Course: Quantum Theory I

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Course title Quantum Theory I
Course code UFY/KT1
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the summer semester.
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Polívka Tomáš, prof. RNDr. Ph.D.
  • Šebelík Václav, Mgr. Ph.D.
Course content
Content: Foundations of Quantum Mechanics. Black body radiation (Wien, Rayleigh-Jeans, Planck), photoelectric effect, Compton scattering, heat capacities of solids, two-slit experiment with electrons, de Broglie waves, wavepacket. Basics of QM. Wavefunstion, statistical interpretation, superposition of states, operators, mean values of coordinate and momentum, operators of coordinates, momentum, angular momentum, energy, commutators, eigenvalues and eigenfunctions. Uncertainty principle. Measurements in QM, properties of operator eingefunctions, simultaneous measurement of physical quantities, uncertainty principle (coordinate, momentum, angular momentum, energy), interaction of apparatus with microobjects. Schrödinger equation. Principal SR, Hamiltonian, stationary SR, basic principles for solution of SR (infinite potential well, particle in a box, degeneration of states, tunneling. Harmonic oscilátor in QM. Full solution of simple harmonic motion in QM, properties of solutions, properties of wavefunctions, concept of zero energy motion and its consequences. Particle in a central force field. Angular momentum in QM, movement in a field of spherical symmetry, Coulombic field, hydrogen atom - quantum statwes, quantum numbers, discrete energy spectrum, propertiers of wavefunctions, atomic orbitals. Spin. Experiments leading to a discovery of spin, multiplet structure of spectrum, splitting of energy levels in magnetic field, spin operators, Pauli matrices, Pauli equation, spin as relativistic effect, total angular momentum. Multielectron atoms. Set of identical particles, Pauli exclusion principle, Slater determinant, helium atom, periodic table. Introduction to chemical bond. Nature of chemical bond, ionic and covalent bond, valence and core electrons, - and -electrons, bond direction, hybridization. Representation theory. Heisenberg and Dirac representations of QM, matrix mechanics, braket Dirac notation, transformation of opertaors and wavefunctions between different representations.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
  • Class attendance - 48 hours per semester
  • Preparation for classes - 80 hours per semester
  • Preparation for exam - 20 hours per semester
Learning outcomes
The aim of the course is to elucidate basic theoretical and experimental concepts of the quantum theory, to explain properties and behavior of particles and simple quantum objects. The introduction of the necessary mathematical methods will enable the student to describe the phenomena studied. The course is divided into 13 lectures followed by exercises in which practical examples to the theory given will be explained.
Knowledge of general physics (basics of mechanics, thermodynamics, optics and atomic physics), knowledge of methods of mathematical analysis (derivation, integrals, differential equations, Fourier transformation)
Prerequisites
Knoeldge of general physics approximaely according to the courses Physics 1-4

Assessment methods and criteria
Student performance assessment, Systematic student observation, Colloquium

Passing colloquial exam, working out the homeworks, passing two written tests, activity during lectures and practicals.
Recommended literature
  • Atkins, P.W., Friedman, R.S.: Molecular Quantum Mechanics.
  • Beiser, A. Úvod do moderní fyziky, Academia 1975.
  • Davydov, A. S. Kvantová mechanika, SPN 1978.
  • Landau, L. D., Lifshitz, E. M, Quantum Mechanics, Non-Relativistic Theory.
  • Messiah, A.: Quantum Mechanics.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Physics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Physics (1) Category: Physics courses 3 Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Physics for future teachers (1) Category: Physics courses - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Biophysics (1) Category: Physics courses - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Biophysics (1) Category: Physics courses 3 Recommended year of study:3, Recommended semester: Summer