Physics BSc
Our group is the core component of the Applied Physics course, delivering teaching at level 4 in:
- Optics (semester 1)
- Electromagnetism (semester 2)
- Quantum mechanics (semester 2)
You will find more course-specific content on Canvas (available when the course will start, in September 2017). We will strive to deliver the Optics module as a blended e-learning experience, with video-recording of the material.
Our head of group is also the Director of Studies for Physics at the University, with responsibility for the success and well-being of all the enrolled students.
The syllabus of the overall course reads as follow.
First Year (Level 4)
Semester 1
Mechanics
Mechanics is the epitome of physics: it describes and explains the behaviour of physical objects around us, from falling apples to orbiting planets. The first great achievement of Physics as a Science was Newton's understanding that the same laws describe both. The wide range of physical phenomena that can be explained from the laws of classical mechanics makes it a pillar of virtually all other scientific fields. This makes this topic one of the oldest and largest subjects in science, engineering and technology. The module will concentrate on Newtonian mechanics as an introduction to the methods and thinking of a physicist. It will also expand on this classical material to introduce more advanced ideas and concepts of Mechanics, including fluid mechanics, applied mechanics and Lagrangian mechanics. The other branch of mechanics, quantum mechanics, will be studied in a different module. The module will thus focus on the study of the motion of classical bodies and teach how to calculate in various reference frames their position, velocity and acceleration as a function of time under the action of applied forces, with applications to projectiles, astronomical bodies and macroscopic rigid bodies. Important concepts such as conservation laws and symmetry are introduced and studied in a plethora of variations. The dynamics of oscillators, in particular the harmonic oscillator, will be studied in great detail, with emphasis of how various terms in the equation correspond to various scenarios describing a physical object, with basic concepts such as driving and dissipation. The value and interest of exact (closed-form) solutions as compared to approximations will be highlighted.
Laboratory sessions will be conducted to develop a firm grasp of Physics as an experimental and applied science, focusing on fundamentals such as the study of pendulums and springs, and reproducing pioneering experiments such as the free-falling objects of Galileo. Along with a traditional pen-and-paper approach, an introduction to fully automatised, computer-assisted modern laboratories will be given through a dynamic wireless smart-cart system.
Optics
Optics is the Science of light. As our most privileged human contact with the surrounding world is through the eye, optics has always been a central topic in our description of the observable universe. Light is also one of the key technological resources with practical applications found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers and fibre optics. Because light is a particular type of electromagnetic waves (with frequencies close to those visible to the naked eye), optical phenomena are just a branch of classical electromagnetism. The full theory is so large however and this particular type is so important that it comes as topic of its own. The module will study two aspects of light: as rays (geometrical optics) and as waves (physical optics). The emphasis will be on geometrical optics with detailed study of optical instrumentation and their applications (magnifiers, cameras, microscope and telescopes, including human vision) in both the classroom and through laboratory sessions. The most important notions of physical optics that provide a more general framework to optical phenomena and prepare more advanced applications, such as interferometry, polarization and diffractive-optics, will be studied at a more introductory level. The module will also survey some advanced notions of photonics in the modern applications of light: the use of lasers, optical detectors, waveguides, fibers and devices for imaging, display and storage, to complete this first outlook on light.
Mathematics
Physics is an exact science and is articulated, even in its most applied and experimental aspects, through mathematics of various types and levels. Mathematics will therefore be a topic that will be studied in all years of the BSc (Hons) Applied Physics course, to develop skills to enter employment fully armed with modern mathematical and numerical methods. The first year will refresh previous knowledge, in particular of calculus (of real and complex numbers), and move on from there to introduce basic real analysis (functions of one variable, trigonometry) assuring a working knowledge of integration and derivation. The bulk of the module will be on i) the theory of ordinary differential equations and ii) linear algebra. Both will be studied with practical considerations in mind but algebra will also be introduced as the study of abstract mathematical structures, with the study of sets, groups and vector spaces. The emphasis will remain on vector calculus and computation with matrices and tensors. Finally, rudimentary notions of probability will be studied, with statistics being covered in laboratory sessions. The module will conclude by introducing functions of several variables & their partial derivatives, to be revisited again on next year.
Semester 2
Electromagnetism 1
Physics is a Science of "unification", striving to find general fundamental principles that explain the largest possible extent of observed phenomena with the simplest set of physical laws. In this respect, electromagnetism is the standard theory that led to the unification of two important branches of physics: electricity and magnetism. Its further extension led to the "standard model" of particle physics. This level 4 module will bring us toward the culmination of the theory, namely Maxwell's equations, through preparatory study of vector calculus and in-depth separate analyses of the electric and magnetic fields. This will create familiarity with the respective phenomenology that are of considerable importance for the subject of applied physics. These phenomenon fall under the denomination of electrostatic (the science of electric charges) and magnetostatic (the science of magnets). Special emphasis will be given to electronic circuits as an applied illustration of important concepts of electrodynamics, and to support the laboratory sessions that will focus on these aspects.
