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# SZZTX

**Course:** Theoretical grounds of applied physics

**Department/Abbreviation:** SLO/SZZTX

**Year:** 2021

**Guarantee:** 'doc. RNDr. Libor Machala, Ph.D.', 'prof. RNDr. Jan Peřina, Ph.D.', 'prof. Jan Řídký, DrSc.'

**Annotation:** Final exam for verification and evaluation of the level of knowledge.

**Course review:**

" Statistical operator, Liouville equation, density matrix, pure and mixed states. Hamiltonian as generator of time translations, evolution operator.Free particle propagator, Green functions. Schrödinger and Heisenberg pictures, Dirac picture.
" Identical particles. Permutations, spin and statistics, fermions and bosons. Covalent bond, ortho and para hydrogen. Fock states, second quantization, creation and annihilation operators.
" Simple scattering theory. Lippmann-Schwinger equation. Scattering apmlitude, cross-section. Born series, Coulomb and Yukawa potentials. Optical theorem.
" Particle content of the Standard Model. Fundamental discoveries (electron, nucleus, neutron, positron, muon,). Classification of particles- qu.numbers, spin isospin, parity. Contemporary state of our knowledge - basic properties of matter and their interactions. Partons, deeply non-elastic scattering. Standard model as a theory of electroweak and strong interactions.
" Interaction of particles with medium (basics): Passage of charged particles through the medium in dependence of their energy. Losses due to ionisation, radiation, Čerenkov radiation, transient radiation, multiple scattering. Electromagnetic and hadron cascades (showers).
" Detectors: Particle detection methods, selected types of detectors: scintillators, Čerenkov detectors, track detectors, calorimeters. Particle accelerators: Principles of accelerating, utilized devices, linear and circular accelerators, fixed target and counter propagating beams.
" Definition of signals, theory of signals and transmission systems. Fourier analysis of deterministic signals and impulses and their practical executions. Laplace and Hilbert transform. Correlation of deterministic signals
" Properties of linear and nonlinear transmission systems. Characteristic functions and quantities of stochastic processes and of their realizations, errors in their estimations. Power spectra of stochastic processes and of their realizations. Transmission of stochastic signal via linear systems.
" Influence of noise on signals. Digital signals and their transmission. Digital transmission systems, their error rate and modeling.
" Basic properties and types of analog modulations of signals. Amplitude modulation and effect of noise on amplitude-modulated signals. Phase modulation and effect of noise on phase-modulated signals. Sampling and impulse modulations of signals. Quantization and digital modulations of signals. Multi-channel signals.
" Definition and basic terms of information theory, information and its quantitative measures, mathematical inequalities in theory of information. Basic types and properties of information entropy. Mean mutual information and its properties. Coding and redundancy of information. Transfer of information via discrete and continuous channels.