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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.
Last update: T_KCHFO (11.02.2015)
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Introduction to basic approaches of the symmetry-based characterization of quantum systems. We show how to classify a physical problem with the help of symmetry analysis and supporting calculations based on the group and representation theory. It is then possible to separate independent degrees of freedom and then to consider only those processes which give nonzero response to an external perturbation. Last update: Ostatnický Tomáš, doc. RNDr., Ph.D. (15.05.2023)
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Written and oral exam. Last update: Ostatnický Tomáš, doc. RNDr., Ph.D. (15.05.2023)
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J. Fišer: Úvod do molekulové symetrie : aplikace teorie grup v chemii, SNTL Praha, 1980. Last update: Ostatnický Tomáš, doc. RNDr., Ph.D. (18.01.2016)
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The written part of the exam is a calculation of one of the typical problems solved during the lectures: crystal field splitting of atomic levels, MO-LCAO method, molecule vibrations, calculation of quantum-mechanical matrix elements. The oral part of the exam will be a theoretical question on one of the areas from the syllabus.
Last update: Ostatnický Tomáš, doc. RNDr., Ph.D. (15.05.2023)
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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. Last update: Ostatnický Tomáš, doc. RNDr., Ph.D. (15.05.2023)
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