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Lecturer(s)
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Nauš Jan, prof. RNDr. CSc.
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Course content
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Use of theory of symmetries in spectroscopies 1) Groups and their structures, conjugated elements and their classes, the first and the second theorem on isomorphism. 2) Linear representation of groups, reducible and irreducible representations, direct addition of representations, functions generated by representations, construction of representations, base of representation formed by vectors and wave functions, notations and properties of irreducible representations. 3) Character of representation, relation of orthogonality, tables of characters, analysis of reducible representations by characters, direct addition and direct product of representations. 4) General selection rules according to symmetry, allowed and banned transitions, degeneration of states, notation of states of molecules and orbitals, polarization of transitions. 5) Atomic and molecular orbitals from the viewpoint of symmetry, hybrid orbitals, symmetry of electron states of molecules. 6) Symmetry of normal vibrations, symmetrical selection rules in infrared and Raman spectroscopy. 7) Complexes of transition metals, theory of crystal field. 8) Orbital symmetry in reaction kinetics. 9) Relation between theory of special functions and theory of representations.
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Learning activities and teaching methods
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Lecture
- Homework for Teaching
- 40 hours per semester
- Preparation for the Exam
- 40 hours per semester
- Attendace
- 42 hours per semester
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Learning outcomes
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The goal of the course is to present a deeper theory of the symmetry effects in spectroscopies. The mathematical group theory is applied to orbitals and the selection rules. The course contains theory of symmetry, group theory and theory of representations, character of representations. Symmetry of molecules, complexes and biological objects is described. The orbitals are introduced based on symmetry. General selection rules are treated by symmetry. The states of atoms and molecules are designated using the symbols of irreducible representations. Polarization of energetic transitions, symmetry of normal vibrations. Crystal filed theory. Complexes of transition metals.
Comprehension Explain the essence of data and be able to interpret them, recognize and classify the given problem, predict the behaviour of the given phenomena.
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Prerequisites
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Basic course of mathematics and some parts of experimental methods of biophysics
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Assessment methods and criteria
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Student performance
Acquiring the theoretical derivation of the rules in application of theory of symetry in spectroscopies.
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Recommended literature
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J. Fišer. (1980). Úvod do molekulové symetrie (Aplikace teorie grup v chemii). SNTL, Praha.
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Litzman, O., Sekanina, M. (1982). Užití teorie grup ve fyzice. Academia, Praha.
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Malíšek, V. (1981). Úvod do optické spektroskopie. UP Olomouc.
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Peřinová, V. (1995). Úvod do teorie speciálních funkcí (část A a B). UP Olomouc.
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Štěpánek, J. (1992). Matematika pro přírodovědece. II. Grupy a tenzory. UK Praha.
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