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PH40084: Advanced quantum theory

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Physics
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take PH30030 OR take PH30043
Further information on descriptions 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 in-depth 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 bra-ket 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; Klein-Gordon equation; Dirac equation, Dirac sea, Lamb shift; Lorentz transformation of spinors; Plane wave spinors; minimal coupling to electromagnetic fields; Non-relativistic limit of the Dirac equation: origin of the spin and spin-orbit coupling; Atomic fine structure.
Quantum information and computation (10 hours): Classical information theory; Quantum Cryptography; Quantum gates and circuits; Quantum no-cloning theorem; Density operators and von Neumann entropy; Quantum entanglement, EPR paradox and Bell's inequalities; Quantum dense coding and teleportation. Quantum computing - Deutch-Jozsa algorithm.
Further information on programme availabilityProgramme availability:

PH40084 is Compulsory on the following programmes:

Department of Physics
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
  • USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
  • USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
Programmes in Natural Sciences
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 4)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 5)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 5)

PH40084 is Optional on the following programmes:

Department of Mathematical Sciences Department of Physics
  • USPH-AFM02 : MPhys(Hons) Physics (Year 4)
  • USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 4)
  • USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 4)
  • USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 5)
  • USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 5)
  • USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 4)
  • USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 4)
  • USPH-AAM10 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
  • USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 5)
  • USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 5)
Programmes in Natural Sciences
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 4)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 5)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 5)
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Biology stream) (Year 4)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 5)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Professional Placement (Year 5)
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) (Year 4)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 5)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Professional Placement (Year 5)

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