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Further Quantum Mechanics - PHY00042M

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  • Department: Physics
  • Module co-ordinator: Dr. Ignacio Wilson-Rae
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2020-21

Module summary

Key further 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 Spring 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 quantum theories of angular momentum and scattering, and the role of symmetries and the algebraic approach in quantum mechanics.

Module learning outcomes

  • Illustrate the relation between symmetries and conservation laws.
  • Deduce and apply the general theory of angular momentum.
  • Deduce and apply the Born approximation and the method of partial waves in potential scattering theory.
  • Apply creation and annihilation operators of the harmonic oscillator.
  • Construct solutions to complex unseen problems in all of the aforementioned topics.

Comprehensive lecture notes should be taken down from the blackboard during lectures. Supplementary notes will be provided and made available through the VLE.

Module content


Symmetries and angular momentum: Symmetries and rotations • Angular momentum multiplets (Ladder operators) • Addition of angular momenta and selection rules including Parity (Clebsch-Gordan coefficients and the Wigner- Eckart theorem).

Potential scattering: Lippmann-Schwinger equation, scattering amplitudes and the Born approximation • Partial waves, phase shifts and resonances.

Quantum states of the harmonic oscillator: Creation and annihilation operators • Coherent states and squeezed states.


Task Length % of module mark
Online Exam
Further Quantum Mechanics exam
N/A 100

Special assessment rules



Task Length % of module mark
Online Exam
Further Quantum Mechanics exam
N/A 100

Module feedback

Exam marks received from supervisor. Detailed model answers provided on the internet..

Indicative reading

Weinberg S: Lectures on quantum mechanics (Cambridge, 2013)

Sakurai J J: Modern quantum mechanics (Addison Wesley, 1994)

Messiah A: Quantum Mechanics Volume II (Dover, 1999)

Landau L D and Lifshitz E M: Quantum Mechanics (Non-relativistic Theory) (Butterworth-Heinemann, 1977)

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