AGH UST Main Page » Doktoranci » Doctoral Schools » AGH Doctoral School » Admissions 2022/2023 » Entry exam topics 2022/2023 » Academic Centre for Materials and Nanotechnology » Physical sciences

The candidate is expected to answer questions from the general list and one of the specialized list of his/her choice.

- Momentum conservation principle
- Angular momentum conservation principle
- Energy conservation principle
- Galileo and Lorentz transformations
- Mass-energy equivalence, examples

- charge conservation principle
- Electrostatic field, scalar potential
- Magnetic field, Vector potential of magnetic field
- Electric charge in magnetic field (examples of applications)
- Electromagnetic wave equation
- Plane and spherical waves
- Interference and diffraction

- Maxwell distribution
- Boltzmann distribution
- Temperature
- I principle of thermodynamics
- Entropy and II principle of thermodynamics

- Black-body radiation
- Photoelectric effect
- Compton effect
- atomic spectral lines
- Electron diffraction on crystal (Davisson-Germer experiment)
- Stern-Gerlach experiment, electron spin
- Postulates of quantum mechanics
- wave function
- uncertainty principle

- atom and its structure
- chemical bonds
- electron band structure of solids
- electrical conductivity of metals, semiconductors and insulators
- superconductivity
- magnetism of solids
- crystal structure

- Synchrotron radiation – generation, properties and examples of applications in biological studies
- Methods in surface science (for example: AES – Auger electron spectroscopy, XPS – X-ray photoelectron spectroscopy, SIMS – secondary ion mass spectrometry)
- Spectroscopic methods in biological and medical investigations (for example: EPR,
- NMR, Mössbauer spectroscopy, Infrared and Raman spectroscopy)
- Microscopies of high resolution (electron microscopy, STM – scanning tunneling microscopy, AFM – atomic force microscopy, confocal microscopy)
- Biological membranes – their structure and properties
- Proteins and enzymatic reactions
- Radiative and non-radiative energy transfer (Jabłoński diagram, Förster resonance energy transfer (FRET), Dexter energy transfer)
- Electron transfer in biological systems (temperature dependent and temperature independent – tunneling)

- Elementary particles – the standard model
- Evolution of the Universe (in particular: creation of elements)
- Properties of atomic nuclei and the methods of their investigation
- Nuclear forces, binding energy, models of atomic nucleus
- Radioactive transformations of atomic nuclei
- Natural radioactivity of rocks, waters and air
- Accelerators of charged particles
- Nuclear reactions (in particular: fission and fusion of nuclei)
- Interaction of charged particles, gamma radiation and neutrons with matter
- Detection of charge particles, gamma radiation and neutrons
- Neutron sources
- Applications of nuclear isotopes (chosen examples)

- Crystallography – basic definitions
- Free-electron model
- Interatomic bonds in solids
- X-ray diffraction
- Phonons
- Electron band-structure
- Semiconductors
- Magnetic properties of matter
- Superconductivity
- Nuclear methods in condensed-matter investigations
- Synchrotron radiation – generation, properties and examples of application
- Basic ideas of new materials: quasicrystals, fullerenes, high-temperature superconductors, conducting polymers, semiconducting nanostructures

- Postulates of quantum mechanics – illustrated by examples
- Physical interpretation of wave function
- Quantum stationary states
- Electron spin: experiment and theory
- Quantum statistics: : bosons and fermions
- Pauli exclusion principle
- Exchange Interaction
- Laplace and Poisson equations and physical processes described by these equations
- Diffusion equation and physical processes described by this equation
- Simple finite-difference methods of solving equations of classical dynamics
- Physical and numerical foundations of classical molecular dynamics
- The method of simulated annealing

- Elementary particles – the Standard Model: material particles and bosons mediating the interactions. Unification of electroweak interactions.
- Relativistic momentum, kinetic energy, total energy, relativistic effects, fourvectors formalizm and relativistic ivariants (e.g. CMS)
- Feynman diagram formalism
- Electromagnetic processes (photoeffect, Compton effect, pair production, total cross section)
- Strong interactions (inelastic scattering)
- Accelerators of charged particles (colliders & fix-target, linear & circular).
- Bethe-Bloch formula.
- Elementary principles in particle detection, spectrometry, tracking and calorimetry.
- Fundamental concepts of collider experiments – on the example of LHC experiments (ATLAS, CMS, ALICE, LHCb).
- The working principles of radiation detectors (gaseous detector, scintillation counter, semiconductor detector, photomultiplier).
- Principles of operation of basic semiconductor devices: p-n junction, bipolar transistor, MOS transistor
- Basic principles of signal processing (signal processing in spectrometric chain, filtering, ENC).

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