Physics

In this course, students employ the Dirac notation and algebraic methods (for example, spin and the harmonic oscillator), are introduced to basic approximation methods, such as perturbation theory and WKB, and look at scattering theory. 

This course explores the universe at the smallest distances and highest energies where quantum mechanics and special relativity collide. Through lectures from world-experts and hands on seminars, students will join the particle physicists from the Large Hadron Collider's ATLAS experiment in analyzing real proton collisions from the world’s largest machine - uncovering the secrets of the building blocks of the universe. The course uses coding notebooks to teach Python data analysis techniques used by professional particle physicists, progressing from the very basics, to rediscovering the Higgs boson, and culminating to an original analysis of real data. Along the way students develop computer coding, big data analysis and machine learning skills that will carry over to the real world.

The course provides an introduction to the theory of Special Relativity and some basic concepts of General Relativity. Topics include the need for Special Relativity (light propagation and key historical experiments); Einstein's principle of relativity, time dilation and length contraction; the geometry of spacetime (Minkowski space); the Lorentz transformation and causality; kinematics, dynamics and electromagnetism in Special Relativity; and a brief introduction to General Relativity.

This course covers basic and advanced techniques for manipulating and controlling laser light and laser pulses. This involves controlling intensity, frequency distribution, temporal profiles in order to design advanced optical systems for specialized tasks in industry as well as research. The course covers the following topics: Light propagation in anisotropic materials; Acusto-optical effects and modulators; electro-optical effects and modulators, non-linear interaction between light and matter; ultrafast optics, propagation of short laser pulses in dispersive non-linear media; and basic laser safety. Assumed prior knowledge: Basic Physics, Mathematics and Optics.

In this course, students get an introduction to common methods of theoretical physics. The course focuses on classical mechanics while including relativity and some electrodynamics, including covariant formulation. Students are introduced to and apply mathematical concepts such as Lagrangians, least-action principle, four-vectors, and tensors.

This course introduces the basic mathematical tools of Quantum Mechanics with a special emphasis on the connection between physical phenomena and mathematical modelling. The Hilbert space of physical states is reviewed as a particular case of a linear vector space. General properties of representation theory are discussed for the case of finite groups and are applied to quantum mechanical systems. Representations of the continuous groups U(1), SO(3), and SU(2) are presented and discussed in relation with invariance under translations and rotations. The general theory of angular momentum is introduced and applied to cases of physical interest. Quantum mechanical results are compared to their classical counterparts for a number of physical systems.

Monte Carlo simulations are a powerful computational technique for probabilistic and deterministic problems with applications to various fields including computer science, finance, economics, engineering, mathematics, and physics. The initial part of the course is about computer-simulated randomness and begins with pseudo-random generators and simulating one-dimensional random variables. From the moment that we can simulate one random variable, we can simulate a whole discrete process, such as Markov chains and use the simulations to extract statistical results of their equilibria. The course also explores applications in Physics via the Ising model and in Statistics via the goodness of fit tests. The course is a mixture of coding with probability theory, and students use the R software for the simulations.

This course treats the fundamental aspects of crystal growth, e.g. the thermodynamic prerequisites for crystal growth such as chemical potential, construction of binary phase diagrams, supersaturation, and nucleation. Further on, surface energies, surface diffusion, and Wulff’s theorem are studied. In the course section on epitaxial growth surface reconstructions, lattice mismatch, and dislocations, as well as characterization – both in- and ex-situ are discussed. Growth techniques and reactor models are also dealt with. During the course, the various moments are illuminated by examples from modern research, especially research on epitaxy of nanostructures. Assumed prior knowledge: FFFF11 Processing and Device Technology, a basic course in thermodynamics and materials science.

This course covers Maxwell equations, optical field-matter interaction, principles of lasers and rate equations, optical resonators, plane waves, ray-tracing, and Gaussian beams.

The course is divided in two parts. The first part of the course starts with a historical introduction to the building of the cosmological model. It is followed by the introduction of key concepts in Einstein’s theory of relativity, which then allows for the introduction of the Friedman-Lemaitre- Robertson-Walker cosmological model for an expanding universe. Several observational probes of cosmology are introduced, such as the cosmic microwave background, supernovae and the large-scale structure. From these, the presence and nature of dark energy and dark matter are examined. The course concludes the first part with a description of the earliest moments of the Universe and the building of a complete timeline for its history. The second part of the course focuses on extragalactic astrophysics. The goal is to overcome the assumption of galaxies as single points and understand the origin of their diversity. This diversity presents some structure, which is quantified in so-called “scaling relations” for different galaxy types. How they connect to the supermassive black holes at the centers of galaxies are discussed. Finally, the course looks into the stellar population composition of galaxies and some of the key evolutionary processes and understand how they lead to observed colors and estimates of galactic distances. Assumed previous knowledge includes NS-106B, NS-108B, NS-112B, NS-120B, NS-121B, NS-220B, and Python or other programming language knowledge (e.g. NS-109B). NS- 251B and NS-268B are recommended.