| Individual course details | ||||||||||
| Study programme | Theoretical and experimental physics | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | ||||||||||
| Name of the course | Symmetry in Physics | |||||||||
| Professor (lectures) | Ivanka Milošević, Milan Damnjanović, Tatjana Vukovic | |||||||||
| Professor/associate (examples/practical) | Marko Milivojević | |||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | 6 | Status (required/elective) | elective | |||||||
| Access requirements | Mathematical physic 1, Mathematical physic 2, Quantum mechanics 1, Quantum mechanics 2 | |||||||||
| Aims of the course | Enlightening of the fundamental and unifying role of symmetry in physics, with application of symmetry based techniques in analysis of physical problems. | |||||||||
| Learning outcomes | Adoption of the symmetry based techniques of solving dynamical problems in varuous fields in physics. Built conceptual chierachy of the lows and phenomena based on symmetry or symmetry breaking. | |||||||||
| Contents of the course | ||||||||||
| Lectures | 1.
Quantum methods and symmetry (symmetry adapted bases). 2. Physical tensors, selection rules, approximations. 3. Basic geometrical symmetries of molecules and crystals (point, line, layer and space groups). 4. Bloch states, Fourier analysis. 5. Identical particles and permutations: Bosons and fermions. 6. Modified Wigner's projectors for symmetry adapted eigenstates (electrons in tight-binding approximation and ions in harmonic approximation) for molecules and crystals. 7. Normal modes (harmonic potential, symmetry of modes, phonon bands). 8. Adiabatic model in quantum mechanics. 9. Electronic levels in molecules: molecular orbitals. 10. Electronic bands in crystals. 11. Symmetry breaking (extrema of invariant functionals, spontaneous symmetry breaking). 12. Phase transitions, theories of fourth order, Jahn-Teller effect. |
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| Examples/ practical classes | Exercises, discussions, seminars, homeworks. | |||||||||
| Recommended books | ||||||||||
| 1 | M.
Damnjanovic, Symmetry in quantum nonrelativistic physics. (amended electronic
version of М.
Дамњановић,
«О симетрији
у квантној
нерелативистичкој
физици», СФИН VIII
1, 1995.) |
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| 2 | И. Милошевић, Д. Стојковић, Т. Вуковић, «Збирка задатака из математичке физике», Београд, Физички факултет 1996. | |||||||||
| 3 | Ј. P. Elliot, P. G. Dawber, « Symmetry in Physics », London, Macmillan, 1979. | |||||||||
| 4 | ||||||||||
| 5 | ||||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples&practicals | Student project | Additional | |||||||
| 3 | 2 | |||||||||
| Teaching and learning methods | ||||||||||
| Assessment (maximal 100) | ||||||||||
| assesed coursework | mark | examination | mark | |||||||
| coursework | 10 | written examination | 50 | |||||||
| practicals | oral examination | 40 | ||||||||
| papers | ||||||||||
| presentations | ||||||||||