Syllabus
1. Role of the symmetry in physics, optical properties of atoms and molecules from the viewpoint of their symmetry.
2. Introduction to the group and representation theory. Stress on their use in the calculations with molecule symmetry. Conservation laws in quantum mechanics. Applications of the group theory on calculations of transition probabilities between two states under the effect of an external perturbation.
3. Selection rules for transitions between electron, vibration (absorption and Raman scattering) and rotation levels. Effect of external and crystal fields on atoms and ions.
4. Role of the spin, non-classical theory, double groups.
5. Symmetry in solid state. Electron spin, symmetry of wavefunctions. Symmetrization of wavefunctions of quasiparticles (excitons, biexcitons), effect of external perturbations on quasiparticles.
6. Construction of Hamiltonian from invariants.
7. Symmetry in magnetic field, magnetic groups.
Annotation
Interaction of electromagnetic radiation with atomic and molecular systems. Group theory and its application in optical spectroscopy of the electronic structure of matter, and vibrational and rotational spectra (splitting of degenerate states in external fields, selection rules).
Spatial symmetry in condensed matter and its implications for analysis of optical experiments.