Module PHYS4191: THEORETICAL PHYSICS 4

Department: Physics

PHYS4191: THEORETICAL PHYSICS 4

Prerequisites

• Foundations of Physics 3 (PHYS3522).

Corequisites

• None.

Excluded Combination of Modules

• Theoretical Physics (PHYS3551).

Aims

• This module is designed primarily for students studying Department of Physics and Natural Sciences degree programmes.
• It builds on the Level 2 modules Foundations of Physics 2 (PHYS2511) and Mathematical Methods in Physics (PHYS2521) and the Level 3 module Foundations of Physics 3 (PHYS3522) and provides a knowledge of quantum physics and electromagnetism appropriate to Level 4 students not specialising in theoretical physics.
• 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: Einstein’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: State of a system and Dirac notation; Linear operators, eigenvalues, Hermitean operators; Expansion of eigenfunctions; Commutation relations, Heisenberg uncertainty; Unitary transforms; Matrix representations; Schrödinger equation and time evolution; Schrödinger, Heisenberg and Interaction pictures; Symmetry principles and conservation; Angular momentum (operator form); Orbital angular momentum (operator form); General angular momentum (operator form); Matrix representation of angular momentum operators; Spin angular momentum; Spin ½; Pauli spin matrices; Total angular momentum; Addition of angular momentum.
• Reading material in Quantum Scattering Theory chosen by the lecturer.

Learning Outcomes

• 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 be able to describe elements of quantum mechanics in a rigorous mathematical way and to manipulate them at the operator level.
• They will have knowledge and understanding obtained by independent study of a substantial topic in Quantum Scattering Theory.

• 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.

• 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, examples classes and independent study.
• 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 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 on DUO.
• Regular problem exercises and example classes 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.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures. This material will be summatively assessed by means of a dissertation. Students will be required to research the given topic 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 though an examination, problem exercises and the dissertation. The examination and problem exercises 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 their skills in researching a topic at an advanced level and making a written presentation.
• The problem exercises and example classes 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

Summative Assessment

Formative Assessment:

Example classes 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