Topics in Mathematical Physics
Winter Term 2025/2026

🇩🇪 German version

(If not up to date here, try looking at the german version)
Lecturer:   Chiara Saffirio
Assistant:   Eric TrĂ©buchon

Lecture Times:
The lecture will take place in person.

Day Time Room
Monday 12:00–14:00 SR 404 (Ernst-Zermelo-StraĂźe 1)
Course Structure
2-hour exercise sessions and weekly exercise sheets. Please submit your solutions in Box 3.31 in the basement of the Mathematical Institute.

Exercise Sheets:
  • Sheet 1 (due Monday, Oct 27, 2025)
  • Sheet 2 (due Monday, Nov 03, 2025)
  • Sheet 3 (due Monday, Nov 10, 2025)
  • Sheet 4 (due Monday, Nov 17, 2025, Updated on 7 Nov)
  • Sheet 5 (due Monday, Nov 24, 2025, Updated on 17 Nov)
  • Sheet 6 (due Monday, Dec 01, 2025)

Each week, a new exercise sheet will be handed out on Monday, and the previous one must be submitted by Monday 14:30. On Wednesday the exercises will be discussed.

Schedule Overview:
Date Event
Mon, 24.11. Submission Sheet 5 & Distribution Sheet 6
Wed, 26.11. Exercise Session Sheet 5
Mon, 01.12. Submission Sheet 6 & Distribution Sheet 7
Wed, 03.12. Exercise Session Sheet 6

Exercise Groups:

Time Tutor Room Contact
Wednesday 10:15–11:45 Phillip Pflaum SR414 (Ernst-Zermelo-Str. 1)

The exercise sessions will be held in person.

Script and Literature

Lecture notes found here: Lecture notes

Further literature:

  • Brian C. Hall: Quantum Theory for Mathematicians, Graduate Texts in Mathematics

Course Content

This course provides an introduction to analytical methods in Mathematical Physics, with a particular focus on the quantum mechanics of many-body systems. The central topic is the rigorous proof of the stability of matter for Coulomb systems such as atoms and molecules. The main question — why macroscopic objects composed of charged particles do not collapse under electromagnetic forces — remained unsolved in classical physics and even in early quantum mechanics. Remarkably, the proof of the stability of matter was the first example of mathematics providing a definitive answer to a fundamental physical question, and an early significant success of quantum mechanics.

Topics include:

  • Mathematical foundations: $L^p$ and Sobolev spaces; Fourier transform
  • Introduction to quantum mechanics and prototype examples
  • Quantum mechanics of many-body systems
  • Hamiltonian operator and its properties; Lieb–Thirring inequalities, electrostatic inequalities, Coulomb energy
  • Proof of the stability of matter

Remarks

Questions about the lecture can be asked in German or English.

Requirements for course and examination credits are described in the current module handbook supplements, which will be published as part of the annotated course catalogue by the end of October 2025.

Course and Examination Requirements

Course Credit:
Participation in the exercise sessions and at least 50% of the points.

Exam:
Oral examination at the end of the semester. Please contact the lecturer by email to schedule a date.

Prerequisites

Analysis III and Linear Algebra.
No prior knowledge of physics is required; all relevant physical concepts will be introduced in the course.

Applicability

Wahlmodul im Optionsbereich (2HfB21)
Wahlpflichtmodul Mathematik (BSc21)
Mathematische Ergänzung (MEd18)
Reine Mathematik (MSc14)
Mathematik (MSc14)
Vertiefungsmodul (MSc14)
Wahlmodul (MSc14)
Elective (MScData24)

The number of ECTS credits can be found in the supplements to the module handbooks.