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