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 |
! Lectures for physicists start again on the 10 of January !
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 18.10.2016 exercises
- Lecture 28.10.2016 Hydrogen Atom slides (by J. Musshoff)
- How to plot spherical harmonics (by J. Musshoff) slides
- Lecture 25.10.2016 slides
- Lecture 25.10.2016 exercises
- Lecture 8.11.2016 slides
- Lecture 8.11.2016 exercises
- Lecture 15.11.2016 slides
- Lecture 15.11.2016 exercises
- Lecture 22.11.2016 slides
- Lecture 22.11.2016 exercises
- Lecture 29.11.2016 slides
- Lecture 29.11.2016 exercises
- Lecture 8.12.2016 exercises
- Lecture 13.12.2016 slides
- Lecture 13.12.2016 exercises
- Lecture 20.12.2016 slides
- Lecture 20.12.2016 Summary of the first part and exam discussion
- Lecture 10.01.2017 slides
- Lecture 10.01.2017 slides
- Lecture 17.01.2017 slides
- Lecture 17.01.2017 slides
- Lecture 24.01.2017 slides
- Lecture 31.01.2017 slides
- Lecture 31.01.2017 original article of Jahn and Teller
- Lecture 7.01.2017 Summary of Lecture and discussion