Mathematical Quantum Mechanics II (Summer 2026)
Phan Thành Nam, Dong Hao Ou Yang, Moodle (ID: 46600, pass: MQM2026).
General Information
Goal: We study the mathematical methods for large quantum systems. We will discuss microscopic theory (many-body quantum mechanics), macroscopic theories (effective equations), and the connection between them.In particular, we will focus on the Fermi gas, focusing on Pauli's exclusion principle, semiclassical analysis, Thomas-Fermi approximation and Hartree-Fock approximation. Previous background in functional analysis, especially operator theory on Hilbert spaces, will be helpful but not mandatory.
Audience : TMP-Master, Master students of Mathematics and Physics. Bachelor students will get "Schein" if pass the course.
Time and place:
- Lectures: Tuesday 8:15-10:00 (B004) and Friday 8:15-10:00 (B004).
- Exercises: Friday 10:15-12:00 (B004).
- Tutorials: Wednesday 10:15-12:00 (B132).
References:
- Elliott H. Lieb and Robert Seiringer. The Stability of Matter in Quantum Mechanics (Textbook 2010, Cambridge University Press)
- Jan Philip Solovej. Many-body quantum mechanics (Lecture notes 2014)
- Phan Thanh Nam. Functional Analysis II (Lecture notes Winter 2020-2021)
Exercises and Tutorials: There will be a homework sheet every week, which will be discussed in the exercise sessions. The tutorial sessions help to review the lectures and complementary materials.
Exams: There will be Midterm and Final exams.
Grade: Final grade is determined by your total performance:
- You can get up to 100 points in the final exam.
- You can get up to 10 points in the midterm exam.
- You can get 1 point for every homework sheet.