Lectures
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Symmetries and the many-body problemRWTH Aachen & GRS Symmetries reveal essential properties of phyiscal systems. This lecture will cover the basics of group theory and some of its application to the central problem of solid-state physics, the many-electron problem. 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
- introduction to group theory
- representation theory
- symmetries and conservation laws
- symmetries and degeneracies
- Lie algebra
- the hydrogen atom and its hidden symmetry
- from atoms to solid-state systems
- double groups, spinors and spinor representations
- band topology
- time-reversal and Kramers degeneracy
- the N-electron problem and the symmetric group
- many-electron states and multiplets
- tensor opertators and the Wigner-Eckart theorem
LECTURE MATERIAL
- Intro Hydrogen Atom slides (by J. Musshoff)
- How to plot spherical harmonics (by J. Musshoff) slides
- Lecture 17.10.2017 slides TOPIC: basics of group theory exercises
- Lecture 24.10.2017 EXERCISES
- Lecture 7.11.2017 slides TOPIC: representation theory exercises
- Lecture 14.11.2017 slides TOPIC: orthogonality theorems
- Lecture 21.11.2017 EXERCISES
- Lecture 28.11.2017 slides TOPIC: classification of groups, energy levels, hidden symmetry H atom exercises
- Lecture 5.12.2017 slides TOPIC:point symmmetry reduction, double groups, spinor representations, Bloch theorem, band topology
- Lecture 12.12.2017 EXERCISES
- Lecture 19.12.2017 slides TOPIC: time reversal, Kramers theorem, Dirac cones exercises
- Lecture 09.01.2018 slides TOPIC: perturbation theory, selection rules, irreducible tensors
- Lecture 16.01.2018 EXERCISES
- Lecture 23.01.2018 slides TOPIC: many-electron states
- Lecture 30.01.2018 slides TOPIC: many-electron states, magnetic groups, summary