Fortgeschrittene mathematische Quantenmechanik (MQM2) - Summer term 2013 (SoSe 2013)

Thomas Østergaard Sørensen

Information on Final Exam: See below

Content of lecture

Time and place:

Lectures (Prof. Sørensen):

Tuesday 10:15--12:00, Room B 132.
Thursday 12:15-14:00, Room B 132.

Homework sessions ("Übungen") (Dr. Sergey Morozov):

Wednesday 16:15--18:00, B 132.
(Solutions to the Homework Sheets will be presented here.)

SPECIAL: WEDNESDAY APRIL 17th: EXERCISES (exercises in class, repetition things from MQM1 etc etc)

Additional Homework sessions ("Zusätzliche Übungen") (Dr. Sergey Morozov):

Wednesday 18:15--19:00.
(Further discussion of homework solutions and the content of the course)

Exercise sessions ("Zusätzliche Übungen") (Dr. Sergey Morozov):

Monday 14:15--16:00, Room B 134. (Starts April 22th.)
(Extra exercises, done partly in class; discussion of things from lecture etc.)

(For organisation and programme for the Homework and Exercise Sessions, see the link above.)

To participate, you need to sign up here.

Office hours:
Thomas Østergaard Sørensen (Room B 408): Thursday, 10:15--11:00.
Sergey Morozov (Room B 404): Monday, 16:15-17:00.

General information for the course:


This course is the continuation of the course Mathematical Quantum Mechanics (MathQM I) in WS12/13, but it is open to students who did not take the first course. The course will introduce the mathematics needed to formulate and study many-body quantum physics. The goal is by the end of the course to be able to describe the basic structures believed to be responsible for superfluidity and superconductivity. The course will introduce the tensor product of Hilbert spaces, in particular, the antisymmetric and symmetric tensor products that correspond respectively to fermionic and bosonic quantum particles. This will lead to the introduction of Fock spaces and the method of second quantization. We will discuss properties of states on Fock spaces, in particular the notion of off-diagonal long range order. By restriction to particular states we will introduce the fermionic theories of Hartree-Fock and Bardeen-Cooper-Schrieffer (relevant for superconductivity) and for bosons the theory of Bogolubov (relevant for superfluidity). These theories are all non-linear variational theories. The main prerequisites are a good knowledge of measure theory, Hilbert spaces and their bounded operators. No knowledge of the spectral theorem will be expected. The presentation will focus on both analytic and algebraic aspects of the theory.


TMP Master Students. Students of Mathematik/Physik/Lehramt.


Analysis, Linear Algebra, Functional Analysis, MathQM I.

Requirement for passing the course:

The course ends with an oral final exam (time and place: to be announced; more details on material and form later).

There will be weekly Homework Sheets that can be handed in for marking (in the designated box near the library on the first floor; see more information below). NO LATE HOMEWORK WILL BE MARKED. No credits will be given for the Homework, but we may ask you questions about the Homework at the exam.

Final Exam:

Time: Monday July 22th, 2013 from 09:00.
Place: B 408 (Office Sørensen)

Form: Oral exam, 30 min.

To sign up/Anmeldung:
Please send an email to Sergey Morozov at the latest Wednesday July 17, 12:00 to sign up for the exam.
Please make sure you are also registered in Lecture Assistant so that we have your data.
Your exam time will be assigned in the Homework Session on Wednesday July 17th.
NB Should you, after having signed up, change your mind, and not want to take the exam after all, then please be so kind as to let Sergey know by email before Monday July 22th, 09:00.

Everything from the Lectures (including results of all problems) up to and including the Lecture on July 11th (that is, the whole Lecture Notes except Appendices B, C, and G).
Homework solutions up until and including the last one.
Excluded: The material only discussed at the Exercise Sessions.

Only offered to the students taking the (first) exam and not passing.


Homework Sheets:

Will be posted on the web every Wednesday by 20:30 (8:30pm) on the exercise homepage.
Solutions are due the following Wednesday at 16:00 (4:00pm) (sharp!) in the designated box.
Suggestions for solutions will be presented in the Homework Sessions the week after (Wednesday). Here you can also collect your marked homework.

First sheet will be posted on April 17th.

Exercise Sheets:

Will be posted on the web every Thursday by 20:30 (8:30pm) on the exercise homepage.

First sheet will be posted on April 16th.


The lectures, the webpage and our main literature are in English. The purpose is double: to strengthen the English knowledge of the German students and to make the lectures accessible to non-German Master students (TMP). The Homework and Exercise Sessions are also held in English, by default. However, Dr. Morozov and Prof. Sørensen are ready to switch to German in private discussions. If you feel that your English is not strong enough to ask questions, please do it in German. The questions on the Homework Sheets will be in English (!!), but the solutions can be turned in either in German or in English.


We will use lecture notes by J.P.Solovej:

  • J. P. Solovej, Many Body Quantum Mechanics, August 30, 2009.

  • Corrections are welcome! (A version with list of corrections will appear here at some point).

    More literature may be needed towards the end of the course. Information will appear here in due time.

    The brief contents of the lectures will keep you updated, here you will find the more precise references of what is done in lecture.

    Last update: July 10th, 2013 by Thomas Østergaard Sørensen.