Variational methods in classical physics will be reviewed and the extension of these ideas in quantum mechanics will be introduced.
Pre-requisites: PHYS2001 AND PHYS2003 AND PHYS2006 AND PHYS2023
Aims and Objectives
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.
- 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
- 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
|Preparation for scheduled sessions||15|
|Wider reading or practice||72|
|Completion of assessment task||8|
|Total study time||150|
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.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
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.
Repeat type: Internal & External