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Mathematical Quantum Mechanics (WiSe 23/24)

Lecturers: Math: A. Triay, Phys: A. Scrinzi, Tutorials and exercises: E.L. Giacomelli
Registration via Moodle (registration code: mqm23)

Description:

In this course we present the basic and fundamental mathematical tools allowing to formulate and use quantum mechanics. In its early days, quantum mechanics have seen two mathematical apparatus competing to formalize it: Heisenberg's matrix mechanics and Schrödinger's wave mechanics. As we will see, these two pictures are in fact equivalent and can be unified using the tools of spectral theory, functional analysis, harmonic analysis, etc.

Content:

(might change during the lecture)

A detailed content of the lectures of a previous version of the course can be found in Prof. Nam's webpage.
In a nutshell:
  • Principles of Quantum Mechanics
  • Spectral theory (aka linear algebra in Hilbert spaces): (un)bounded / compact operators, spectrum in infinite dimension, self-adjoint extensions, spectral theorem, ...
  • Analysis: Lebesgue spaces, Sobolev spaces, Fourier transform, ...
  • Applications: Quantum dynamics, Bound states, Scattering theory, Many-Body systems, Positive temperature (entropy)

Audience:

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

Schedule:

- Lectures: Tuesday 16:15-17:45 and Friday 10:15-11:45, Room: B006
- Tutorium: Wednesday 08:30-10:00, and Exercises: Thursday 08:30-10:00, Room B006 (held by Dr. E.L. Giacomelli)
- First lecture Tuesday 17 October, First execise session and and tutorial Wednesday 25 and Thursday 26 October.

References:
  • Prof. Nam's lecture notes
  • M, Lewin (2022). Théorie spectrale et mécanique quantique (Vol. 87). Springer International Publishing. Link 1, Link 2
  • 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.