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Quantum Mechanics II - MAT00025H

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  • Department: Mathematics
  • Module co-ordinator: Prof. Atsushi Higuchi
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23
    • See module specification for other years: 2021-22

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

Pre-requisite modules for Natural Sciences students:

  • MAT00026I Linear Algebra
  • MAT00034I Applied Mathematics


  • MAT00036I Applied Mathematics Option 1


Module will run

Occurrence Teaching period
A Spring Term 2022-23

Module aims

This module aims to expand students’ knowledge in quantum mechanics and enable them to apply the theory of quantum mechanics more widely through approximation methods. It also aims to enable them to appreciate the deeper mathematical structure of quantum mechanics and to provide the foundation for Quantum Field Theory in stage 4.

Module learning outcomes

At the end of the module you should be able to :

  • Understand the mathematical structure of quantum mechanics.
  • Understand the role of symmetries played in quantum mechanical systems.

  • Be able to identify and use suitable approximation methods for energy eigenvalue problems in quantum mechanics that cannot be solved exactly.

  • Be able to calculate transition probabilities in simple time-dependent quantum systems.

Module content


  • The space of states in quantum mechanics; Hermitian and unitary operators; projection operators; observables; measurement postulates; compatible and incompatible observables.

  • The representations of the angular-momentum algebra ; spherical harmonics; the spin angular momentum; the relationship between SU(2) and SO(3).

  • Symmetries in quantum mechanics: Stone’s theorem (without proof); the momentum and angular-momentum operators as generators of symmetries; discrete symmetries.

  • The time-evolution operator: the Schrödinger and Heisenberg pictures.

  • Systems of identical particles: bosons and fermions.

  • Approximation methods for the time-independent Schrödinger equation: time-independent perturbation theory (first order); the variational method..

  • Dirac’s delta function; momentum eigenstates in three dimensions.

  • Time-dependent perturbation theory; transition probability to first order.

Academic and graduate skills

  • Academic skills: students will develop their calculus and algebra skills further in the context of a theory essential in describing the physical world at the microscopic level.

  • Graduate skills: through lectures, problems classes and seminars, students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They develop problem-solving skills and learn how to apply techniques to unseen problems.


Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Quantum Mechanics II
2 hours 100

Special assessment rules



Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Quantum Mechanics II
2 hours 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

R Shankar, Principles of Quantum Mechanics, Springer (U 0.123 SHA)

S Gasiorowicz, Quantum Physics (2nd edition), J. Wiley.

L I Schiff, Quantum Mechanics, McGraw-Hill (U 0.123 SCH)

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.