MSc in Physics: Final Exam Topics

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  1. Approximate methods in quantum mechanics. Time-independent perturbation method without and with degeneracy. Explanation of the time-dependent perturbation theory.
  2. Description of mixed states in quantum mechanics. Introduction and properties of the density operator. The time evolution operator.
  3. Quantization of the electromagnetic field, quasiprobability distribution functions, non-classical states of light (thermal, Fock, coherent, squeezed, "Schrödinger's Cat" state).
  4. Atom-field interaction in dipole approximation. Two level atom in a single-mode cavity, rotating wave approximation, dynamics. Rabi oscillation, Jaynes-Cummings-Paul model.
  5. The notion of a qubit, quantum gates, teleportation, dense coding, Deutsch-algorithm.
  6. The theory of entanglement, entanglement measures, multipartite entanglement.
  7. Properties and models of the atomic nucleus. Binding energy, size, spin, magnetic moment, isospin. The drop model, the Fermi-gas model, the shell model.
  8. Fundamental particles and their interactions. Classification of fundamental particles. Basic properties and symmetries of the weak, electromagnetic and strong interaction.
  9. Statistical physics of quantum mechanical oscillator. Heat capacity of crystals, explanation of the freezing of degrees of freedom.
  10. The ideal gas. Analysis of the ideal Bose and Fermi gas based on grand canonical ensemble using the occupation number approach.
  11. Crystal lattices. Bravais lattice, basis. Coordination number. The most common lattice types. Primitive cell, the Wigner–Seitz cell. The inverse lattice, first Brillouin zone.
  12. Lattice vibrations. The adiabatic (Born–Oppenheimer) approximation. Harmonic approximation. Dispersion relation of lattice vibrations. Acoustic and optical branches.
  13. Gauss beams and modes of laser resonators. Application of matrices in geometric and wave optics.
  14. Absorption and emission of light, the cross section. The amplification coefficient. Saturation. Homogeneous and inhomogeneous line broadening.
  15. Nonlinear optical processes. Methods of phase matching.
  16. LTI systems, signals in the time and frequency domain, Shannon-Nyquist theorem, Fourier and Laplace transforms used in circuit analysis and design, z-transforms, analogue and digital filters