Introduction to Group Theory with Applications in Molecular and Solid State Physics Karsten Horn Fritz-Haber-Institut der Max-Planck-Gesellschaft  030 8412 3100, e-mail horn@fhi-berlin.mpg.de Symmetry - old concept, already known to Greek natural philosophy Group theory: mathematical theory, developed in 19th century Application to physics in the 1920’s : Bethe 1929, Wigner 1931, Kohlrausch 1935 Why apply group theory in physics? “It is often hard or even impossible to obtain a solution to the Schrödinger equation - however, a large part of qualitative results can be obtained by group theory. Almost all the rules of spectroscopy follow from the symmetry of a problem ” E.Wigner, 1931 1. Symmetry elements and point groups 1.1. Symmetry elements and operations 1.2. Group concepts 1.3. Classification of point groups, including the Platonic Solids 1.4. Finding the point group that a molecule belongs to 2. Group representations 2.1. An intuitive approach 2.2. The great orthogonality theorem (GOT) 2.3. Theorems about irreducible representations 2.4. Basis functions 2.5. Relation between representation theory and quantum mechanics 2.6. Character tables and how to use them 2.7. Examples: symmetry of physical properties, tensor symmetries 3. Molecular Orbitals and Group Theory 3.1. Elementary representations of the full rotation group 3.2. Basics of MO theory 3.3. Projection and Transfer Operators 3.4. Symmetry of LCAO orbitals 3.5. Direct product groups, matrix elements, selection rules 3.6. Correlation diagrams 4. Vibrations in molecules 4.1. Number and symmetry of normal modes in molecules 4.2. Vibronic wave functions 4.3. IR and Raman selection rules 5. Electron bands in solids 5.1. Symmetry properties of solids 5.2. Wave functions of energy bands 5.3. The group of the wave vector 5.4. Band degeneracy, compatibility Outline If you come up with a symmetry- related problem from your own work, bring it in and we can discuss it (time permitting)