FURTHER QUANTUM THEORY

Dr Hannabuss 16 lectures MT

Wednesday 10.00

Thursday 12.00

condensation
The creation of a
Bose-Einstein condensate
at JILA, Boulder, Colorado

Lecture Notes*
Interesting links
Problem sheets*
Outline solutions*
 
* Accessible only from sites within Oxford University.

Aims

This course builds directly on the first course in quantum mechanics and investigates what happens when quantum theory is combined with special relativity, and in particular how intrinsic particle spin and anti-particles arise. As background the course first explores the quantum mechanical angular momentum and how this is related to the statistical properties of identical particles.

Prerequisite:

b7

Synopsis

Spherically symmetric potentials, angular momentum, commutation relations, spectrum and matrix representation. Orbital angular momentum and the Coulomb potential. Identical particles, symmetric and anti-symmetric states, Fermi-Dirac and Bose-Einstein statistics and atomic structure.

Relativistic wave equations, the Klein-Gordon equation and Yukawa potential. Dirac equation, conservation of probability, free particle solutions, relativistic Hamiltonian, spin, magnetic moment, spin-orbit coupling, particle anti-particle conjugation. Lorentz covariance, commutation relations and symmetry.

Examples of infinite-dimensional linear systems. Quantization. Waves in a finite region. The Casimir effect. The canonical commutation relations for free bosonic fields. The canonical anticommutation relations for free fermionic fields. The Dirac vacuum vector.

Reading


Link to Mathematical Institute Home Page
Link to Mathematics at Balliol

This page was last updated
on 26 September 2002
by
KC Hannabuss
email:
kch@ermine.ox.ac.uk