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Mathematical Quantum Mechanics (WiSe 26/27)

Lecturers: A. Triay (Mathematics), L. Müller (Physics)
Tutorials and exercises: A. Ramer dos Santos
Registration via Moodle (registration code: mqm) and LSF.

Description:

This course is a rigorous introduction to the (some) mathematics of quantum mechanics and in particular to operator theory. We will discuss the theory of unbounded operators and their self-adjoint extensions, the spectral theorem, Sobolev embeddings, Weyl theory, quantum dynamics, semi-classical analysis, quantum entropy, C* algebra (finite and infinite dimensional). No prior knowledge in Physics is required.


Credits:
9 (6+3) ECTS.

Audience:

Master students of Mathematics and Physics, TMP-Master. Bachelor students will get "Schein" when they pass the course.

Schedule:

- Lectures: Tuesday 14:15-15:45 and Friday 10:15-11:45, Room: B006
- Tutorium: Wednesday 14:15-15:45, and Exercises: Thursday 08:15-09:45, Room B005
- First lecture Tuesday 13 October, First execise session and tutorial Wednesday 21 and Thursday 23 October.

References:
  • P.T. Nam and A. Scrinzi, lecture notes
  • M, Lewin (2022). Spectral Theory and Quantum Mechanics Link 1, Link 2 (french)
  • S. J. Gustafson and I. M. Sigal, Mathematical Concepts of Quantum Mechanics, 2nd Ed., Springer, 2011.
  • G. Teschl, Mathematical methods in quantum mechanics, AMS 2009.
  • Reed and Simon, Methods of modern mathematical physics, Volume I-IV.
  • Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext 2011
  • Lieb-Loss: Analysis, Amer. Math. Soc. 2001.
  • E. H. Lieb and R. Seiringer, The stability of matter in quantum mechanics, Cambridge University Press, 2009.