Quantum Mechanics
Quantum mechanics describes objects at small scales and low energies. Since our technology relies heavily on miniaturisation, quantum effects become increasingly important in the applied and engineering branches of physics. Every field of physics has its "quantum counterpart". Furthermore, quantum physics is so counter-intuitive that it makes a complete break with so-called "classical physics", even though the latter includes modern developments such as relativity that revolutionised our understanding of the nature of time and space. Being familiar with quantum concepts is not only important from the scientific viewpoint but also from cultural and philosophical point of views: from the quantum Zeno effect to Schrödinger's cat. Quantum physics is so pivotal in modern physics that some aspects of it will be studied in at all three levels of study in the BSc (Hons) Applied Physics course.
This level 4 module will introduce the problems with classical physics and the need for a paradigm change, how this was made through the concept of a wavefunction and its associated Schrödinger equation. Solving the latter on elementary cases with time-independent Hamiltonian will allow to delve into the interpretation and meaning of the theory. Its axiomatic formulation in an Hilbert space will introduce the formal and abstract aspects. The concept of quantum correlations will be introduced and contrasted to classical physics, with an introduction to the concepts leading to Bell's inequalities. Special emphasis will be given to applications of quantum physics and how it promises another technology revolution for the coming decades. The module will conclude on the two-body problem in quantum mechanics, introducing the notion of bosons and fermions.
Scientific Computing
With the advent and generalisation of computers, Science has taken a new turn. It is now possible to make breakthrough discoveries or reach record-breaking calculations with a standard home computer. Whilst this influences all of the Sciences, Physics is particularly affected since a physical problem is often reduced to solving an equation, which can usually be done numerically. The unique skillsets of Physicists in adapting computer resources to the wide variety of their problems make them highly sought in numerous areas extraneous to their speciality, such as in finance and banking, where they have proven to be the most versatile, resourceful and able users of computer simulations. Since numerical methods are a considerable resource, that will prove useful whatever the future occupation of any physicist will be, the topic will be studied throughout the course.
This module will first introduce the use of computer resources in networking systems. The unix/linux-based scientific computing environment will be introduced for its scripting features, data processing tools as well as for the standard scientific document typesetting system (LaTeX). This environment will contribute to applications for the Enterprise and Employability Award through content-based rather than look-focused approach in setting up a resume, motivation letter and writting an application, and later for the preparation of Research-level scientific reports for the laboratory experiments. The module will then introduce basic algorithms and teach elementary numerical methods such as solving sets of linear equations, methods of interpolation, finding roots of nonlinear equations, evaluating integrals and will introduce direct methods for solving ordinary differential equations. The modules will be intensively based on laboratory sessions and practical work and will also teach the necessary programming skills. To endow the student with modern and powerful tools, the course will be taught in the Python programming language, which is a high-level language fairly easy to learn and affording great code readability. This will form a good starting point for development of other programming languages that will be needed on the professional market (where Python is also highly sought). It allows for interacting programming through ipython and Jupyter that is of great pedagogical value. All of these resources are open sources so students can study and apply their knowledge outside of the university.
Second Year (Level 5)
Semester 1
Electromagnetism 2
This module builds upon the material studied in the 4AP004-Electromagnetism I, which concluded with the presentation of Maxwell's equations, brought together by separate studies of electric and magnetic phenomena. This level 5 module combines the equations, adding the one final piece brought by Maxwell, and show how this complete description of the time-and-space varying electromagnetic field opens a whole new realm of physical phenomena and applications. The module will show in particular how light emerges out of the equations and, remarkably, how the speed of light in a vacuum arises as a universal constant that is dependent only on the electrical permittivity and magnetic permeability of free space. It will study light's propagation subsequent to its radiation by a source, a problem known as "electrodynamics". The study of light's interaction with matter will allow to revisit one's knowledge of optics from a more fundamental point of view and better appreciate the hierarchy of the subfields of physics. Intensive laboratory sessions will provide insights through a variety of microwave experiments.
