Dr Hannabuss 16 lectures HT 2012Tuesday and Thursday 2.00 Suitable for third and fourth year students who have done a b7 quantum course. 




This course builds directly on the first course in quantum mechanics and covers a series of important topics, particularly features of systems containing several particles. The behaviour of identical particles in quantum theory is more subtle than in classical mechanics, and an understanding of these features allows one to understand the periodic table of elements and the rigidity of matter. It also introduces a new property of entanglement linking particles which can be quite widely dispersed.
There are rarely neat solutions to problems involving several particles, so usually one needs some approximation methods. In very complicated systems, such as the molecules of gas in a container, quantum mechanical uncertainty is compounded by ignorance about other details of the system and requires tools of quantum statistical mechanics.
Two state quantum systems enable one to encode binary information in a new way which permits superpositions. This leads to a quantum theory of information processing, and by exploiting entanglement to other ideas such as quantum teleportation.
Identical particles, symmetric and antisymmetric states, FermiDirac and BoseEinstein statistics and atomic structure.
Heisenberg representation, interaction representation, time dependent perturbation theory and FeynmanDyson expansion. Approximation methods, RayleighSchrödinger timeindependent perturbation theory and variation principles. The virial theorem. Helium.
Mixed states, density operators. The example of spin systems. Purification. Gibbs states and the KMS condition.
Entanglement. The EPR paradox, Bell's inequalities, Aspect's experiment. GHZ states
Quantum information processing, qubits and quantum computing. The nocloning theorem, quantum teleportation. Quantum logic gates. Quantum operations. The quantum Fourier transform. Shor's algorithm.
