FURTHER QUANTUM THEORYDr Hannabuss 16 lectures MTWednesday 10.00 Thursday 12.00 




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 antiparticles arise. As background the course first explores the quantum mechanical angular momentum and how this is related to the statistical properties of identical particles.
b7
Spherically symmetric potentials, angular momentum, commutation relations, spectrum and matrix representation. Orbital angular momentum and the Coulomb potential. Identical particles, symmetric and antisymmetric states, FermiDirac and BoseEinstein statistics and atomic structure.
Relativistic wave equations, the KleinGordon equation and Yukawa potential. Dirac equation, conservation of probability, free particle solutions, relativistic Hamiltonian, spin, magnetic moment, spinorbit coupling, particle antiparticle conjugation. Lorentz covariance, commutation relations and symmetry.
Examples of infinitedimensional 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.
Most of the material can be found in
K.C. Hannabuss, Introduction to Quantum Theory, OUP, (1997) Sections 4.14.3, 8.18.6, 8.8, 16.116.4, 17.117.10, 18.118.3.
and in
G.R. Screaton, Further Quantum Mechanics, Mathematical Institute Notes (1991) Chapters 1, 2, 3, 6, 7.
Notes on the field theory will be put on the web as pdf files. Lecture Notes*

