| Course Unit Code | 480-4001/01 |
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| Number of ECTS Credits Allocated | 3 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First 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 | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| SLA0112 | doc. RNDr. Petr Slaný, Ph.D. |
| Summary |
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| Hamilton's principle of least action is one of the principles on which to formulate all the equations of modern physics and which also serves as a tool for finding new theories. The course is devoted to its application in the framework of Lagrangian and Hamiltonian formalism in classical and quantum mechanics. |
| Learning Outcomes of the Course Unit |
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1. Present and, on selected examples, demonstrate the application of lagrange and hamilton formalism in physics.
2. Point out some interesting aspects of quantum theory.
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| Course Contents |
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1. Basics of calculus
2. The principle least action (Hamilton's principle)
3. Conservation laws, the theory of E. Noether
4. Problem of two bodies, Kepler's task
5. Hamilton's canonical equations, Poisson's brackets
6. Canonic transformation, Liouville's theorem, Hamilton-Jacobi theory
7. Quantum mechanics, commutator and uncertainty relations
8. Time evolution of the quantum state, Feynman's formulation of quantum mechanics
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| Recommended or Required Reading |
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| Required Reading: |
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R. Shankar – Principles of Quantum Mechanics, Plenum Press, New York and London, 1994
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L. D. Landau, J. M. Lifšic – Úvod do teoretickej fyziky I, Alfa, Bratislava, 1980
J. Horský, J. Novotný – Mechanika ve fyzice, Academia, Praha, 2001
P. Kulhánek – Vybrané kapitoly z teoretické fyziky, AGA, Praha, 2016
R. Shankar – Principles of Quantum Mechanics, Plenum Press, New York and London, 1994
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| Recommended Reading: |
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| R. P. Feynman, R. B. Leighton, M. Sands – Feynmanovy přednášky z fyziky, Fragment, Praha, 2000 |
| R. P. Feynman, R. B. Leighton, M. Sands – Feynmanovy přednášky z fyziky, Fragment, Praha, 2000 |
| Planned learning activities and teaching methods |
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| Lectures, Seminars |
| 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 | Credit | | |