Lectures
WS 16/17 | ||
Group Theory in Solid State Physics RWTH Aachen & GRS Every process in physics is governed by selection rules that are consequences of symmetry requirements. It is hard to imagine that much progress could have been made in deducing the laws of nature or tackle the many-body problem without the existence of certain symmetries. Group Theory is the mathematical tool to deal with them. This lecture will cover the basics of group theory and the most relevant applications in condensed matter theory. Admission: Literature: M.S. Dresselhaus, G.Dresselhaus, A.Jorio, Group Theory - Application to the Physics of Condensed Matter M. Tinkham Group Theory and Quantum Mechanics E. Pavarini, in the Lecture Notes of the Autumn School on Correlated Electrons: from Models to Materials download |
LECTURE CONTENT
- solid state physics as many-body problem
- symmetries in physics and conservation laws
- basics of abstract group theory
- representatiions and characters
- orthogonality theorems
- symmetries and operators
- the hydrogen atom; orbitals, symmetries, and hidden symmetry
- molecular orbitals
- molecular vibrations
- equivalence representation
- crystal-field
- the Jahn-Teller theorem
- from molecules to solids: translational invariance
- the Bloch theorem from group theory
- symmetries in the tight-binding approach
- how to construct a band structure from symmetries alone
- double groups
- Kramers theorem and time reversal symmetry
- magnetic groups
- many-electron states, statistic and symmetries
- atomic multi-electron states and multiplets
- symmetry and strong correlation effects
- chirality
- topological effects
- broken symmetry and Goldstone modes
LECTURE MATERIAL
- Lecture 18.10.2016 slides
- Lecture 18.10.2015 exercises
- Lecture 28.10.2015 Hydrogen Atom slides (by J. Musshoff)
- How to plot spherical harmonics (by J. Musshoff) slides