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Advanced Quantum Mechanics - PHY00019M

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  • Department: Physics
  • Module co-ordinator: Prof. Rex Godby
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2020-21

Module summary

Key advanced topics in quantum mechanics that bridge the gap between earlier courses and physics research

Related modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

To enrol on this module, students will need to have taken Quantum Mechanics courses in Stages 1-3 Physics, or the equivalent

Module will run

Occurrence Teaching cycle
A Autumn Term 2020-21

Module aims

The overall aim of the module is to develop in students a knowledge of key advanced topics in quantum mechanics that bridge the gap between earlier courses and physics research. Specifically:

To study the consequences of the time-dependence of the wavefunction in quantum mechanics, the emergence of the basic laws of classical mechanics from quantum mechanics, the quantum mechanics of many-particle systems, and second quantisation.

 

Module learning outcomes

  • Calculate the time-dependence of a wavefunction, and its consequences for observables.
  • Derive and apply the results of time-dependent perturbation theory up to first order.
  • Derive and apply Fermi's golden rule, and explain the relevance to selection rules for atomic transitions.
  • Explain the origin of the laws of classical mechanics using simple calculations of the types given in lectures.
  • Explain and apply the laws of quantum mechanics for many-particle systems and the main techniques used to study their implications.
  • Derive the main results of second quantisation.
  • Describe, and apply to unseen problems, all the topics in the syllabus.

Comprehensive lecture notes should be taken down from the blackboard during lectures, and will be supplemented by summary notes and handouts distributed on paper. These documents, together with electronic resources, audio recordings of lectures and a record of problems set, lecture rescheduling and similar information, will be made available through the VLE.

Module content

Syllabus

Time-dependence: Brief review of time-dependent Schrödinger equation; stationary states; time-evolution of general wavefunctions; time evolution operator; time-energy uncertainty relation. Time-dependent perturbation theory. Fermi's golden rule; selection rules for atomic transitions re-examined. Ehrenfest’s theorem. [5 lectures]

The classical limit: Classical mechanics of particles as a limit of quantum mechanics, mostly studied through wavepacket motion. [2]

Many-particle systems: Identical particles and exchange symmetry, fermions and bosons, the Pauli Principle; use of Slater determinants. Variational principle for many-electron systems; the Hartree and Hartree-Fock approximations. Density-functional theory and the local-density approximation. [5]

Second quantisation: Creation, annihilation and number operators; their use for many-particle systems; anti- commutation relations; field operators; Heisenberg picture. Introduction to many-body perturbation theory. Introduction to quantisation of the electromagnetic field. [6]

Assessment

Task Length % of module mark
University - closed examination
Advanced Quantum Mechanics Exam
1.5 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
University - closed examination
Advanced Quantum Mechanics Exam
1.5 hours 100

Module feedback

You will receive exam marks from your supervisor. Detailed model answers will be provided on the intranet. You should discuss your performance with your supervisor. The marked scripts will not be returned to you.

Individual meetings with supervisor will take place where you can discuss your academic progress in detail.

Indicative reading

Rae A I M: Quantum mechanics (Taylor & Francis)***

Merzbacher E: Quantum mechanics (Wiley, 1998) **

Schiff L I: Quantum mechanics (McGraw-Hill) **

Ziman J M: Elements of advanced quantum theory (CUP)*



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.

Coronavirus (COVID-19): changes to courses

The 2020/21 academic year will start in September. We aim to deliver as much face-to-face teaching as we can, supported by high quality online alternatives where we must.

Find details of the measures we're planning to protect our community.

Course changes for new students