All Physics Courses

General physics for students in social sciences. Basic principles of classical and modern physics.Physics I (3+1+0) 3 ECTS 5

Properties of elementary functions; their graphs and values at special arguments. Expansions and approximation techniques used in scientific problems. Coordinate systems; areas and volumes of basic geometrical objects.(1+1+0) 1 ECTS 2

LATEX and MATLAB basics.(0+0+2) 1 ECTS 2

This course explores the ultimate limits to communication and computation with an emphasis on the physical nature of information and information processing. Topics include: Information and computation, digital signals, codes and compression, algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, Shannon entropy. The concept of entropy applied to channel capacity and to the second law of thermodynamics, and energy and temperature of physical systems are handled using the principle of maximum entropy.(3+1+0) 3 ECTS 5

Solar system: planets and the Sun, Milkyway. Other galaxies and the Hubble’s law. Bigbang. Inflation. The first few minutes, primordial nucleosynthesis. Cosmic Microwave Background (CMB) radiation. Life cycle of stars. Death of stars, supernovae. Brown dwarfs, white dwarfs. Neutron stars, concepts of general relativity, black holes, gamma ray bursts. Hawking radiation and evaporation of black holes. Dark matter and dark energy. The future of the universe.(3+1+0) 3 ECTS 5

Approximate calculations. Errors and rounding. Numerical approximations of functions. Numeric differentiation and integration. Monte Carlo methods. Random numbers. (3+2+0) 3 ECTS 6

Electromagnetic oscillations, AC circuits. Maxwell’s equations,electromagnetic waves, light and its propagation, reflection, refraction, geometrical optics, interference and diffraction, gratings and spectra, polarization, the particle-like properties of electromagnetic radiation: photons, Bohr model and the spectrum of the hydrogen atom.Physics IV (3+1+2) 4 ECTS 6

A survey course primarily for non-science students, with heavily visual character (slides and some videos). No calculus or science background needed. Contents of, and sizes in the cosmos. The Sun. Solar energy. Stellar observations. Double stars. Classification of stars. Birth and evolution of stars. Death of stars. white dwarfs, novae, supernovae, neutron stars, black holes. The Milky Way. Galaxies and the expansion of the universe. The Big Bang. Space exploration. Commercialization of space. future life in space. Space travel. SETI:Search for extraterrestrial intelligence. (3+1+0) 3 ECTS 5

Elements of probability theory, Bernoulli, Poisson and Gaussian probability distributions. Random walk and diffusion. Thermal motion, molecular distribution of energy in crystals and gases, definition of temperature and the Boltzmann factor, statistical characterization of thermal equilibrium, entropy. Entropy and heat: second law of thermodynamics. Entropy of mixing. Open systems and free energy minimum principles. Applications of the equilibrium conditions: the Clausius-Clapeyron equation, Raoult’s law, Henry’s law, Osmotic pressure. Ideal gases with internal degrees of freedom. Third law of thermodynamics. (3+2+0) 3 ECTS 5

The ocean floor. Ocean water and ocean life. The dynamic ocean. The atmosphere: Moisture, clouds, precipitation, air pressure and wind. Weather patterns and severe storms. World climates and global climate change. Origins of of modern astronomy. Our solar system. Light, astronomical observations and the Sun. Beyond our solar system(3+1+0)3 ECTS 6

Review of basic mathematical tools used in mechanics. Dynamics of particles and systems of particles, motion under a central force, conservation of energy and momentum, dynamics of rigid body motion. Introduction to the mechanics of continua. Relativistic dynamics.

Overview of a data acquisition and analysis system. Analog to digital converters. Range, unipolar and bipolar modes, multiplexing. Sample-and-hold circuits, single ended and differential inputs, computers. Software, data format and storage space, digital-to-analog converters. Sampling rates, low-pass filters, oversampling, aliasing. Maximum frequency present in a signal, digital-to-analog conversion. Transducers: Temperature, strain, force, acceleration, displacement, pressure. Isolation amplifiers, nonlinear sensors, linearization. Data manipulation: Data format; statistics; peak, through, and zero crossing detection. Data processing: Curve fitting, filters, spectral analysis, correlation, chaos.(3+0+0) 3