Solid State Physics
Solid state physics is an introduction to condensed matter physics, within which you will study the particular topic of widest interest: that of rigid matter. This topic is both better understood and of greatest practical use for technology and industry, the bulk of which relies on a particular types of solids—semiconductors—that provide the bulk material for electronic devices. Solid state physics considers how large-scale properties of solids arise from fundamental phenomena taking place in crystalline ordering of densely packed atoms. It is a rich and fruitful field that illustrates how simple ideas lead to extremely complex behaviours when involving many-body physics. It also brings together various subfields of physics, from classical to quantum mechanics, electromagnetism and statistics, to this playground and considers how various phenomena have different origins or, in contrast, stem from a combination of several disciplines. This develops the ability to explain something out of a simple model. Solid state physics focuses on the mechanical (e.g., hardness and elasticity), thermal, electrical, magnetic and optical properties of crystals. This module will describe all these aspects in details with a joint theoretical description in class and laboratory experimentation, contrasting different types of solids as probed through these various characteristics.
Mathematical Methods
This module will strengthen the mathematical apparatus required to support the increasing knowledge and depth of description of the physical phenomena, now extending to functions of several variables and their associated partial differential equations. Calculus of vector field will also be covered in parallel through the Electromagnism II module. Complex analysis will extend calculus to the case of complex functions of complex variables, showing the stronger notion of derivatives through the CauchyRiemann's theorem and the notion of analycity. The module will then starts a paradigm shift towards providing the "Mathematical Methods" which are useful in physics, that consist of specialized techniques and tools from a given Mathematical discipline, that the physicist does not usually need to know in its entirety. Finally, the study of dynamical systems will be studied with some emphasis on applications for applied Physics (bistability and hysteresis of nonlinear oscillators, laser thresholds, Liénard systems, relaxation oscillations, etc.)
Semester 2
Thermodynamics and Statistics
The unit to measure the "number of things", the mole, is unfathomably large, of the order of $10^{23}$ objects. In such conditions, describing a mole of, say, a gas, seems a daunting task, given the sheer amount of underlying constituents that interact between each other. It is one insight of thermodynamics and statistical physics that such complex objects can however be described, essentially completely and exactly with only a few variables. In fact, the larger the number of objects, the more accurate the description. An important illustration is the case of thermodynamics, the science of heat-flow and its relation to work, that is such a macroscopic consequence of statistical (and quantum) mechanics. An understanding of thermal physics is crucial, not only to modern physics, but also to chemistry, biology, computer science and, of course, several subfields of engineering. The module introduces key notions of statistical mechanics, with a strong emphasis on thermodynamics, but surveying also the other fields of interest for applied Physics, namely, solid state physics, optics and also complex systems.
Quantum Physics
This level 5 module on quantum mechanics will first extend the theory to a three-dimensional setting, taking advantage of a now better familiarity with more advanced mathematical tools, and then turn to applications of the theory to various cases and concepts of applied interest, including the description of the fundamental, and most common, atom in the universe: hydrogen. It will be shown how quantum mechanics explains the empirically observed spectroscopic lines of this and other chemical compounds. The physics of spin will be studied in detail, considering problems such as the dynamics of an electron in a magnetic field, already studied in the electromagnetism modules, being revisited here by the quantum theory. The addition of angular momenta will provide an opportunity to play with quantum algebra and see how quantum numbers behave in an unfamiliar fashion that requires much practice to be acquainted with. Useful and important computational techniques will be studied, such as perturbation theory, to provide a finer description of the hydrogen atom, or the variational principle, to study the molecule of Helium. Other techniques, such as the WKB approximation, adiabatic approximation, etc., will prepare the student for advanced use of the quantum theory in the description and understanding of the most contemporary systems and problems of modern physics, to be fully unravelled at level 6.
Numerical Methods
This module will, in line with the expertise now acquired in the other disciplines of applied physics, provide the tools to solve numerical problems that are time-dependent, in particular those involving fields. Concrete problems that arise from other modules, such as solving the heat equation in nontrivial geometries, computing a flow with various models and approximations, propagating a complex wavefunction or solving Maxwell equations, will be brought to the computer and studied there numerically, with emphasis on notions such as stability and convergence. This module will also provide a first experience with research-type problems involving the student's own analysis and judgement, to direct the most promising directions for further exploration.
Third Year (Level 6)
Semester 1
Condensed Matter Physics
Condensed matter physics describes the wide variety of condensed phases of matter, including, but not limited to, the most familiar forms that are the liquid and solid states, whose dedicated study makes a topic of its own. Indeed, condensed matter extends to more exotic phases such as glasses, liquid crystals, quasi-crystals, plasmas, (anti)ferromagnets or non-Newtonian fluids (that change their viscosity or flow behaviour under stress), to name a few. Condensed matter also describes fundamental states of matter ruled by quantum phenomena, including Bose-Einstein condensates, superconductors that conduct electricity without losses, and superfluids that flow without resistance. As such, condensed matter relies extensively on a combination of quantum mechanics, electromagnetism and statistical mechanics. It is an advanced topic that requires a firm understanding of all these disciplines, that, when brought together, give rise to the emergence of new concepts, following Anderson's credo: "More is different". The module will cover such important modern notions of contemporary physics, including broken symmetries, order parameters and topology.
