## Scope of questions for State exams of Master's degree program

Branch: Quantum Technologies

Subject: Methods of Quantum Technologies

Subjects regarding the questions:

- 02KTPA1 Quantum Field Theory 1
- 02KO1 Quantum Optics 1
- 11TPLA1 Theory of Solid State 1
- 12KGOZ1 Quantum Generators of Optical Radiation 1
- 02KIK Quantum Information and Communication

- Relativistic hydrogen atom – relativistic particle in spherically symmetric electromagnetic field, solution of the hydrogen atom with the Dirac, fine and hyperfine structure of hydrogen.
- Symmetries and their applications in relativistic quantum theory – representations of Lorentz group, invariance of Klein-Gordon and Dirac equation with respect to Lorentz transformations, discrete symmetries C, P and T.
- Quantization of free fields – canonical quantization of scalar and bispinor fields, creation and annihilation operators, Fock’s space.
- Laser as a quantum generator of radiation – interaction of resonant radiation with the matter, population inversion, principle of optical radiation amplification, principle of laser radiation generation, basic elements of laser generator.
- Laser radiation properties – spectroscopic properties of laser radiation, spatial and temporal coherence, propagation of laser beams and their transformation.
- Mathematical methods of Quantum Optics – operator exponential, ladder operators,operator ordering theorems for the Heisenberg algebra, su(2) and su(1,1) algebras, Baker–Campbell–Hausdorff theorem and its special cases, Fourier transform, Dirac delta function.
- Light–matter interaction –two-level atoms, dipole approximation, Jaynes-Cummings model, resonant and off-resonant transitions, bare and dressed states, dipole force, momentum and angular momentum exchange between photon and matter particle.
- Electrons in a periodic potential –many-particle wavefunctions, Bloch functions, bandstructure of solids, methods of electronic-structure calculations for solids.
- Quasiparticles in solids –thermodynamic equilibrium, transport properties of solids, application of Green’s functions in solids.
- Quantum information approach to finite dimensional systems –von Neuman entropy, two-particle separable and entangled pure states, Schmidt decomposition, mixed bipartite states, reduced density matrix, quantum operations, completely positive trace preserving maps, partial transposition.