Metrology culture: Metrology and global trade, the four stages of the SI, types of metrology: primary, secondary and industrial metrology; maintenance of standards; calibration. Temperature Metrology: International Temperature Scale of 1990 (ITS-90) and realisation of the kelvin; Contact Temperature measurements; thermoelectric effects. Electrical Metrology: International realisation of d.c. electrical quantities through fundamental constants of physics: the volt – Josephson junction and the Ohm – quantum Hall effect; electrical standards. Dimensional metrology: international realisation of the meter. Temporal metrology: The cesium clock; optical frequency standards; dimensional standards; artefacts (Gauge blocks, micrometers, Vernier callipers, ring gauges, dial gauges). Uncertainty calculations; uncertainty budgets; updating the international definitions : The kilogram (kg), ampere (A), mole (mol), and kelvin (K). (3+0+0) 3

The aim of the course is to expose students to the basic idea of relativity, quantum physics and to the wide range of applications of these ideas. A survey of applications include the structure of atoms, molecules and nuclei, radioactivity and nuclear reactions, elementary particles, solid-state physics, astrophysics and cosmology. Emphasis on understanding physics of quantal phenomena and on order of magnitude estimates rather than formalism.

Curvilinear coordinates and tensor analysis. Further applications of complex variables: conformal mapping asymptotic methods, steepest descent, stationary phase, WKB method. Partial differential equations: boundary value problems involving the Laplace, wave and diffusion equations. Introduction to groups and group representations.

Continuation of PHYS 331 with emphasis on integrated circuits and the use of field-effect transistors in electronic circuit switching and digital methods: Linear and non-linear analog systems, combinational and sequential digital systems, metal-oxide semiconductor/large scale integrated (MOS/LSI) digital systems, digital to analog and analog to digital (D/A and A/D) systems.(2+1+2) 3

This course is intended to provide a basic understanding of radiation and its interactions with biological materials. Types of radiation and energy deposition mechanisms will be discussed. A general understanding of processes leading to cellular damage due to radiation will be sought. Topics will include: * various effects of radiation on biological systems * basic mechanisms of cell survival * environmental sources of radiation * aspects of radiation protection Level: The course is suitable for advanced-level undergraduates. (3+0+0) 3

Basics of astrophsical studies, positions of stars and their proper motions, distance determination to nearby stars; brightness calculations, angular radii of stars, spectral classification of stars, equations of stellar structure, physics of stellar interiors. (3+2+0) 3

Review of Maxwell's equations, and derivation of their differential form. Importance of continuity equation and displacement current. Derivation of EM wave equation in vacuum, simple solutions and their basic properties, including Poynting's vector etc. Interaction of radiation with matter, physical basis of the index of refraction. Boundary conditions and simple discussion of reflection and refraction of EM waves from conductors and insulators.

Electron ballistics and applications, electron emission (field, thermal and photoelectric.) Energy levels and energy bands. Conduction in metals and semiconductors. Electron statistics, Shottky barriers, p-n junctions and applications. Bipolar, field-effect and metal-oxide -semiconductor (MOS) transistors. Photoelectric devices. Negative resistance devices. (3+2+0) 3

Vector analysis, solution of electrostatic problems: Poissons’s and Laplace’s equations, method of images. Electrostatics in dielectric media, electrostatic energy. Electric current, magnetic field of steady current, electromagnetic induction, magnetic properties of matter, magnetic energy.

Fundamental concepts of relativity and quantum physics and their applications to the structure of single and multielectron atoms. Introduction to mathematical foundations of quantum physics. Emphasis on understanding quintal phenomena and order of magnitude estimates. Cannot be taken for credit in addition to PHYS 311.

Wave packets and uncertainity relations, the Schrodinger equation, one dimensional Potentials, the Schrodinger equation in three dimensions, angular momentum, the hydrogen atom, spin angular mimentum, the elementary treatment of addition of angular momenta, the structure of atoms and molecules, first order perturbation theory. (3+2+0) 3

Time dependent perturbation theory and applications. Scattering theory. Born approximation, partial waves, phase shifts and cross sections. Spin dependent scattering amplitudes. Introduction to relativistic quantum mechanics.(3+2+0) 3

Review and further study of the properties of quantum gases. Second quantization. Fluctuations and the fluctuation-dissipation theorem. Interacting Bose and Fermi systems. Superfluidity and super conductivity. Introduction to many body theory, Feynman and Goldstone diagrams. Selected applications in nuclear and solid-state physics. (3+2+0) 3

