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PH40084: Advanced quantum theory

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Physics
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Follow this link for further information on period slots Period: Semester 2
Follow this link for further information on unit assessment Assessment: EX 100%
Follow this link for further information on supplementary assessment Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites: Before taking this unit you must take PH30030
Follow this link for further information on unit content 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:
* explain in detail the salient differences between classical physics and quantum physics;
* demonstrate an in-depth understanding of the realm of quantum optics and its major applications and frontline research;
* give a mathematical description of the quantum principles of vector states, Hilbert space and quantum interference;
* use and apply Dirac formalism to light-matter optical phenomena;
* explain optical absorption and refraction using a quantum framework;
* outline and critically assess the following major applications of coherent light-matter interactions; Rabi oscillations, Ramsey interference, electromagnetically induced transparency and laser cooling;
* discuss the principles of quantum cryptography and computing.

Numeracy T/F A, Problem Solving T/F A.

Relativistic quantum mechanics (7 hours): Principle of inertia, Lorentz transformation, Klein-Gordon equation, Dirac equation, spinors, addition of relativistic velocities, Lorentz boost of spinors, free particle solutions, interaction with the electromagnetic field, non-relativistic limit of Dirac's equation, origin of the electron spin, spin-orbit interaction, solutions of Dirac's equation for the hydrogen atom.
The physics of high magnetic fields (3 hours): Landau quantization, 2D and 3D density of states in a magnetic field, Shubnikov de Haas and van Alphen effects, oscillations of the Fermi level, Quantum Hall Effect.
Spin in electric and magnetic fields (2 hours): Larmor precession and 4π periodicity of the spin phase, neutron interference experiments, spin resonance, Rabi oscillations, Rashba Hamiltonian, Spin transistor, Aharonov Casher and Aharonov-Bohm effects.
Quantum optics (10 hours): Phenomenology of optical processes (e.g. absorption, emission and scattering). Quantum mechanical principles and Dirac notations. Semi-classical interaction of radiation with matter, Hamiltonian of 2-level and 3-level atoms in electromagnetic field. Evolution of a quantum system, Rabi oscillations and quantum interference. Applications: Electromagnetically induced transparency and coherent population trapping. Lasing without inversion. Ramsey interference. Opto-mechanical effect: laser cooling.
Quantum Information (2 hours): Quantum cryptography and computing.
Follow this link for further information on programme availabilityProgramme availability:

PH40084 is Compulsory on the following programmes:

Department of Physics
  • USPH-AFM02 : MPhys Physics (Full-time) - Year 4
  • USPH-AFM04 : MPhys Physics with Research Placement (Full-time) - Year 4
  • USPH-AAM03 : MPhys Physics with Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

PH40084 is Optional on the following programmes:

Programmes in Natural Sciences
  • UXXX-AFM01 : MSci (hons) Natural Sciences (Full-time) - Year 4
  • UXXX-AKM02 : MSci (hons) Natural Sciences with Professional Placement (Full-time with Thick Sandwich Placement) - Year 5
  • UXXX-AAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 5

* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.