School of Chemical and Physical Sciences

Faculty of Natural Sciences

For academic year: 2023/24 Last Updated: 13 February 2024

PHY-20032 - Mathematical Physics

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In this module the student will be exposed to motion in a central potential and in axially symmetric potentials. Following the discussion of motion in these types of potential, a study of orbits and Rutherford scattering will be carried out.

The module will also discuss variational principles in physics and explore how such principles can be used to describe the behaviour of physical systems. Following on from this the module will cover, in a rigorous way, the concept known as ``the action" in physics, the calculus of variations, and obtain the Euler-Lagrange equations. This will lead to a study of Lagrangian mechanics, and possibly Hamiltonian mechanics, with a focus on examples from various parts of physics, e.g. optics, mechanics, electromagnetism, and quantum mechanics.

The module will also cover some of the different special functions that arise in physics in a rigorous way, discuss how these can be represented, and relate them to different physical phenomenon. The module will then proceed to discuss how these functions arise from the solution of certain equations, i.e. ordinary and partial differential equations. These equations will be discussed with examples taken from gravity, optics, electromagnetism and quantum mechanics to show their relevance to physical phenomenon.

The module will also discuss variational principles in physics and explore how such principles can be used to describe the behaviour of physical systems. Following on from this the module will cover, in a rigorous way, the concept known as ``the action" in physics, the calculus of variations, and obtain the Euler-Lagrange equations. This will lead to a study of Lagrangian mechanics, and possibly Hamiltonian mechanics, with a focus on examples from various parts of physics, e.g. optics, mechanics, electromagnetism, and quantum mechanics.

The module will also cover some of the different special functions that arise in physics in a rigorous way, discuss how these can be represented, and relate them to different physical phenomenon. The module will then proceed to discuss how these functions arise from the solution of certain equations, i.e. ordinary and partial differential equations. These equations will be discussed with examples taken from gravity, optics, electromagnetism and quantum mechanics to show their relevance to physical phenomenon.

This module aims to expose the student to the study of motion in different types of force fields, to the study of analytical mechanics in a rigorous way, to variational principles in physics and the calculus of variations, and to some of the special functions that occur in physics, both in terms of how they arise mathematically and how they relate to physical phenomenon.

http://lists.lib.keele.ac.uk/modules/phy-20032/lists

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Lectures: 24 (scheduled)

Problem classes: 12 hours (scheduled)

Assessed Problem Sheets: 45 hours (estimated; not scheduled)

Self study and revision: 67 hours (estimated; not scheduled)

Final Examination: 2 hours

Problem classes: 12 hours (scheduled)

Assessed Problem Sheets: 45 hours (estimated; not scheduled)

Self study and revision: 67 hours (estimated; not scheduled)

Final Examination: 2 hours

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Unseen 2-hour exam

Students answer a number of compulsory, short questions (for 40% of the total exam mark) and two longer questions from a choice of four. Questions test a mix of factual knowledge and problem-solving ability and can require mathematical and numerical calculations or descriptive answers or combinations thereof.

Assessed Problem Sheets

Three sets of mathematical and/or numerical problems with each set weighted at 10% of the total module mark.

Tutorials

Assessment is based on tutor observation of students' problem solving skills and progress during timetabled sessions. Student learning will be supported by the presence of a tutor and demonstrators.