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Lecture: Advanced Quantum Mechanics (MSc)

Lecturer: David Gross. Exercises: Johan Aberg. Time and venue: Mondays 10am, Tuesdays 8.15am, HS III.



Here are the final grades of the second exam.

We have the exam-exhibition on Friday (22nd) 11:00 - 12:00 in 0.03 in the New Theory Building.

The second exam takes place on September 18, in Hörsaal II, at 14:00 - 17:00.

Like for the first exam, we do not allow you to bring calculators, or any cheat-sheet. However, we will have an inbuilt cheat-sheet on the exam itself (like in the mock-exam).

It seems like the registration for the second exam is now open in Klips. Everyone who can register via Klips should do so. However, if you are a bachelor student, you should register via email to me. Also, if you are a master student and passed the first exam, but want to improve your grade, I believe that Klips will also not accept your registration.  If so, you should register to me via email. (I am not entirely sure what the rule is for when one can improve the grade, but if the first exam was the first time that you could possibly take it, then I believe that you should be fine.) Please include your matrikel number, and mention whether you are a bachelor student, grade-improving master student, or if there is some other reason that Klis don't accept you. Just so I can keep track of things. The deadline for registering via email is the same as for Klips.

Here are the final grades for the first exam.

Here are the preliminary grades for the first exam.

Apparently there has been some hickup with the homepage, so that the announcement about the exam exhibition disappeared at some point. (We had the exhibition today (Tuseday) 15-16.) Because of this homepage-mishap there is a new chance at this Wednesday (2/8) at 16:00-17:00 somewhere at the ground floor of the New Theory building. (It is too late to book a room now, but I believe that we will find some space to occupy.)


The first exam is on Monday 24th of July 13:00 - 16:00.

I believe Klips says that it takes place in both HSI and HSII, but we will most likely only need HSI. In any case, come to HSI, and in case of need we will re-direct you to HSII.

As for the rules of the game, we do not allow you to bring calculators, or any cheat-sheet. However, we will have an inbuilt cheat-sheet on the exam itself (like in the mock-exam).

Here is a mock-exam. I hope that it gives a reasonable feeling for how the real exams will look like.

Here is the list of admissions. In case you do not find yourself on it, although you believe that you should be on it, then send me (Johan Aberg) an email as soon as possible, including your name, matrikel number, and which group you belonged to. Please note that this list only includes admissions from this year. It does not include admissions that you may have got some previous year.


  • The lecture on Monday, the 12th of June will be online (pre-recorded videos).

Unfortunately, I have to attend an important and unmovable meeting on Monday from 10am. I have pre-recorded the material for Monday's lecture, and also updated the lecture notes. Videos:

  1. Light-matter coupling
  2. Computing coupling amplitudes
  3. Spontaneous emission

I know it's not ideal for your sleep budget that the Monday rather than the Tuesday lecture has been moved online, but that is beyond my power to influence. The three videos cover the remaining topics in the quantum theory of the EM field. I will briefly display the material during the Tuesday lecture and take questions.

Public service announcement: In case the EM field chapter confused you and you're a little bit behind, do come on Tuesday. We'll start by recapping special relativity in preparation for relativistic quantum mechanics - so there's a new chance to get back into the flow.


  • A Slack channel is being set up. You should be able to join with your Uni email.
  • The lecture is primarily meant to be attended in person. So while we will publish video recordings via the Uni's OpenCast system on the course's Ilias page, I won't put much effort into editing and cutting these videos.
  • Evolving lecture notes.

Course description

This lecture covers more advanced aspects of quantum mechanics. Topics include:

  • Multi-partite quantum systems
    • Mixed states and their danymics
    • Dynamics of coupled systems
    • Quantum many-body systems as computers
    • Bell inequalities and their implications
  • Indistinguishable particles
    • Bosonic and Fermionic Hilbert spaces
    • Second quantization
    • The Bose gas, superfluidity, and spontaneous symmetry breaking
  • Quantum theory of light
  • Relativistic quantum mechanics
  • Scattering theory

Exercise classes

The idea is that you should register for an exrcise class via Klips. It looks like Klips is open now for registrations.

