BMETE11AF40 |
Group Theory for Physicists |
2 |
2 |
0 |
E |
5 |
5 |
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Dr. Fehér Titusz |
The aim of the course is to introduce the principles of group theory to physics students: we learn how the symmetries of a system can be used to describe it, and how the symmetries of nature manifest themselves in laws of physics. We apply the concepts of group and representation theory to practical problems. Theory: Symmetries in nature and physics. Definition and basic properties of groups. Some special groups. Homomorphism, isomorphism. Subgroups, cosets, Lagrange's theorem. Normal subgroup, quotient group, first isomorphism theorem. Conjugate, conjugacy classes, centralizer. Group action, orbit, stabilizer. Representations and their properties, equivalent representations, irreducible representations. Schur's lemma. Character of representations, propertires of characters, character tables. Direct sum of representations and their reduction. Product representations. Lie groups, infinitesimal generators, Lie algebras. Topological properties, universal covering group. Rotation group and its representations. Lorentz group and other matrix groups. Calculation: Description of normal modes, crystals, and quantum mechanical wave functions using group theory. Selection rules.
Literature:
– H.F. Jones: Groups, Representations and Physics (IOP Publishing, 1998) – R.L. Liboff: Primer for Point and Space Groups (Springer, 2003). – M.S. Dresselhaus, G. Dresselhaus, A. Jorio: Group Theory - Application to the Physics of Condensed Matter (Springer, 2008). |
BMETE15AF34 |
Electrodynamics 2 |
2 |
0 |
0 |
E |
2 |
2 |
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Dr. Takács Gábor |
Electrostatics: Solving Laplace's equation in spherical and cylindrical coordinates. Grounded sphere in external field, electric field near a sharp cone. Multipole expansion in spherical harmonics. – Magnetic and quasistatic fields: magnetic scalar potential, solution methods in nonlinear materials. – Electromagnetic waves in vacuum and matter. Microscopic model for polarizability. Dispersion, plasma frequency, Kramers-Kroing relations. – Wave guides, resonant cavity. Losses, quality factor. – Radiation field of oscillating charges. Electric dipole and quadrupole, magnetic dipole radiations. – Scattering of electromagnetic waves, cross section. Scattering on solids and gases. – Lienard-Wiechert potential of moving charge, field strength, radiated power, angular distribution, spectrum. Synchrotron radiation. Cherenkov and transitional radiations. – Elements of relativistic electrodynamics.
Literature:
– David J. Griffiths: Introduction to Electrodynamics (Pearson) – John D. Jackson: Classical Electrodynamics (Wiley) |
BMETE15AF42 |
Practical Course in Electrodynamics 2 |
0 |
2 |
0 |
M |
3 |
3 |
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Dr. Takács Gábor |
Problem solving class accompanying Electrodynamics 2.
Literature:
– David J. Griffiths: Introduction to Electrodynamics (Pearson) – John D. Jackson: Classical Electrodynamics (Wiley) |
BMETE15AF36 |
Quantum Mechanics 2 |
2 |
0 |
0 |
E |
2 |
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2 |
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Dr. Szunyogh László |
This course conveys advanced knowledge on Quantum Mechanics according to the following topics: The WKB approach, quasi-classical quantization. Scattering theory, scattering amplitude and cross section, Green functions, Lippmann-Schwinger equation, Born series, method of partial waves. Motion in electromagnetic field, Aharonov-Bohm effect, Landau levels. Time evolution and pictures in Quantum Mechanics (Schrödinger, Heisenberg and Dirac pictures). Adiabatic motion and Berry phase. Relativistic Quantum Mechanics, Klein-Gordon equation, Dirac equation, continuity equation, Lorentz invariance, spin and total angular momentum. Free electron and positron. Non-relativistic limit, spin-orbit interaction.
Literature:
– Franz Schwabl: Quantummechanics, Springer 1990 – Albert Messiah: Quantummechanics, Vol. 1-2, North Holland, 1986 |
BMETE15AF43 |
Practical Course in Quantum Mechanics 2 |
0 |
2 |
0 |
M |
3 |
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3 |
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Dr. Szunyogh László |
Problem solving course related to the topics of the course Quantum Mechanics 2.
Literature:
– Siegfried Flügge: Practical Quantum Mechanics, Springer, 1994 |
BMETE15AF32 |
Mechanics 2 |
2 |
0 |
0 |
E |
2 |
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2 |
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Dr. Zaránd Gergely Attila |
Relativistic mechanics: Lorentz-transformations, four-vectors and Minkowski space, relativistic collisions, relativistic action and equations of motion. Relativistic particle in an electromagnetic field. Lagrange-theory of continuum mechanics: Lagrange density of a string, Euler-Lagrange equations, energy density. Application to quantum mechanics and to harmonic media, Klein-Gordon equations. Hamiltonian formulation of continuum mechanics. Symmetries: Noether's theorem, symplectic formulation of Hamiltonian mechanics. Poisson's brackets, integrability. Canonical transformations, Hamilton-Jacobi equations, action-angle variables. Nonlinearity, second harmonic generation, parametric resonance. Basics of dynamical systems and chaos.
Literature:
– H. Goldstein: Classical Mechanics, Addison-Wesley. – J.R. Taylor, Classical Mechanics, University Science Books. |
BMETE15AF44 |
Practical Course in Mechanics 2 |
0 |
2 |
0 |
M |
3 |
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3 |
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Dr. Zaránd Gergely Attila |
Problem solving class accompanying Mechanics 2.
