F6030 Quantum mechanics

Faculty of Science
Autumn 2001
Extent and Intensity
4/2/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Aleš Lacina, CSc. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
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.
Prerequisites (in Czech)
F4060 Introduction to microphysics
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
The postulates and mathematical tools of quantum mechanics. Schrödinger equation. Simple applications - square potentials. Approximation methods of quantum mechanics. The angular momentum. Central fields. The hydrogen atom. Spin. Fundamentals of quantum mechanics of many body systems. Basic concepts of chemical bond. Quantum mechanics at university and at school.
Syllabus
  • Electromagnetic radiation as a system of photons. Historical development of views on nature of light, blackbody radiation, the quantum hypothesis, photoelectric emission, scattering of radiation by free electrons, polarization of light from the point of view of the photon hypothesis. The structure of the atom. Historical development of views on structure of matter, early models of the atom, Rutherford's scattering experiment, the planetary model of the atom. Electronic structure of atoms I. The planetary model of the atom from the classical point of view, problem of its stability, the Bohr model for hydrogen atom, the Sommerfeld's generalization of the Bohr model, Franck-Hertz's experiment, optical spectra of atoms, X-ray spectra. The ware particle dualism and its physical interpretation. The de Broglie's hypothesis, Davisson-Germer's and Thomson's experiments, Young's double slit experiment with classical particles, waves and microobjects. Fundamental of quantum mechanics. The wave function, superposition principle and its physical meaning, wave packet, the uncertainty relation and its physical consequences, measurement in microworld, the relation of classical and quantum mechanics. The Schroedinger equation. The Schroedinger equation as the equation of motion of quantum mechanics, the stationary Schroedinger equation and its solution for some simple potential models, quantum effects. Approximation of real situations by means of simple potential models. Thermoemission, autoemission, contact potential, p-n junction, interaction of two microobjects, nuclear transitions, radioactivity, the band model of solids, electrical conductivity. Electronic structure of atoms II. The quantum description of the hydrogen atom, electronic configurations of many electron atoms, the Mendeleev periodical system. Nuclear structure. Nuclear forces, classification of nuclei, radioactivity, nuclear reactions, nuclear fusion and fission. Text ze sylabu 1998 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. The Schrödinger equation. The time development of the state of a microobject, general Schroedinger equation, physical implications of Schroedinger equation, causality in quantum mechanics, the stationary Schroedinger equation, the properties of stationary states. Simple applications. 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. Approximation methods. Discontinuous potentials, WKB approximation, estimations of ground-state parameters of bound systems, perturbation and variation methods. The angular momentum. Commutation rules and eigenvalues, quantization and degeneracy, geometrical interpretation, addition of angular momenta. Central fields. Quantization of energy and angular momentum, radial and angular probability density. The hydrogen atom, energy spectrum, geometrical visualisation of the charge density in the hydrogen atom, hybridization. Uhlenbeck and Goudsmit's hypothesis, Stern-Gerlach's experiment, the Pauli equation, spin effects in the hydrogen atom. 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. Quantum mechanics at university and at school. A survey of the most frequent elementary treatments and their critical analysis.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
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 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation.
  • Enrolment Statistics (Autumn 2001, recent)
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