Undergraduate Programme and Module Handbook 2023-2024

# Module PHYS4241: THEORETICAL PHYSICS 4

## Department: Physics

### PHYS4241: THEORETICAL PHYSICS 4

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2023/24 | Module Cap | Location | Durham |
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#### Prerequisites

- Theoretical Physics 2 (PHYS2631) AND Foundations of Physics 3A (PHYS3621).

#### Corequisites

- Foundations of Physics 4A (PHYS4251) if Foundations of Physics 3A (PHYS3621) was not taken in Year 3

#### Excluded Combination of Modules

- Theoretical Physics 3 (PHYS3661).

#### Aims

- This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
- It builds on the modules Theoretical Physics 2 (PHYS2631) and Foundations of Physics 3A (PHYS3621) by introducing more advanced methods in electromagnetism that can be used to investigate more realistic problems and concepts, and by introducing more advanced topics in quantum mechanics as well as addressing further applications and conceptual issues of measurement and interpretation.
- It develops transferable skills in researching a topic at an advanced level and making a written presentation on the findings.

#### Content

- The syllabus contains:
- Relativistic Electrodynamics: Einsteinâ€™s postulates, the geometry of relativity, Lorentz transformations, structure of space-time, proper time and proper velocity, relativistic energy and momentum, relativistic kinematics, relativistic dynamics, magnetism as a relativistic phenomenon, how the fields transform, the field tensor, electrodynamics in tensor notation, relativistic potentials, scalar and vector potentials, gauge transformations, Coulomb gauge, retarded potentials, fields of a moving point charge, dipole radiation, radiation from point charges.
- Quantum Theory: Scattering experiments and cross sections; potential scattering (general features); spherical Bessel functions (application: the bound states of a spherical square well); the method of partial waves (scattering phase shift, scattering length, resonances, applications); the integral equation of potential scattering; the Born approximation; collisions between identical particles, introduction to multichannel scattering; the density matrix (ensemble averages, the density matrix for a spin-1/2 system and spin-polarization); quantum mechanical ensembles and applications to single-particle systems; systems of non-interacting particles (Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics, ideal Fermi-Dirac and Bose-Einstein gases); the Klein-Gordon equation; the Dirac equation; covariant formulation of Dirac theory; plane wave solutions of the Dirac equation; solutions of the Dirac equation for a central potential; negative energy states and hole theory; non-relativistic limit of the Dirac equation; measurements and interpretation (hidden variables, the EPR paradox, Bellâ€™s theorem, the problem of measurement).

#### Learning Outcomes

Subject-specific Knowledge:

- Having studied this module, students will have developed a working knowledge of tensor calculus, and be able to apply their understanding to relativistic electromagnetism.
- They will have a systematic understanding of quantum theory, including collision theory and relativistic quantum mechanics.

Subject-specific Skills:

- In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.
- They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.

Key Skills:

- Students will have developed skills in researching a topic at an advanced level and making a written presentation.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Teaching will be by lectures and workshops.
- The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.
- Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.
- Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.
- Lecturers will provide a list of advanced topics related to the module content. Students will be required to research one of these topics in depth and write a dissertation on it. Some guidance on the research and feedback on the dissertation will be provided by the lecturer.
- Student performance will be summatively assessed through an open-book examination and a dissertation and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The dissertation will provide the means for students to demonstrate skills in researching a topic at an advanced level and making a written presentation.
- The problem exercises and progress test will provide opportunities for feedback, for students to gauge their progress, and for staff to monitor progress throughout the duration of the module.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 38 | 2 per week | 1 Hour | 38 | |

Workshops | 17 | Weekly | 1 Hour | 17 | |

Preparation and Reading | 145 | ||||

Total | 200 |

#### Summative Assessment

Component: Open-book examination | Component Weighting: 80% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Open-book examination | 100% | ||

Component: Dissertation | Component Weighting: 20% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

dissertation | 1500 words | 100% |

#### Formative Assessment:

Problem exercises and self-assessment; one progress test, workshops and problems solved therein.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University