Mathematical Quantum Mechanics (Winter 2025-2026)

Phan Thành Nam (Math. Lecturer)
Robert Helling (Phys. Lecturer)
Alan Ramer dos Santos (Exercises)

Homework, Moodle (ID: 42326)

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Preparatory Course: October 6–10, 2025

Lectures: Every day, 10:15–12:00 (B047)

Exercises: Tuesday 16:15–18:00 (B047) and Friday 16:15–18:00 (B132)

Revision of mathematical background needed for Mathematical Quantum Mechanics

General Information

Goal: We study the fundamental mathematical concepts of quantum mechanics. In particular, we will discuss principles of quantum mechanics, self-adjoint operators, quadratic forms and Friedrichs extension, spectral theorems, Schrödinger operators, quantum dynamics, scattering theory, semiclassical analysis, and quantum entropy.

Audience : TMP-Master, Master students of Mathematics and Physics. Bachelor students will get "Schein" if pass the course.

Time and place:

• Lectures: Wednesday 8:15-10:00 (B005) and Friday 10:15-12:00 (B005).
• Exercises: Tuesday 14:15-16:00 (B006).
• Tutorials: Friday 16:15-18:00 (A027).

References:

• P.T. Nam and A. Scrinzi. Mathematical Quantum Mechanics (Lecture notes Winter 2018-2019)
• G. Teschl, Mathematical methods in quantum mechanics, AMS 2009.
• E. Lieb and M. Loss, Analysis, Amer. Math. Soc. 2001.

Exercises and Tutorials: There will be a homework sheet every week, which will be discussed in the exercise session. The tutorial sessions help to review the lectures and complementary materials.

Exams: There are written midterm and final exams. You can bring your notes (lecture notes, homework sheets and tutorial materials). Electronic devices are not allowed.

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.
  

You need 50 points to pass the course and 85 points to get the final grade 1.0.

Contents of the lectures

15.10.2025. Introduction.