Examination topics in the 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)
  • 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).