The University of Southampton
Courses

# PHYS3007 Theories of Matter, Space and Time

## Module Overview

Variational methods in classical physics will be reviewed and the extension of these ideas in quantum mechanics will be introduced.

### Aims and Objectives

#### Module Aims

The aim of this course is to provide a deeper understanding in a number of areas in which study has already begun in previous courses. Much of the course will concentrate on the transition from classical 19th Century physics to the new ideas of 20th Century physics, relativity and quantum mechanics. The laws of dynamics and electrodynamics will be developed in a fully relativistic notation.

#### Learning Outcomes

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Understand 4-vector notation and be able to perform dynamics and electro dynamics calculations using them
• Understand the differential form of Maxwell's equations and be able to derive the wave equation in free space for light
• Understand the use of variational methods in a variety of problems including Newtonian dynamics.

### Syllabus

- Principles of Least Action Calculus of variation: the Euler-Lagrange equations - Fermat's Principle of least time: light in vacuum and in media - Lagrangian dynamics and examples - First integrals - Special Relativity Postulates - Lorentz transformations as generalized rotations - 4-vectors and index conventions - Proper time and definitions of rel. ìu, au, pu and derivation of E = mc2 - Eqns of relativistic dynamics and 4-momentum conservation. E.g. Compton effect, Doppler effect, particle decay - Electromagnetism - Maxwell's equations in differential form - Wave equations in free space - Potential, Vector Potential and Laplace's equation - Gauge transformations 4-vector current, 4-vector potential and - Relativistic formulation of Maxwell's equations - Field strength tensor and its Lorentz transformation - Aspects of Quantum Mechanics - Momentum space wave functions - Completeness and orthogonality - Feynman's Path Integral Formulation of Quantum Mechanics - a derivation of the free particle kernel in one dimension, - its application to barrier problems - the connection with the usual Schrodinger equation - Klein-Gordon equation, interpretation of negative energy states

### Learning and Teaching

TypeHours
Follow-up work15
Revision10
Lecture30
Preparation for scheduled sessions15
Total study time150

### Assessment

#### Assessment Strategy

All 3 sheets count for the purposes of assessment, and mitigation for missed modules requires students to make a request to the Special Considerations Board in the usual way.

#### Summative

MethodPercentage contribution
Examination  (2 hours) 90%
Problem Sheets 10%

#### Repeat

MethodPercentage contribution
Coursework marks carried forward %
Examination %

#### Referral

MethodPercentage contribution
Coursework marks carried forward %
Examination %

#### Repeat Information

Repeat type: Internal & External