Continuation of Phys 442 Experimental Physics I. Hall effect in semiconductors, gamma-ray attenuation, laser applications, Na-doublet wavelength separation, Fabry-Perot interferometer, coherence length, diffraction of matter waves, Stefan Boltzman law and other modern physics experiments. A quick review of computers, programming, internet, vacuum techniques, particle accelerators, passage of radiation through matter and radiation safety. (2+0+4) 4

Computational methods used in astronomy. Study of celestial charts and atlases, as well as the analysis of astronomical data, use of computer programs on these subjects.(3+2+0) 3

Galactic and extra-galactic x-ray sources. Instrumentation, X-ray emission mechanisms, and the spectra of X-ray sources. (3+2+0) 3

A broad overview of numerical methods for solving all major problems in physics, including linear and nonlinear equations: Newton’s method, least-square problems and modelling, polynomial and spline interpolations, numerical differentiations, the Runge-Kutta method, numerical quadrature, probability distributions and random number generations, and the Monte Carlo method. Application of these methods to problems such as body problems, semiclassical quantization of molecular vibration, and the Ising model. Prerequisites: Consent of the instructor. (3+1+0) 3 ECTS 6

Generation, manipulation, propagation, and application of coherent radiation. Fundamental processes in lasers and masers. The basic theory of interaction of electromagnetic radiation with resonant atomic transitions. Laser oscillations, Raman effect, and non-linear optics. Light modulation, introduction to quantum noise theory.(3+2+0) 3 ECTS 6

Nuclear structure: liquid drop model, simple shell model, rotational and vibrational nuclei. Natural and artificial radioactivity, alpha, beta and gamma radiation. Nuclear reactions and cross-sections. Optical model, compound nucleus reactions, direct reactions. Heavy ion reactions. Fission.(3+2+0) 3 ECTS 6

Study of selected topics in physics not covered in other courses at undergraduate level. (3+0+0) 3 ECTS 6

Supervised reading and library work. Choice of material according to individual needs. Both written and oral presentations are required (1+0+0) 1 ECTS 3

Electrostatics and magnetostatics. Time-dependent fields and Maxwell’s equations. Multipole expansion of the radiation field. The interaction of radiation with matter. Interference and diffraction. Wave guides and cavities. Electromagnetism and relativity. (4+1+0) 4 ECTS 10

Functions of a real variable. Functions of a complex variable. Matrix algebra. Differential equations on the real axis. Linear vector spaces.(4+1+0) 4 ECTS 10

Kinematics, dynamics, and four-dimensional formulation of special relativity. The equivalence principle, introduction to classical differential geometry. Einstein’s equations and simple applications. Introduction to Big Bang cosmology and Inflation theories. White dwarfs, neutron stars and black holes. (4+1+0) 4 ECTS 10

Bound state problems. Approximation methods. Time dependent and independent perturbation theories. Scattering theory. Applications. Introduction to relativistic quantum mechanics and path integrals. (4+1+0) 4 ECTS 10

Cluster expansion for non-ideal classical and quantum gases, virial coefficients, phase transitions, magnetism. Ising model in two dimensions. Introduction to critical phenomena. (4+1+0) 4 ECTS 10

Laboratory experiments fundamental to the development of modern physics. Design and construction of experimental setups and data collection instruments.(2+0+4) 4 ECTS 10

Historical survey of workstations, Unix and Linux. Setting up a Linux.Workstation. Unix fundamentals. Graphics and Visualization. GPL’d scientific applications in Linux including the TeX/LaTeX system, the GNU compiler suite, linear algebra and matrix tools, statistical packages, symbolic programming tools. Use of program libraries. Techniques for power users. Supercomputer clusters, vector and parallel computing/using GPU. (3+0+2) 4 ECTS 10

Steady state behavior of dynamical systems. Poincare maps, stability and Liapunov exponents, limit sets, stable and unstable manifolds, phase portraits, construction of bifurcation diagrams. Fractals, dimensions and their determination, the Kaplan-Yorke conjecture, the embedding theorem, attractor reconstruction methods. Weakly deterministic systems and noise reduction (4+1+0) 4 ECTS 10

