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

#### 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