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Quantum Dynamics

Module MA5004

This Module is offered by TUM Department of Mathematics.

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

MA5004 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from WS 2016/7 to SS 2017.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


time-evolution of quantum systems (Schrödinger and Heisenberg picture), exponentiation of self-adjoint linear operators and polynomial approximations of the matrix exponential, Ehrenfest's theorem, Egorov's theorem and linearized initial value representations

Learning Outcome

At the end of module the students have mathematical understanding of basic techniques for analysing quantum dynamical systems.They can apply these techniques to concrete model systems and have programming skills for simple numerical


MA1302 Introduction to Numerical Analysis
MA3001 Functional Analysis

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

The module consists of the lecture supplemented by an exercise session. The lecture material is presented on the blackboard and by video projection. The students are encouraged to study course references and course subjects. The exercise session consists of theoretical and numerical programming exercises. The exercises contribute to a better understanding of the lecture materials.


blackboard lecture, numerical demonstrations, exercises


B. Hall, Quantum Theory for Mathematicians, Springer, 2013;
C. Lubich, From Quantum to Classical Molecular Dynamics, Reduced Models and Numerical Analysis, EMS, 2008;
B. Thaller, Visual Quantum Mechanics, Springer, 2000

Module Exam

Description of exams and course work

The examination is a 60 minutes' written test without any auxiliary resources. The students are asked to explain basic mathematical properties of quantum dynamical systems. They demonstrate their ability for applying theoretical concepts to concrete model systems. They can read, understand, and write short numerical programmes for simple quantum dynamical approximation schemes.

Exam Repetition

The exam may be repeated at the end of the semester.

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