Creation and annihilation operators, Fock space description of the many body problems. Electrons and phonons, spin-waves, basic Green’s functions, linear response theory, quasi-particle concept. Hatree-Fock approximation, collective excitations, BCS theory, Bogoliubov’s theory of BEC, Hubbard model.(4+1+0) 4 ECTS 10

Description of instruments used in detecting X-ray emission in various wavelengths. Methods of data analysis. Production mechanisms of X-ray emission. Galactic and extra-galactic X-ray sources and systems. X-ray binaries. Background radiation.(4+1+0) 4 ECTS 10

Saminars offered by faculty, guest speakers, and/or graduate students designed to widen students’ perspectives on specific topics of interest and to expand their range of scientific research techniques and publication ethics.

Study of selected advanced topics under the supervision of one or more faculty members. Both written and oral presentations are required. (3+0+0) 3 ECTS 10

Symmetry properties. Second quantization. Quantum theory of electromagnetic field. Introduction to quantum electrodynamics. Applications involving electromagnetic and weak interactions.(4+1+0) 4 ECTS 10

Special relativity. Foundations of general relativity. Einstein-Hilbert variational principle. Hamiltonian formalism for Einstein field equations. Gravitational collapse. Gravitational radiation.(4+1+0) 4 ECTS 10

Fundamental concepts in differential geometry: manifolds, vector fields, tensors and forms, exterior derivative and Lie derivative. Symplectic manifolds and Hamiltonian mechanics. Lie groups and group actions on manifolds. Coadjoint orbits as examples of symplectic manifolds. Momentum map construction. Poisson manifolds. Some applications to integrable systems (4+1+0) 4 ECTS 10

Theory of chemical bonding. Molecular structure. Molecules in electric and magnetic fields. Symmetry and symmetry operations. Electronic, vibrational and rotational spectra. Techniques of molecular spectroscopy. Nuclear Magnetic Resonance. Properties of macromolecules.(4+1+0) 4 ECTS 10

Classical theory of the harmonic crystal, quantum theory of the harmonic crystal, measuring phonon dispersion relations, anharmonic effects in crystals, phonons in metals. Dielectric properties of insulators, semiconductors, magnetic properties of solids, superconductivity.(4+1+0) 4 ECTS 10

Optical generation, attenuation and amplification. Resonance fluorescence and light scattering. Nonlinear quantum optics. Quantum cryptography. Quantum computing. Entangled states and quantum teleportation.(4+1+0) 4 ECTS 10

Advanced study of experiment and theory of nuclear structure. SU(N) symmetries and the Standard Model. Quark model of hadrons. Baryon-baryon interaction. Weak Interactions in Nuclei. Nuclear Reactions, relativistic heavy ion collisions, optical model, meson-nucleus reactions. Mean field models. Nuclei far from stability, nuclear astrophysics, big-bang and stellar nucleosynthesis.(4+1+0) 4 ECTS 10

Nuclear Chromodynamics, introduction to Quantum Chromodynamics (QCD), structure of nucleons, lattice QCD, phases of hadronic matter and relativistic heavy ion collisions, medium-energy physics, nuclear and nucleon structure, and dynamics studied with medium- and high-energy probes (neutrinos, photons, electrons, nucleons, pions, and kaons). Studies of weak and strong interactions.(4+1+0) 4 ECTS 10

Phenomenology of particle properties and interactions; Experimental results. Conservation laws. Accelerators, particle detectors and techniques. Strong interactions, quark model predictions. Quantum Electrodynamics and Feynman diagrams.(4+1+0) 4 ECTS 10

Classical field theory. Canonical quantization. Dirac field. Interacting fields, perturbation theory. S-matrix and the LSZ formalism. Feynman graphs. Elementary processes. Radiative corrections. Regularization. Renormalization.(4+1+0) 4 ECTS 10

Ideas and current techniques in physics related to the study of critical phenomena in statistical mechanics and field theory. Landau theory of phase transitions, critical indices, scaling and universality, renormalization group, duality transformations, lattice gauge theory.(4+1+0) 4 ECTS 10

Study of selected advanced topics under the supervision of one or more faculty members.(4+1+0) 4 ECTS 10

Special topics not covered in other courses at PhD level (4+1+0) 4 ECTS 10

Guidance of doctoral students towards preparation and presentation of a research proposal in physics.(2+0+4) 4 ECTS 10