| Individual course details | ||||||||||
| Study programme | THEORETICAL AND EXPERIMENTAL PHYSICS | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | Undergraduate Studies | |||||||||
| Name of the course | Mathematical Physics 2 | |||||||||
| Professor (lectures) | Tatjana Vukovic, Sasa Dmitrovic, Milan Damnjanovic, Ivanka Milosevic | |||||||||
| Professor/associate (examples/practical) | Sasa Dmitrovic | |||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | 9 | Status (required/elective) | required | |||||||
| Access requirements | Mathematics 1B, Mathematics 2B, Mathematics 4B, Mathematics 4B | |||||||||
| Aims of the course | Acquiring the basic knowledge necessary for understanding quantum mechanics as well as the other areas of contemporary physics. | |||||||||
| Learning outcomes | To master the basic concepts and techniques of the theory of Hilbert spaces, finite and Lie groups, important in physics, at the level of understanding their application in physics courses of the third and fourth year. | |||||||||
| Contents of the course | ||||||||||
| Lectures | 1.
Metric and topological spaces and manifolds: continuity and differentiability
of physical fields, connectivity, compactness. 2. Hilbert and Lebesque spaces: infinite-dimensional spaces of state, distribution, d-function, plane waves, orthonormal basis, equipped Hilbert space. 3. Operators and hypergeometric equation: spectrum of physical observables, distribution and continuous spectrum, second order equations in physics, orthogonal polynomials and special functions, harmonic and Coulomb potential. 4. Final groups: structure, symmetry and groups of transformations in physics, factor group, products of groups. 5. Representation theory of groups: unitary representations and quantum probability, decomposable and irreducible representations. 6. Transformation properties of physical quantities, characters, group projectors. 7. Sum and product of representations, selection rules. 8. Lie algebras: structural constants, representations, classification, Heisenberg algebra. 9. Semisimle Lie algebras, physical observables, roots and weights, representations, Casimir operators. 10. Lie groups: topological features. 11. Covering group and its algebra, generators, translation and impulses, representations and unitarity. 12. Multi-valued representations, direct products of representations. 13. Lie Groups and algebras of particular importance in physics: SO(3, R), SU(2), Lorentz group. Poincare group, its representations, mass and spin of elementary particles. |
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| Examples/ practical classes | Written exercises: elaboration of terms used in lectures, solving problems and examples relevant for physics. | |||||||||
| Recommended books | ||||||||||
| 1 | M. Дамњановић, Хилбертови простори и групе, Физички факултет, Београд 2000 (рецензиран уџбеник са задацима). | |||||||||
| 2 | Richtmyer R., Principles of Advanced Mathematical Physics, Springer, Berlin, 1978. | |||||||||
| 3 | J. P. Elliot, P. G. Dawber, Symmetry in Physics, London, Macmillan, 1979. | |||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples&practicals | Student project | Additional | |||||||
| 4 | 4 | |||||||||
| Teaching and learning methods | Lectures, written exercises (solving problems, homework). |
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| Assessment (maximal 100) | ||||||||||
| assesed coursework | mark | examination | mark | |||||||
| coursework | 5 | written examination | 30 | |||||||
| practicals | oral examination | 50 | ||||||||
| papers | 15 | |||||||||
| presentations | ||||||||||