After successful completion of the course, students are able to explain basic and advanced concepts from the listed areas of group and representation theory. They can apply methods from group theory to specific problems in abstract group theory and quantum mechanics, and develop appropriate strategies for solving them. Furthermore, they are able to use problem-solving techniques to systematically approach other advanced physical problems.
This exercise is methodically complemented by the lecture Gruppentheorie.
Skills
Knowledge
Upon completing the course, students learn the following skills. They are able to
explain physical problems and concepts as well as mathematical solutions (k2);
work out mathematical solutions to physical problems in the area of group theory and its applications independently or in a group (k3);
transfer concepts and solution approaches to new and unknown problems, and select and apply suitable mathematical methods (k3/k4);
present their solutions to the group and discuss different approaches (k3/k4).
During the course, students acquire knowledge in the following areas and concepts of group and representation theory, including applications in modern quantum mechanics, solid state and molecular physics:
symmetries as linear mappings on vector spaces;
groups; equivalence classes;
reducible and irreducible representations;
fundamental theorems of representation theory;
characters;
reduction of reducible representations;
3D rotation group;
selection rules in quantum mechanics;
point symmetries;
examples from molecular/solid state physics.
Criteria for evaluation
short written tests, number and quality of successfully solved problems Details will be announced at the beginning of the semester.
Methods
solving the exercise problems as homework or during the exercise sessions, as well as discussing the course content and solutions in class
Language
German
Study material
will be announced in the course
Changing subject?
No
Further information
course language may be changed to english if requested