If you can register via Klips. please do so. However, if you are a bachelor-student, I believe that you cannot register via klips. Klips might also refuse if you are not a physics-student. If so, write me (Johan Aberg) an email telling that you are a bachelor student (non-physics student), which class you want, and your matrikel-number, and I will add you manually (as long as there are places available).

The first exercise class is on Wednesday April 5. This is a somwhat less well-defined recap-class, since we would discuss solutions to the first sheet on Wednesday April 12.

The exercise classes all take place on Wednesdays.

Group When Where Tutor
1 08:00 - 09:30 Seminarraum Theorie 215 Maksimilian Usoltcev
2 10:00 - 11:30 Seminarraum Theorie 215 Blanca Hergueta
3 12:00 - 13:30 Seminarraum I Physik 223/224 Reza Doostani
4 14:00 - 15:30 Konferenzraum Theorie 216 Sangeet Srinivasan
5 16:00 - 17:30 Konferenzraum Theorie 216 Karim Chahine
6 14:00 - 15:30 Online (Link) Laurens Ligthart


Exercise Sheets

The exercises can be handed in by groups of at most three people.

The first exercise class is on Wednesday April 5. This is a somwhat less well-defined recap-class, since we would discuss solutions to the first sheet on Wednesday April 12.


  • Sheet 1 Due Sunday April 9, at 24:00
  • Sheet 2 Due Sunday April 16, at 24:00
  • Sheet 3 Due Sunday April 23, at 24:00. There were a couple of typos that now are updated. In the last line of 3e) `` |0>_spin-state whenever the particle is in path 1'' has now been corrected to ``|1>_spin-state whenever the particle is in path 1''. In 3f) HV_θ is now replaced by HU_θ.
  • Sheet 4 Due Sunday April 30, at 24:00
  • Sheet 5 Due Sunday May 7, at 24:00
  • Sheet 6 Due Sunday May 14, at 24:00
  • Sheet 7 Due Sunday May 21, at 24:00. There was a typo in problem 2g). There you should confirm three commutation relations. For the first of these it said [a_k,a_k'^{\dagger}] = 0, but it should be [a_k,a_k'] = 0. This is now corrected. Turned out to also be the more or less opposite typo in problem 1a). The last [a_k,a_k'] should be [a_k,a_k'^{\dagger}]. This is now also corrected.
  • Sheet 8 Due Sunday May 28, at 24:00. In equation (1), added a space between  a^{\dagger}_{-\vec{k}} and the comma, in order to avoid the risk that it is confused with a^{\dagger}_{-\vec{k}'}. Also, in 3b), in the column matrices, the N has been changed to K.
  • Sheet 9 Due Sunday June 11, at 24:00.
  • Sheet 10 Due Sunday June 18, at 24:00. In the hint to problem 1b) I had written a|\alpha> = \alpha>. I have now corrected it to  a|\alpha> = \alpha |\alpha>.
  • Sheet 11 Due Sunday June 25, at 24:00. In problem 2 f)  there was a \beta that should have been an \alpha, in the left hand side equation. This is now corrected.
  • Sheet12 Due Sunday July 2, at 24:00. In equation (4) in the gold star exercise, there was a factor 1/2 missing in the spatial derivaties. This is now corrected.
  • Sheet 13 (Last sheet) Due Sunday July 9, at 24:00.



For questions about the exercises, please contact: Johan Aberg.


For admission to the exam, one has to have gathered at lest 50% of the points from the exercise sheets.

Recommended reading

  • Sakurai: Modern Quantum Mechanics
  • Ballentine: Quantum Mechanics
  • Strocchi: Elements of Quantum Mechanics of Infinite Systems
  • Cohen-Tannoudji et al: Quantum Mechanics I & II
  • More will be added