Course Unit Code | 480-2052/01 |
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Number of ECTS Credits Allocated | 5 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | Third Year |
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Semester when the Course Unit is delivered | Winter Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| ALE02 | Doc. Dr. RNDr. Petr Alexa |
Summary |
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The course introduces the most important aspects of non-relativistic quantum mechanics. It includes the fundamental
postulates of quantum mechanics and their applications to square wells and barriers, the linear harmonic oscillator
and spherical potentials and the hydrogen atom. The remarcable properties of quantum particles and the resulting
macroscopic effects are discussed. |
Learning Outcomes of the Course Unit |
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Explain the fundamental principles of quantum-mechanical approach to problem solving.
Apply this theory to selected simple problems.
Discuss the achieved results and their measurable consequences. |
Course Contents |
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1. Introduction - historical context and the need for a new theory.
2. Postulates of quantum mechanics, Schrödinger equation, time dependent and stationary, the equation of continuity.
3. Operators - linear Hermitian operators, variables, measurability. Coordinate representation.
4. Basic properties of operators, eigenfunctions and eigenvalues, mean value, operators corresponding to the selected physical variables and their properties.
5. Free particle waves, wavepackets. The uncertainty relation.
6. Model applications of stationary Schrödinger equation - piece-wise constant potential, infinitely deep rectangular potential well - continuous and discrete energy spectrum.
7. Other applications: step potential, rectangular potential well, square barrier potentials - tunneling effect.
8. Approximations of selected real-life situations by rectangular potentials.
9. The harmonic oscillator in the coordinate representation and the Fock's representation.
10. Spherically symmetric field, the hydrogen atom. Spin.
11. Indistinguishable particles, the Pauli principle. Atoms with more
than one electrons. Optical and X-ray spectrum.
12. The basic approximations in the theory of chemical bonding.
13. Interpretation of quantum mechanics. |
Recommended or Required Reading |
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Required Reading: |
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MERZBACHER, E.: Quantum mechanics, John Wiley & Sons, NY, 1998. |
SKÁLA, L.: Úvod do kvantové mechaniky, Academia Praha 2005
BEISER, A.: Úvod do moderní fyziky, Academia, Praha 1975 |
Recommended Reading: |
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SAKURAI, J. J.: Modern Quantum mechanics, Benjamin/Cummings, Menlo Park,
Calif. 1985
MERZBACHER, E.: Quantum mechanics, Wiley, New York 1970 |
STUCHLÍK, Z.: Kvantová fyzika, VŠB Ostrava, 1988;
KLÍMA, J., VELICKÝ, B.: Kvantová mechanika I., MFF UK, Praha 1992 ;
FORMÁNEK, J.: Úvod do kvantové teorie, Academia, Praha 1983 (vybrané partie);
FEYNMAN, R. P., LEIGHTON, R. B., SANDS, M.: Feynmanove prednášky z fyziky 5, Alfa, Bratislava 1990;
HRIVNÁK, Ľ., BEZÁK, V., FOLTIN, J., OŽVOLD, M.: Teória tuhých látok, Veda,
SAV Bratislava 1985 (I. kapitola);
LACINA, A.: Cvičení z kvantové mechaniky pro posluchače učitelství fyziky,
PřF UJEP, Brno 1989;
HALLIDAY, D., RESNICK, R., WALKER J.: Fyzika. Část 5, Moderní fyzika. VUT v Brně, nakl. Vutium a nakl. Prometheus
Praha, 2000.
MERZBACHER, E.: Quantum mechanics, Wiley, New York 1970 |
Planned learning activities and teaching methods |
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Lectures, Tutorials |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 40 | 20 |
Examination | Examination | 60 (60) | 11 |
Písemná část zkoušky | Written test | 20 | 10 |
Ústní část zkoušky | Oral examination | 40 | 1 |