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Lecturer(s)
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Erhart Jiří, prof. Mgr. Ph.D.
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Šulc Miroslav, doc. RNDr. Ph.D.
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Brandejs Jan, Mgr.
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Course content
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Lectures: 1. Introduction - historical outline. Experiments hinting towards incompleteness of classical theory. 2. Uncertainty principle, determinism of classical physics and probability interpretation of quantum mechanics. 3. Comparison of description of observables and states in classical and quantum theory, correspondence principle. 4. Wave function and its interpretation as probability amplitude, superposition principle. 5. Wave-particle duality, de Broglie relations, double-slit experiment. 6. Mathematical description: complex numbers, vector spaces, scalar product, matrix representation, Hilbert space, wave function, basis and dimension, superposition, operators, hermicity, unitarity, symmetries. 7. State of a particle as a ray in Hilbert space, superposition of states as a linear combination of vectors. 8. Physical observables and hermitian operators correspondence, meaning of unitarity, relations between operators. 9. Examples of wave functions (scalar, spinor, vector), wave packets, group and phase velocity, mass and dispersion. 10. Dirac symbolism. Operators as matrices, eigenstates and eigenvalues, examples. 11. Operators corresponding to concrete observables, meaning of commutator relations, uncertainties, eigenstates and eigenvalues, types of spectra, measurement, simultanneously measurable quantities, mean values. 12. Orbital angular momentum, corresponding operators, eigenstates, eigenvalues. Spin and its operators, Pauli matrices, operators. 13. Time evolution of states, Hamiltonian, Schrődinger equation, examples. Conservation laws, correspondence principle. Interactions. 14. Identical particles, fermions, bosons, Pauli excluding principle and its consequences in periodic table, shapes of orbitals, superconductivity, superfluidity, boson condensate. Problem classes: consist of solving simple problems illuminating the material from the lectures.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments)
- Class attendance
- 20 hours per semester
- Preparation for exam
- 64 hours per semester
- Class attendance
- 56 hours per semester
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Learning outcomes
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Experimental foundations of quantum physics, basic principles, mathematical apparatus, physical axioms, angular momentum in quantum physics, examples.
Learning the basic principles of quantum physics.
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Prerequisites
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Fundamental course of physics
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Assessment methods and criteria
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Combined examination, Student's performance analysis, Didactic test
Taking part in problem classes, solving and presenting homework problems, oral and written exam. During online education period consultations mainly online, as well as handing over the assignments.
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Recommended literature
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BRANDT S., DAHMEN H.D. Kvantová mechanika v obrazoch. Bratislava, 1990.
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DAVYDOV, A.S. Kvantová mechanika. Praha: SPN, 1978.
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KVASNICA,J. Kvantová fyzika. Ústí nad Labem, 1984.
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LACINA, A. Cvičení z kvantové mechaniky pro posluchače učitelství fyziky. Brno, 1989.
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SKÁLA., L. Úvod do kvantové mechaniky. Praha, 2012. ISBN 9788024620220.
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