PH40084: Advanced quantum theory
Academic Year:  2020/1 
Owning Department/School:  Department of Physics 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2 
Assessment:  EX 100% 
Supplementary Assessment: 

Requisites:  Before taking this module you must take PH30030 OR take PH30043 
Description:  Aims: The aim of this unit is to increase the breadth and depth of students' knowledge and understanding of quantum physics, in both fundamental aspects of quantum mechanics and modern applications of quantum theory. Learning Outcomes: After taking this unit the student should be able to: * thoroughly understand the mathematical foundations and underlying principles of quantum mechanics; * demonstrate an indepth understanding of how a quantum description involving many degrees of freedom is described mathematically; * explain in detail the predictions of relativistic quantum theory: the necessity of spin, the concept of antiparticle, the polarization of the vacuum, spinors, and the fine structure of atoms; * calculate the effects of magnetic and electric fields on spin ½ particles; * understand that information is physical, and critically appraise how this alters from the classical to quantum domain; * explain in detail the concept of quantum entanglement, the EPR paradox, experimental tests of Bell's inequalities; * illustrate uses of entanglement in quantum information protocols, such as quantum cryptography, dense coding and teleportation. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Principles of quantum mechanics (4 hours): Complex vector spaces; Dirac's braket notation; Linear operators; Projectors, positive, hermitian and unitary operators; Postulates of quantum mechanics and quantum measurements; Composite quantum systems and tensor products. Relativistic quantum mechanics (8 hours): Inertia principle and invariance under Lorentz transformation; KleinGordon equation; Dirac equation, Dirac sea, Lamb shift; Lorentz transformation of spinors; Plane wave spinors; minimal coupling to electromagnetic fields; Nonrelativistic limit of the Dirac equation: origin of the spin and spinorbit coupling; Atomic fine structure. Quantum information and computation (10 hours): Classical information theory; Quantum Cryptography; Quantum gates and circuits; Quantum nocloning theorem; Density operators and von Neumann entropy; Quantum entanglement, EPR paradox and Bell's inequalities; Quantum dense coding and teleportation. Quantum computing  DeutchJozsa algorithm. 
Programme availability: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020 
PH40084 is Compulsory on the following programmes:Department of Physics
PH40084 is Optional on the following programmes:Department of Mathematical Sciences

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