Mathematical Quantum Theory
This course is offered by the Institute of Mathematics as a core course within the
Master Program in Mathematical Physics
Students enrolled in the regular mathematics or physics programs in Tübingen (or similarly prepared students) are also welcome!
Course goals.
This course presents the mathematical formalism that underlies quantum mechanics. Quantum mechanics describes most of the matter around us and is one of the most successful physical theories. This course teaches the mathematical framework from functional analysis and spectral theory that grounds quantum mechanics rigorously. A central role is played by the theory of unbounded operators on Hilbert spaces, especially the spectral theorem for unbounded, self-adjoint operators. Along the way, the derived results are used to make various physical concepts mathematically precise, e.g., wave functions, observables, Schrödinger operators, continuous vs. discrete spectrum, and quantum dynamics.
The course serves both as an advanced course in operator theory and as an introduction to mathematical physics.
Prerequisites.
A firm background in mathematical analysis is required. This includes working knowledge of measure theory (especially Lp spaces) and basic functional analysis (especially Hilbert spaces). Familiarity with tools from partial differential equations, in particular Sobolev spaces and the Fourier transform, is also useful.
Having previously taken a physics class on quantum mechanics is very helpful for understanding the motivations behind the results, but not strictly necessary.
Course syllabus
More information is available from the syllabus. (Last update: October 20, 2022)
Registration
If you are planning to take this course, please register on the following websites.
(1) The Tübingen-internal ILIAS course site will be the central hub for all course materials. To register at the beginning of lectures, log in to ILIAS, navigate to
Magazinand use the course password "mqt2022".
(2) The registration for exercise sessions and exams is handled via URM. Please use this link:
https://urm.math.uni-tuebingen.de/
If any questions persist, do not hesitate to email the instructor, Marius Lemm.