UF1U202 Quantum Mechanics I

Faculty of Philosophy and Science in Opava
Winter 2020
Extent and Intensity
4/2/0. 10 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Petr Slaný, Ph.D. (lecturer)
doc. RNDr. Petr Slaný, Ph.D. (seminar tutor)
Mgr. Evariste Norbert Boj (seminar tutor)
Guaranteed by
doc. RNDr. Petr Slaný, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Prerequisites (in Czech)
( UF1U004 Theoretical Mechanics || UF1U054 Theoretical Mechanics ) && TYP_STUDIA(B)
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After introductory lectures devoted to the origins and history of quantum mechanics is given a systematic interpretation of its foundations. Use of mathematical apparatus is implemented on the basis of physical requirements.
Syllabus
  • * The history of quantum physics. Blackbody radiation, photoelectric effect, Compton scattering, Franck-Hertz experiment, Bohr model of the atom, corpuscular-wave dualism, de Broglie waves, the double-slit experiment.
    * Basic concepts and principles of quantum physics. The concept of the wave function and probability interpretation, the principle of superposition, the role of operators in quantum physics.
    * Mathematical theory of operators. Eigenvalue problem of operators discrete, continuous and mixed spectrum non-degenerate and degenerate spectrum pure and mixed states, density matrix.
    * Reduction of the wave function and the process of measurement. Operators of basic physical quantities.
    * Uncertainty relations, Heisenberg's uncertainty relation.
    * Time evolution of the wave function and conservation laws. Hamiltonian of the system and its importance, stationary states, the SchrÝdinger equation. Continuity equation of quantum mechanics, the probability density and the probability current density. Ehrenfest's theorems, quasiclassical approximation.
    * Geometrization of quantum physics. Hilbert space, representation of the state vector and operators.
    * Solutions of the SchrÝdinger equation. Free particle potential well and a three-dimensional box linear harmonic oscillator passage and reflection on a barrier, tunneling effect.
    * Angular momentum operator, its eigenvalues â€<†* Two-body problem, motion in a central force field motion in the Coulomb field, the hydrogen atom. The hydrogen atom in a magnetic field, the normal Zeeman effect.
    * Spin. Stern-Gerlach experiment, the spin operator, spinors.
    * Structure of atoms. The energy levels of atoms, states of electrons, Mendeleyev periodic table.
    * Basics of relativistic quantum mechanics. The Klein-Gordon equation, the Dirac equation, spin of the electron, antiparticles.
    * Interpretations of Quantum Mechanics, dekoherence.
Literature
    required literature
  • Lubomír Skála. Úvod do kvantové mechaniky. Praha, 2005. ISBN 80-200-1316-4. info
    recommended literature
  • F. Schwabl. Quantum Mechanics. Berlin Heidelberg, 2007. ISBN 978-3-540-71932-8. info
  • J. Pišút, L. Gomolčák, V. Černý. Úvod do kvantovej mechaniky. Bratislava, 1983. info
    not specified
  • J. Formánek. Úvod do kvantové teorie I, II. Praha, 2004. info
  • R. Shankar. Principles of Quantum Mechanics. New York, 1994. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
Teacher's information
* 75% attendance in seminars, active participation
* 50% success in written exam, passing an oral exam
The course is also listed under the following terms Winter 1998, Summer 1999, Winter 1999, Summer 2000, Winter 2000, Summer 2001, Winter 2001, Summer 2002, Winter 2002, Summer 2003, Winter 2003, Summer 2004, Winter 2004, Summer 2005, Winter 2005, Summer 2006, Winter 2006, Summer 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (recent)
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