F6030 Quantum mechanics

Faculty of Science
Autumn 2011
Extent and Intensity
3/2/0. 5 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Aleš Lacina, CSc. (lecturer)
Guaranteed by
doc. RNDr. Aleš Lacina, CSc.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: doc. RNDr. Aleš Lacina, CSc.
Timetable
Mon 8:00–8:50 F3,03015, Mon 9:00–9:50 Fs2 6/4003, Mon 14:00–15:50 F4,03017, Thu 8:00–9:50 F3,03015
Prerequisites (in Czech)
F4050 Introduction to Microphysics || F4060 Introduction to microphysics || F4100 Introduction to Microphysics
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of the course, students should understand and be able to explain and to use: The postulates and mathematical tools of quantum mechanics. Schrödinger equation and its simple applications. Approximation methods of quantum mechanics. Fundamentals of quantum mechanics of many body systems. Basic concepts of chemical bond. Interconnection between quantum mechanics at university and at school.
Syllabus
  • 1. The postulates and the mathematical tools of quantum mechanics (wave function and state vector, the superposition principle, hermitian operators, expansion in eigenfunctions, representations, physical quantities in quantum mechanics, measurement in microworld, the expectation values of physical quantities, uncertainty principle).
  • 2. The Schrödinger equation (the time development of the state of a microobject, general Schrödinger equation, physical implications of Schrödinger equation, causality in quantum mechanics, the stationary Schrödinger equation, the properties of stationary states).
  • 3. Simple applications of quantum mechanics (square potential models - thermoemission, autoemission, contact potential, radioactivity, transitions of nuclei, molecules and their interactions, the band model of solids, harmonic oscillator, the relation between energy degeneracy and the symmetry of the problem).
  • 4. Approximation methods (discontinuous potentials, WKB approximation, estimations of ground-state characteristics of bound systems, perturbation and variation methods).
  • 5. The angular momentum (commutation rules and eigenvalues, quantization and degeneracy, geometrical interpretation, addition of angular momenta.
  • 6. Central fields (scatterring and bound states, quantization of energy and angular momentum, radial and angular probability density). 7. The hydrogen atom (energy spectrum, geometrical visualisation of the charge density in the hydrogen atom, hybridization.
  • 8. Spin. (Uhlenbeck and Goudsmit's hypothesis, Stern-Gerlach's experiment, the Pauli equation, spin effects in the hydrogen atom).
  • 9. Quantum mechanics of many body systems (indistinguishability principle, the exchange interaction, boson and fermion systems, the Pauli exclusion principle, the one-particle approximation, the self-consistent field method, many electrons atoms, the Mendeleev periodic system, chemical bond).
  • 10. Quantum mechanics at university and at school (a survey of the most frequent elementary treatments and their critical analysis).
Literature
  • 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
  • Wichman, Eyvind H. Quantum Physics (Berkeley Physics Course, Vol.IV). New York: McGraw-Hill Book Company. (Ruský překlad: Kvantovaja fizika. Moskva: Nauka, 1974.)
  • 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
  • LACINA, Aleš. Cvičení z kvantové mechaniky pro posluchače učitelství fyziky. Vyd. 1. Brno: Rektorát UJEP, 1989, 103 s. ISBN 8021000678. URL info
Teaching methods
Lecture with a seminar; two written tests in the course of the term.
Assessment methods
Examination consists of two parts: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Spring 2000, Autumn 2010 - only for the accreditation, Spring 2001, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, spring 2012 - acreditation.
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