The list of topics for the entry exam to the AGH Doctoral School in discipline Physical sciences

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

I. General topics:

1. Fundamentals of classical and relativistic mechanics:

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

2. Electromagnetism:

  • 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

3. Thermodynamics and statistical physics:

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

 4. Experimental and theoretical foundations of quantum mechanics:

  • 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

5. Structure of matter:

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


II. Specialized topics

1. Fundamentals of biophysics

  • 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)

2. Fundamentals of nuclear physics

  • 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)

 3. Fundamentals of solid state physics:

  • 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

 4. Fundamentals of theoretical and computational physics

  • 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

5. Elements of  elementary particle interactions and detection techniques

  • 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)
  • Feynmana 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-Blocha 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).