Computational analysis
The mathematical and computational aspects of physics will be brought together in a single module to provide the tools required for the student to develop their own capacity in identifying and solving problems. Topics in Mathematics will include Fourier and Laplace analysis, variational calculus, Green functions, and Optimization. More computer-oriented topics will introduce students to the field that sits at the boundary of Physics and Mathematics and Computer Science and that emerges as a discipline of its own: known as "numerical experiments" (or "simulation experiment"). Topics in this subject will include Monte Carlo methods, theory of algorithms and some notion of complexity and information theory, as well as an introduction to parallel and distributed programming. Emphasis will be given to computational analysis of the systems studied in Condensed Matter physics module (6AP001).
Research 1
This module will prepare the level 6 student to undertake, under supervision, autonomous work in a University environment to produce original research. This will aid future employability, opening up the possibility to apply for a masters course or to join the most dynamic areas of the employment market place. This module will bring together all the skills developed and perfected up till now, including literature review, rapid understanding and distilling of considerable amounts of complex information, as well as a capacity to identify the required tools to tackle a problem. This first-semester module will present students with a set of problems, with various levels of laboratory, computer, and theory-based content (in most cases with a blend of all these). These problems will be discussed with a personal research-active tutor, so as to agree on a topic of mutual interest and the direction to explore. In this first stage, students will undertake a literature review and produce a scientific poster and written reports relating to research undertaken. The poster will be presented to the rest of the Physics students (including level 4 & 5 students), who will provide feedback and comments.
Semester 2
Applied Physics
This module on Applied Physics will apply one's knowledge of Physics into the design, engineering and development of applications and technology. In this respect, it strongly overlaps with the subject of engineering. However, while the later focuses on making things work, applied physics focuses on how and why things works. Applied physics can be of a purely theoretical character, and some of the most important open problems of physics are precisely of this type, e.g., how to make a superconductor at room temperature; or how does unconventional superconductivity, that seems a road towards this goal, work?; or what other mechanisms could one imagine to explore other way to reach that goal? This module will, nevertheless, be strongly laboratory-based. It will cover a large breadth of advanced topics in optics and electronics and how they can be used to implement various types of devices. It will also build foundations and material for research-oriented work, to be undertaken as part of this year's study or in preparation for one's future career. Topics will range from the study of advanced optics and electronics, laser beams, liquid crystals, semiconductor heterostructures, metamaterials, opto-electronic devices, photonics, nonlinear and ultrafast optics.
Quantum Optics
This last module on quantum physics will quantize the electromagnetic field to reach the most successful Physical theory, that which inspired the so-called "standard model" of particle physics, namely, quantum electrodynamics. We will stay at a non-relativistic and more applied level to study a sub-field known as "quantum optics", which describes interactions of light and matter at the microscopic level. The underlying concepts are important to describe basic phenomenology such as blackbody radiation or the photo-electric effect, which started the whole field of quantum physics. More generally, they are also of increasing importance for the design of contemporary light-based technology, known as "photonics", increasingly at the edge of the fundamental barrier of dealing with a few or single particles. This would allow the implementation of quantum information processing, for which quantum optics is one of the most actively investigated platforms. Laboratory experiments will accompany this module, to bring students in contacts with single particles and their quantum behaviour, now dealt with at a concrete and applied level. Theoretically, an overview will be given of the more advanced material needed at the research-level in several areas of condensed matter physics, namely, quantum field theory.
Research 2
This module builds upon the "Research 1" module (6AP003), engaging students in active research related to an identified problem. A weekly meeting will bring together the student and their personal research-active tutor, and/or the rest of the class, to describe progress, ideas, problems and difficulties and, if applicable, results. At the end of the module, the student will provide i) a 15 minutes oral presentation in conference style, in front of a panel of referees who will ask questions on the research results, and a ii) written report in the form and style of a research article. In case of valuable results in a nontrivial problem, the latter will be submitted for publication and evaluated by research peers beyond the walls of the university.
2017/2018 Edition
This is the first edition, the beginning of a great enterprise. People who like to build and who want to achieve, welcome!
This is the academic calendar:
And these are the weekly-calendars for Applied Physics: