Module information: Second semester, 16 credits, 6 hours contact time per week.

Content: We study electric fields and magnetic fields that may change with time, leading to electromagnetic induction and Maxwell’s equations. These form the basis for mathematical modelling of electromagnetic waves. Quantum mechanics is introduced by studying quantum properties and the wave-particle duality of light. Taking the simple examples, such as the harmonic oscillator as first example we write down the Schrödinger equation in one dimension (essentially how its energy changes with position). From this equation we show that the quantum system is charcterised by eigenvalues and eigenfunctions. Time dependence, wave packets and tunnelling of quantum particles are discussed.

Relevance: The electrodynamics part of this module introduces Maxwell’s equations which describe all of electrodynamics and introduces the concept of electromagnetic waves. The module prepares the student for the further study of optics, special relativity and electric and magnetic fields interacting with matter. The quantum mechanics part of the module builds on the wave mechanics from Physics 224 to introduce the basic concepts of quantum mechanics, where a particle can only have particular quantised energies and is described by a wave function. This module is a first step to cutting-edge fields in physics and engineering where quantum properties and the interaction of light with matter is used in applications such as optical sensing and measuring, opto-electronics, lasers, the study of the universe by light and radio telescopes.

Outcomes: The electromagnetism part will enable the student to understand and appreciate the most important equations of electromagnetism, the Maxwell equations. The main goal is to show that the properties of electromagnetic waves can be derived from the Maxwell equations. This prepares the student to apply these equations in future modules.

The quantum mechanics part enables an understanding of the reasons why quantum mechanics is needed to describe the microscopic world. Students will understand what the Schrödinger equation is and why it is important and will be able to solve this equation for simple one-dimensional systems. Students will also solve and interpret the simplest quantum mechanical scattering processes which demonstrate how we get information about particles on the microscopic level.

Module information: First semester, 16 credits, 6 hours contact time per week.

Content: This module focusses on quantum systems with spherically symmetric potentials, with atoms as an important example. Such systems are described mathematically by spherical harmonic functions and have energy eigenvalues, but also orbital angular momentum and may also have spin angular momentum. The hydrogen atom is a discussed in detail as example. A calculation technique, time-independent perturbation theory, is introduced and used to study small perturbations to such a system.

Relevance: This module forms a core of quantum mechanics, one of the pillars of the physics. A systematic approach is followed to introduce the concepts, and one highlight is the explanation for the spectrum of hydrogen, which is treated in careful detail. The module leads directly to the Honours module in quantum physics and is also the basis for all modules in atomic and nuclear physics, solid state physics and a variety of laser and spectral physics applications.

Outcomes: The students are skilled in the practical application of quantum mechanical principles in three dimensional microscopic systems like nuclei, atoms and crystals.

Module information: Third quarter of the year, 8 credits, 6 hours contact time per week during the third quarter.

Content: In this module we study how electromagnetic waves (light) and material (consisting of atoms and molecules) interact. We describe the polarisation and magnetisation of materials. The propagation of electromagnetic waves in material and the behaviour of electromagnetic waves when passing from one medium to another is derived. Theory of special relativity is introduced as a principle that changes how we think about space and time, and therefore about everything. Studying how objects and electromagnetic waves interact when travelling very fast we can answer interesting questions.

Relevance: Electromagnetism is the basis for understanding the properties of materials, electronics, light and lasers. Together with Special Relativity it makes GPS devices, space missions and the understanding of the universe possible. We start with our knowledge of electromagnetic fields and waves, but now also taking the electric and magnetic properties of material into account. This enables us to predict how electromagnetic waves (light) will behave in different materials and at interfaces. This theory is essential for understanding of optics and photonics (light-matter interaction), lasers, solid state physics, and the advanced electromagnetism in Honours. The Special Relativity that has been discussed in first year is revised and developed further. We reach the point where we can predict what it would look like if one would travel at relativistic velocities. We learn the vector notation that is essential for further study (in Honours/postgraduate) of field theory and relativistic theories in quantum mechanics, nuclear physics and cosmology.

Outcomes: This course prepares the student for more advanced applications of electromagnetism, particularly in a medium. The student is also equipped with a working knowledge of special relativity. This course forms the foundations of more advanced courses in electromagnetism, optics, as well as advanced courses founded on relativity.

Module information: Second semester, 16 credits, 6 hours contact time per week.

Content: In this module students learn statistical concepts and numerical algorithms and apply these by coding their own simulation of a physical system (for example interacting particles in a gas or a magnetic crystal). The Monte Carlo method that is used is not only a numerical solution tool, but a means of performing numerical experiments from which much physics of many-particle systems can be learned (such as about phase transitions). Concepts such as deduction and induction, calculations with distributions of data, transformations and generating functions are introduced and applied.

