture as a source of the homework assignments.ÌýÌý
    Ìý

Schedule

With the instructor stuck in Europe at the beginning, the first 5 lectures of the course will be on video, plus Q&A with instructor via zoom.

Make sure to view the lectures in time, i.e., by 4pm on the day in question. Then:

Tuesdays: from 5pm, there will be live Q&A with the instructor via Zoom.

Thursdays: from 4pm, there will be live Q&A with the instructor via Zoom.Ìý

The videos are from a previous teaching of the course in 36 short lectures i.e., in the format of three lectures weekly. Since our course is taught in the format twice weekly, each of our 24 lectures is 1.5 videos long.

The videos are sometimes a bit longer than 50min. They cover the regular material of this course, though at times a bit slower and/or in more detail. Ìý

Lecture 1 (Thu Sep 5): view all of , and the first half of by 4pm. From 4pm, Q&A via .

Lecture 2 (Tue Sep 10): view second half of , and all of by 4pm. From 5pm, Q&A via .

Lecture 3 (Thu Sep 12): view all of , and the first half of by 4pm. From 4pm, Q&A via .

Lecture 4 (Tue Sep 17): view second half of , and all of Ìýby 4pm. From 5pm, Q&A via .

Homework 1 isÌýdue: 5:30pm on Tue Sep 17.
ConsistsÌýof all the exercises in Ch.2 of the lecture notes.

Lecture 5 (Thu Sep 19): view all of , and the first half of by 4pm. From 4pm, Q&A via .

Lecture 6 (Tue Sep 24): From today, in person in room AL-211, as originally scheduled.

Homework 2 is due: 11:30pm on TueÌýSep 24.Ìý
Consists of the exercises 3.1-3.14, in the lecture notes.

Lecture 7 (Thu Sep 26)

Lecture 8 (Tue Oct 1)

Homework 3 is due: 11:30pm on Tue Oct 1.
Consists of the exercises 3.15-3.23 in the lecture notes.

Lecture 9 (Thu Oct 3)

Lecture 10 (Tue Oct 8)

Lecture 11 (Thu Oct 10)

Tue 15: no class b/c reading week

Thu 17: no class b/c reading week

Homework 4 is due: 11:30pm on Fri Oct 18.
Consists of the exercises 3.24-5.1 in the lecture notes.

Lecture 12 (Tue Oct 22)

Lecture 13 (Thu Oct 24)

Lecture 14 (Tue Oct 29)

Homework 5 is due: 12:30am on Wed Oct 30.
Consists of the exercises 5.2-7.2 in the lecture notes.Ìý

Lecture 15 (Thu Oct 31)

Lecture 16 (Tue Nov 5)

*** Midterm on Thursday Nov 7,Ìý11:30am-12:20pm in RCH301 (new location!)Ìý***

Lecture 17 (Thu Nov 7)

Homework 6Ìýis due: 11:30pm on Thu Nov 7.
Consists of the exercises 8.1-8.7Ìýin the lecture notes.Ìý

Lecture 18 (Tue Nov 12)

Lecture 19 (Thu Nov 14)

Lecture 20 (Tue Nov 19)

Homework 7 is due: 11:30pm on Tue Nov 19.
Consists of the exercises 8.8-10.4 in the lecture notes.

Lecture 21 (Thu Nov 21)

Lecture 22 (Tue Nov 26)

Lecture 23 (Thu Nov 28)

Homework 8 is due: 11:30pm on Thu Nov 28.Ìý
Consists of theÌýexercises 11.1 - 16.1ÌýinÌýthe lecture notes.

Lecture 24 (Tue Dec 3)

Final exam:ÌýÌýFriday, Dec. 13, 12:30-3pm, room MC1085

All homework is to be submitted via Crowdmark.Ìý


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Content

The aim of AMATH 473 / PHYS 454 is to give a deep 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).

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For those who can't make it to class, e.g., because illness, the lecture videos andÌýlecture notes from a prior teaching of this course, in 2020, can be found here:ÌýÌý

Notice that this course was previously taught (inÌý2020) in the format of 3 lectures ofÌý50min each per week. Our course in 2024 is taught in the format of 2 lectures of 75min per week, hence we will cover in 24 long lectures what in 2020 was covered in 36 short lectures. So, roughly, lectures 1,2 this year areÌýlectures 1,2,3 in 2020 and lectures 14,15Ìýthis year areÌýlecturesÌý21,22,23 in 2020 etc.ÌýÌý

Caution: Listed below are the lecture notes from 2020. The text and exercises have changed somewhat since. This means that for the purpose of finding the homework assignment you cannot use the lecture notes below. For homework, thereforeÌýalways use the current lecture notes listed above.ÌýÌý
Ìý

Here are the recordings and lecture notes of theÌýlectures of 2020:


Lecture 1, , Notes Ch.2.1-2.3.3 ÌýÌý

Lecture 2,Ìý, Notes Ch.2.33-2.5

Lecture 3, , Notes Ch.3.1-3.2

Lecture 4, , Notes Ch.3.2

Lecture 5, , Notes 3.4-3.4.4 Ìý

Lecture 6, , Ch.3.4.5

Lecture 7, , Ch.3.4.6-3.6

Lecture 8, , Lecture notes so far

Lecture 9, , Lecture notes so far

Lecture 10, , Lecture notes so far

Lecture 11, , Lecture notes so far

Lecture 12,Ìý, Lecture notes so far

Lecture 13,Ìý, Lecture notes so far

Lecture 14, , Lecture notes so far

Lecture 15, , Lecture notes so far

Lecture 16, , Lecture notes so far

Lecture 17, , Lecture notes so far

Lecture 18, , Lecture notes so far

Lecture 19, , Lecture notes so far

Lecture 20, , Lecture notes so far

Lecture 21, , Lecture notes so far

Lecture 22, , Lecture notes so far

Lecture 23, , Lecture notes so far

Lecture 24, , Lecture notes so far

Lecture 25, , Lecture notes so far

Lecture 26, , Lecture notes so far Ìý

Lecture 27, , Lecture notes so far

Lecture 28, , Lecture notes so far

Lecture 29, , Lecture notes so far

Lecture 30, , Lecture notes so far

Lecture 31, , Lecture notes so far

Lecture 32, , Lecture notes so far

Lecture 33, , Lecture notes so far

Lecture 34, , Lecture notes so far

Lecture 35,Ìý,ÌýLecture notes so far

Lecture 36, , Full lecture notes

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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 mostÌý10 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 "" 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.Ìý

  • 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.