PX3248: Theoretical Physics
| School | Cardiff School of Physics & Astronomy |
| Department Code | PHYSX |
| Module Code | PX3248 |
| External Subject Code | 100425 |
| Number of Credits | 10 |
| Level | L6 |
| Language of Delivery | English |
| Module Leader | Professor Wolfgang Langbein |
| Semester | Spring Semester |
| Academic Year | 2015/6 |
Outline Description of Module
To develop understanding in the use of advanced techniques of mathematical physics.
To develop proficiency in using these techniques.
To apply these methods to physical problems.
On completion of the module a student should be able to
Derive and apply the concepts of functionals, variational methods and the use of constraints to a range of problems.
Derive and use Lagrangian and Hamiltonian mechanics.
Describe and apply the properties of groups, be able to construct group multiplication tables and derive representations and apply them to simple problems.
Solve unseen problems based on the techniques studied in this course.
How the module will be delivered
Lectures 22 x 1 hr, marked Exercises.
Skills that will be practised and developed
Mathematics. Problem solving. Investigative skills. Analytical skills.
How the module will be assessed
Examination and Continuous Assessment
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Spring Semester | 80 | Theoretical Physics | 2 |
| Written Assessment | 20 | Theoretical Physics | N/A |
Syllabus content
Calculus of variations: Fermat’s principle. Concepts of a functional and its variation. Stationary points and Euler-Lagrange equations.
Newtonian mechanics as an external principle: Lagrangian and the action. Constraints. Generalised coordinates. Lagrange multipliers.
Noether’s theorem: and conservative quantities.
Hamiltonian mechanics: Generalised velocities. Hamiltonian. Hamilton’s equations. Poisson brackets. Liouville’s theorem.
Applications: Path-integral formulation of quantum mechanics. Classical limit. Applications to continuous systems, physical fields. Rayleigh-Ritz variational techniques and Sturm-Liouville systems.
Group theory: Properties of groups and their application to symmetry and other problems. Group multiplication tables, character tables, representations. Degenerate modes forming a representation.
Background Reading and Resource List
Mathematical Methods for Physics and Engineering, K F Riley, M P Hobson and S J Bence (Cambridge University Press).
Mathematical Methods for Physicists, G B Arfken and H J Weber (Academic Press).