Module overview
Variational methods in classical physics will be reviewed and the extension of these ideas in quantum mechanics will be introduced.
Linked modules
Pre-requisites: PHYS2001 AND PHYS2003 AND PHYS2006 AND PHYS2023
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Understand the use of variational methods in a variety of problems including Newtonian dynamics.
- 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
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
| Type | Hours |
|---|---|
| Revision | 10 |
| Completion of assessment task | 8 |
| Lecture | 30 |
| Preparation for scheduled sessions | 15 |
| Wider reading or practice | 72 |
| Follow-up work | 15 |
| Total study time | 150 |
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
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Examination | 90% |
| Problem Sheets | 10% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Coursework marks carried forward | 10% |
| Examination | 90% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 90% |
| Coursework marks carried forward | 10% |
Repeat Information
Repeat type: Internal & External