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Mathematical Quantum Mechanics II (SoSe 24)
Lecturers: A. Triay, Exercises: P. MadsenRegistration via Moodle (registration code: mqm24)
Description:
The goal of this lecture is to give an overview of a selected topics in mathematical quantum mechanics closely related to current research. A primary focus will be given on many-body quantum mechanics, the study of effective theories and their derivations.
This is an advanced course.
A strong background in analysis is assumed (PDE, Distribution and Sobolev spaces, functional analysis, spectral theory).
It is not necessary to have taken the course MQM I to follow MQM II (but it is a plus, for more info check Prof. Nam' lecture notes.)
Credits:
9 (6+3) ECTS.Content:
(tentative planning)We will follow partly Prof Nam's lecture notes from 2020.
In the best of worlds, we will cover
- Principles of Quantum Mechanics, Many-body Schrödinger operator, particle statistics
- Bosons: Hartree and Bogoliubov theory, Fock space, mean-field approximation
- Fermions: Hartree-Fock approximation, Lieb-Thirring inequalities, semi-classical limit
- Positive temperature, statistics
- Non-relativistic quantum mechanics: Dirac operators
Audience:
Master students of Mathematics and Physics, TMP-Master. Bachelor students will get "Schein" when they pass the course.Schedule:
- Lectures: Monday 14:15-15:45 B006 and Thursday 16:15-17:45 Room B046
- Exercises: Friday 10:15-11:45 Room B004
First week: the lectures will take place on Thursday 18 April and Friday 19 April and there will be no exercise session. The first exercise session will be on Friday 26 April.
References:
Primary:- Prof. Nam's lecture notes of MQMII
- J.P. Solovej, Many-body quantum mechanics, Lecture notes 2014.
- E. H. Lieb and R. Seiringer, The stability of matter in quantum mechanics, Cambridge University Press, 2009.
- M. Reed and B. Simon, Methods of modern mathematical physics, Volume I-IV.
- Prof. Nam's lecture notes of MQMI
- 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.
- E. H. Lieb, M. Loss, Analysis, Graduate studies in mathematics, AMS, 2001
- Haim Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext 2011