Literature:
– H. Goldstein: Classical Mechanics, Addison-Wesley. – J.R. Taylor, Classical Mechanics, University Science Books. |
BMETE11AF41 |
Computer Solution of Technical and Physical Problems |
0 |
0 |
2 |
M |
3 |
3 |
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Dr. Varga Gábor |
In the frame of this subject basic models of different technical and physical applications are investigated (among others: one and many body problems, Poisson equation, flow dynamics, plate deformation, heat conductivity, wave equation, Schrödinger equation). Relating to these problems on computer implemented MATLAB programs are written. During the computer implementation not only the physical aspects of the models are analyzed but the required numerical methods too. The programming tool is the MATLAB program language.
Literature:
– G.D. Smith: Numerical Solution of Partial Differential Equations, 1979. – MATLAB documentation (http://www.mathworks.com/help/matlab/). |
BMETE15AF46 |
Theory of Relativity |
2 |
0 |
0 |
E |
3 |
3 |
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Dr. Lévay Péter Pál |
Minkowski spacetime, four vectors. Lorentz and Poincaré groups. Time dilation, Lorentz contraction, relativity of simultaneity. Addition of velocity, rapidity. Causality, Zeeman's theorem. Proper time, four velocity, four acceleration. Relativistic dynamics. Hyperbolic motion. Principle of Equivalence. Geodesic hypothesis. Principle of covariance. Local systems of inertia. Riemann and pseudo Riemann geometry, Christoffel symbols. Geodesics. Covariant derivative, parallel transport. The Newtonian limit. Connection between the metric tensor and the gravitational potential. Geodesics from a variational principle. Riemann tensor and its properties. Riemann tensor and its connection with parallel transport. Geodesic deviation. Ricci tensor, scalar curvature. Bianchi identity, Einstein tensor. Energy-momentum tensor. Conservation of energy and momentum. Einstein's equation, Einstein-Hilbert action, cosmological term. Schwarzschild's solution. The perihelium precession of Mercury.
Literature:
– G. Naber: The Geometry of Minkowski Space-Time, Springer 1992. – S.M. Carroll: An Introduction to General relativity Spacetime and Geometry, Addison Wesley 2004. |
BMETE12AF31 |
Fundaments and Applications of Materials Science |
2 |
0 |
0 |
E |
3 |
3 |
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Dr. Réti Ferenc |
The aim of the subject is to give a basic knowledge in the modern materials science and its use in different areas of physics and engineering. Topics: Materials science and engineering. Modern materials, requirements in their use. Role of primary and secondary bonding in properties of materials. Importance of thermal processes, thermodynamics, thermochemistry, Hess principle, Born-Haber cycle. Chemical potential, equilibrium constant. Reaction rate equations. Arrhenius and Eyring equation. Importance of crystal imperfections e.g. in electrical and mechanical properties. Equilibrium concentration of crystal imperfections. Sensors in engineering. Principles, physical and chemical sensors. Pressure sensors, thermometers, strain gauges, magnetic sensors. Non-destructive testing. Flaw detection by ultrasound, X-ray. Magnetic tests. Practical examples. Alternative energy sources and energy carriers; contradictions of the field. Hydrogen economy, bio-ethanol. Fuel cells as continuous power sources.
Literature:
– M. Tisza: Fundaments of Materials Science, Miskolci Egyetemi Kiadó, 2008. – P.W. Atkins, Physical-Chemistry, Tankönyvkiadó, 2002. – W.D. Callister, Jr.: Materials Science and Engineering, An Introduction, John Wiley and Sons Inc., 6th edition, 2003. |
BMETE12AF33 |
Microtechnology and Nanotechnology |
2 |
0 |
0 |
M |
3 |
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3 |
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Dr. Kiss Gábor |
Definition of microtechnology, nanotechnology and molecular nanotechnology, their comparison and interrelation. Conditions of the technology. Micro- and nanophysics. Thin layer deposition methods: physical (vacuum evaporation, laser ablation evaporation, molecular beam epitaxy, sputtering). Doping (diffusion, ion implantation). Litography (photo, X-ray, electron beam, ion beam). Layer removing technologies: wet „chemical” etching, dry etching (plasma, ion beam). Layer characterisation methods: X-ray diffraction, transmission electron microscopy, scanning electron microscopy, secondary ion mass spectrometry, X-ray photoelectron spectroscopy, Auger electron microscopy, scanning tunneling microscopy, atomic force microscopy. Conventional electronic devices: bipolar transistor, field effect transistor. Thick layer technology: screen printing, burning, thick layer pastes. Nanometer devices: single electron devices, resonant tunnel effect devices, micro-electromechanical systems, sensors, image detectors, displays.
Literature:
– R. Waser (Ed.): Nanoelectronics and information technology, Wiley-VCH, 2003. |
BMETE11AF38 |
Computer Controlled Measurements |
0 |
0 |
2 |
M |
3 |
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3 |
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Dr. Halbritter András Ernő |
The participants gain experience in computer controlled measurements and in the programming of scientific instruments and data acquisition system. To this end the following topics are covered: communication with the instruments via serial, GPIB, and USB ports. Programming of data acqusitin cards. Programming of complex measurement control platforms, plotting and saving the data, programming of timelines, in situ data analysis. The course consists of 4 hour long computer laboratory exercises every second week. In the first part of the semester fundamental programming skills are obtained through simple example programs. In the second part the participants individually program complex measurement control and data analysis platforms, like nonlinear curve fitting by Monte Carlo method, full computer control of a digital multimeter, digital oscilloscope program using a data acquisition card. |