Following a brief review of ordinary differential equations, the lecture deals with partial differential equations in detail, with applications across physics. Separation of variables, physical boundary conditions and Fourier expansion are introduced using the Laplace equation to determine a temperature profile in a hot plate. These techniques are subsequently transferred to the Poisson, diffusion and wave equations. The lecture ends with an introduction to Fourier transforms.
Dyma fersiwn Cymraeg y nodiadau fg260 Ffiseg Mathemategol hefyd. [more]
This section of the Condensed Matter module covers the different ways of describing the structure of solids: crystal lattices and coordination polyhedra. Diffraction techniques are used to study crystal structures and their imperfections. In the magnetism section, dia-, para- and ferromagnetic states and the transitions between them are compared. Other collective phenomena in solids such as superconductivity and ferroelectricity are also covered. There is also a practical x-ray diffraction workshop included in this module. [more]
Third-year lab consists of a project for all physics students. This is usually a year-long effort, although joint students do a shorter version in the second semester only. Students generally work in pairs, although finalists are expected to write an individual report at the end. A wide range of projects is available to choose from on the website, and we are also happy to consider students' own ideas if they fit with the goals of the module. Please speak to potential supervisors! Each project is structured into a literature review, project planning, experimental and dissemination phase. Projects can be experimental, observational, theoretical or software development. Dyma fersiwn Cymraeg y ddogfennaeth prosiect BSc hefyd. [more]
I no longer teach this module but have decided to leave the notes online for general reference. These pages give an overview of simple quantum systems which can be solved analytically, increasing in complexity up to the hydrogen-like atom, while delivering the necessary mathematics in examples. The concept of approximating solutions to the Schrödinger equation by linear combination is introduced and applied to atoms more complex than hydrogen and to molecules and solids made up of many atoms. The quantum-mechanical property of spin is discussed in terms of its implications for experimental physics. [more]
These are notes of a Fourier workshop I used to run over three days for our 3rd year MPhys students. This is now covered in other modules, but I've decided to keep the notes online as they may be useful to someone out there. [more]