F5082 Basic Quantum Mechanics

Faculty of Science
Autumn 2024
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Tomáš Hoder, Ph.D. (lecturer)
Mgr. Jiří Vohánka, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Tomáš Hoder, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Tomáš Hoder, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Fri 8:00–9:50 F4,03017
  • Timetable of Seminar Groups:
F5082/01: Tue 18:00–19:50 F3,03015
Prerequisites
F4100 Introduction to Microphysics
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The subject is an introductory university course in non-relativistic quantum mechanics. It builds on the knowledge of experimental assumptions and the physical-historical context of the emergence of this discipline, which is acquired in the course General Physics (subject: Introduction to Microphysics), and also deepens it. Emphasis is placed on a thorough explanation of the basic concepts, notions, and ideas of quantum mechanics. Detailed commentary is provided not only on their interrelationships but also on broader contexts, with the aim of convincingly demonstrating that (and how) human reason has been able to master an area of nature that is inaccessible to direct sensory perception, to the extent that scientific and technical applications are possible. In view of physics students focused on education, the possibilities of simplifying the explanation of this topic to a high school level are also briefly discussed.
Learning outcomes
By the end of the course, the student should be able to understand, explain, and practically use: the postulates and mathematical apparatus of quantum mechanics, including their physical interpretation; the Schrödinger equation and its simple applications; the basic concepts of the quantum description of ensembles of identical micro-objects; and the possibility of simplifying university-level quantum mechanics for a high school environment.
Syllabus
  • 1. The Beginnings of Quantum Mechanics, Waves vs. Particles (revision and deepening of the understanding of the physics of the microworld).
  • 2. Mathematical Apparatus of Quantum Mechanics and Its Physical Interpretation (wave function and state vector, superposition principle, Hermitian operators, expansion of the wave function into their eigenfunctions, representations, physical quantities in quantum mechanics, measurement in the microworld, expectation values of physical quantities, uncertainty principle).
  • 3. Postulates of Quantum Mechanics and the Schrödinger Equation (time evolution of the state of a micro-object, general Schrödinger equation, physical implications of the Schrödinger equation).
  • 4.The Schrödinger Equation and Its 1D Solutions (potential step models - thermionic emission, autoemission, contact potential; harmonic oscillator, connection between the degeneracy of energy levels and the symmetry of the problem).
  • 5. Angular Momentum, 3D Issues, and the Hydrogen Atom (commutation relations and eigenvalues, quantization and degeneracy, geometric interpretation, micro-object in a centrally symmetric field, scattering and bound states, quantization of energy and angular momentum, radial and angular probability density, hydrogen atom, energy spectrum, graphical representation of charge density in the hydrogen atom).
  • 6. Spin (spin hypothesis, Stern-Gerlach experiment, Pauli equation, spin effects in the hydrogen atom).
  • 7. Identical Particles (principle of indistinguishability, exchange interaction, systems of bosons and fermions, Pauli exclusion principle, single-particle approximation, self-consistent field method, multi-electron atoms, Mendeleev's periodic table).
  • 8. Simplification for High Schools.
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. 2nd ed. Chichester: Wiley, 2009, xvi, 671. ISBN 9780470026793. info
  • SKÁLA, Lubomír. Úvod do kvantové mechaniky. Vyd. 1. Praha: Academia, 2005, 281 s. ISBN 8020013164. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky. 2. vyd. Bratislava: Alfa, 1983, 551 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. Vyd. 1. Brno: Rektorát UJEP, 1981, 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. Vyd. 1. Brno: Rektorát UJEP, 1983, 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1978, 685 s. URL info
  • BLOCHINCEV, Dimitrij Ivanovič. Základy kvantové mechaniky. Translated by Jan Cejpek. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956, 545 s. URL info
  • WICHMANN, Eyvind H. Kvantovaja fizika. Edited by Alexandr Ovsejevič Vajsenberg, Translated by Aleksandr Iosifovič Ša. Moskva: Nauka, 1974, 414 s. info
  • LACINA, Aleš. Cvičení z kvantové mechaniky pro posluchače učitelství fyziky. Brno: Univerzita Jana Evangelisty Purkyně v Brně, 1989, 104 pp. info
  • DANIN, Daniil Semenovič. Pravdepodobnostný svet. Bratislava: Alfa, 1986. info
  • POLKINGHORNE, J. C. Kvantový svět. Vyd. 1. Praha: Aurora, 2000, 159 s. ISBN 80-7299-017-9. info
  • POLKINGHORNE J. C. Kvantová teorie (Quantum Theory: A Very Short Introduction). Praha: Dokořán, 2007. info
Teaching methods
lecture and exercise
Assessment methods
active participation in exercises; two written tests during the semester; at least 60% in each
exam - written and oral
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
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