Quantum Dynamics
Module MA5004
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 workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 45 h | 5 CP |
Content, Learning Outcome and Preconditions
Content
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
approximations.
approximations.
Preconditions
MA1302 Introduction to Numerical Analysis
MA3001 Functional 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.
Media
blackboard lecture, numerical demonstrations, exercises
Literature
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
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.