Mathematical Quantum Mechanics 2

Module PH7007

This module is offered by Ludwig-Maximilians University Munich (LMU). It is available for TUM students only within a joint degree program (e. g. M. Sc. Quantum Science & Technology).

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH7007 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload	Contact hours	Credits (ECTS)
270 h	h	9 CP

Responsible coordinator of the module PH7007 is Christian Hainzl.

Content, Learning Outcome and Preconditions

Content

This module offers an overview on advanced chapters of mathematical quantum mechanics. We start with many-body Coulomb systems, and prove the HVZ theorem and stability of matter. Then we consider semi-classical approximations, in particular Thomas-Fermi Theory and Hartree-Fock-approximation to many body ground states. Next, we consider many-body Bose and Fermi-gases and discuss Bogoliubov’s approach to Bose-Einstein (BEC) condenstation. As well we give a proof of BEC in interacting systems. At the end, we discuss Fermi-gases including aspects of superconductivity. The main goal of this module is to offer an overview of the most successful current research directions for quantum problems that can be tackled by rigorous mathematical methods.

Learning Outcome

Students become familiar with advanced methods of mathematical quantum mechanics. They are able to understand analytic methods and apply those to quantum mechanical questions.

Preconditions

No prerequisites in addition to the requirements for the Master’s program in Quantum Science and Technology. Familiarity with mathematical quantum mechanics 1 is assumed.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

SS 2021

Type	SWS	Title	Lecturer(s)	Dates	Links
VO	4.0	Mathematische Quantenmechanik II	Hainzl, C.	see LSF at LMU Munich	current
UE	2.0	Übungen zu Mathematische Quantenmechanik II	Hainzl, C. Giacomelli, E.	see LSF at LMU Munich	current

Learning and Teaching Methods

The module consists of a lecture series (4 SWS) and exercise classes (2 SWS), comprising two lecture sessions and one exercise session per week.

The main teaching material is presented on the blackboard. Lectures are supplemented by weekly problem sets, deepening the understanding of core concepts through concrete calculations. Solutions to the problem sets are discussed in the exercise sessions.

Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core tools of condensed matter many-body physics and field theory and for practicing to solve typical exam problems.

Media

Blackboard presentations, slides.

Literature

Standard textbooks on many-body theory, e.g.:

• Elliott Lieb und Michael Loss “Analysis”

• Gerald Teschl “Mathematical Methods in Quantum Mechanics”

• Lecture-notes for different subjects will be provided during the course

Module Exam

Description of exams and course work

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.

For example an assignment in the exam might be:

Show that a Schrödinger Hamiltonian where the potential has some given decay properties has an infinite number of bound states
Show that the atomic Thomas-Fermi-Energy converges to the true ground state energy in the limit of large nuclear charge