Relevance: Simulation and inference play a key role in understanding systems and data in physics and in general. The underlying statistical concepts and Monte Carlo algorithms are used extensively in numerical work, including high-dimensional integrals, complicated systems of interacting particles, data compression and analysis and many others. Here we introduce the necessary computational and statistical tools and concepts to write such codes and to analyse the data they produce. The simulations will be of benefit to students following honours statistical physics (Physics 721), complementing the analytical approaches there. The third-year module, Physics 314, introduces some of the ideas relevant to this module, but also exposes students to the nature of the physical systems that we would want to study using computer simulations. This module is also relevant to all data science related environments and programmes.

Outcomes

• Insight and competency in the concepts and methods of stochastic systems and inference.
• Appreciation of the importance of random number generators and pitfalls in using them.
• Working knowledge of Monte Carlo simulation and its applications.
• Competency in the application of a numerical computer language.
• The ability to write and debug computer simulations.
• Developed skills in compiling and maintaining a record of own work and thoughts.

Module information: Fourth quarter, 8 credits, 6 hours contact time per week during the fourth quarter.

Content: In atomic physics we apply quantum mechanics to the electrons of atoms. The magnetic dipole moments of electrons and spin-orbit coupling explains the energy level structure of multi-electron atoms and the Zeeman spliting of energy levels in a magnetic field. We describe the interaction between light and an atom quantum mechanically, showing how light can be used to precisely control the quantum states of atoms, as is done in cutting-edge quantum computing techniques. Quantum mechanics applied in Nuclear physics explains the structure and properties of nuclei. It leads to the fundamental principles of nuclear stability, radioactive decay, nuclear reactions and the scattering of high energy particles by nuclei.

Relevance: The manipulation of atoms by light is an example of the sophisticated control of quantum mechanical systems on which cutting-edge fields such as quantum computing, quantum information, and ultra-accurate atomic clocks modern rely. The course gives a basic overview of atomic structure, and then studies interactions between atoms and light or static electric and magnetic fields, with a focus on how these interactions can be exploited to control the atom’s quantum state. Many of the concepts studied will be useful for students interested in doing research in either theoretical or experimental laser physics, quantum optics, atomic physics, quantum metrology or quantum information processing. The nuclear physics part of this module equips students with skills and conceptual understanding of nuclear structure, nuclear stability and decay, binding energy, cross sections and nuclear reaction mechanisms. This is an important foundation for further postgraduate studies, not only in nuclear physics, but also radiation and health, laser and theoretical physics programmes.

Outcomes

• Understanding of the concepts of atomic structure and magnetic coupling.
• Skills in the combination of quantum mechanics and classical electromagnetism.
• Skills in the use of the Bloch sphere to represent a qubit, with the two-level atom as example.
• Familiarity with phenomena in the interaction between atoms and electromagnetic fields such as the Zeeman and Stark effects, Rabi oscillations, laser cooling, optical trapping, optical lattices.
• Application of principles of conservation laws, energy and momentum quantisation and exponential decay.
• Familiarity with the terminology of nuclear physics.
• Skills in calculations and problem solving in nuclear physics.

Module information: 8 credits, full year

Content: In this module students work on individual projects on topics aligned with research done in the department and the content of their second and third year modules.

Relevance: This provides students with the opportunity to apply and refine their technical skills and to engage, somewhat independently, with the physics literature. Each student is required to prepare a report and presentation detailing their work, which is a valuable exercise in scientific communication and serves as a primer for the sizable project component of the theory honours programme.

Outcomes: This course exposes the student to independent project work. The student is skilled in the use and reading of physics articles and textbooks and the writing of a scientific report.

Module information: 16 credits, 3 hours per week in the first semester and 6 hours per week in the second semester.

Content: Students The module consists of practical laboratory work in Physics. Students work in small groups to do selected experiments, engaging in experimental design, data analysis and scientific communication. The experimental topics are related to the experimental research in the Department, including nuclear physics, laser physics, optics and quantum information.

Relevance: The module consists only of practical sessions. It requires the students to perform a wide range of experiments in the field of laser physics and nuclear physics with a focus on independent experimentation, including experiment planning and design. The students will be required to write scientific reports and present oral accounts of experimental procedure and results. The skills of independent planning, scientific writing and presentation are essential for post graduate studies and scientific careers. The topics of the experiments are always closely aligned with the research topics in the Physics department, therefore providing the students with insight into the local research.

Outcomes: The student should be able to perform experiments of known or unknown phenomena with a degree of independence, using a variety of techniques for measurement and data analysis. This includes:

• Understanding of the problem. Study of underlying theory.
• Planning of experiment and setup of instrumentation.
• Doing measurements systematically, recording data.
• Data evaluation, possibly modelling, presentation.
• Interpretation of results in terms of the original problem.
• Presentation of results: written report and oral presentation.
• Experiments should be fun!
• Experiments are related to real research projects carried out at Department.