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Quantum Mechanics I - MAT00024H

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

Module summary

This module introduces a number of basic topics from quantum theory, providing solid foundations both from a conceptual and a mathematical point of view.

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

Pre-Requisites for Natural Sciences Students:

  • MAT00036I Applied Mathematics Option I
  • MAT00041I Linear Algebra for the Natural Sciences

Module will run

Occurrence Teaching period
A Autumn Term 2021-22

Module aims

This module aims to deepen the understanding of quantum mechanics, building on a first encounter with the theory Second Stage. The emphasis will be on the mathematical foundations of quantum mechanics as well as the conceptual changes compared to classical mechanics.

Module learning outcomes

  • Understand the abstract operator formalism of quantum mechanics for quantum states and observables

  • Understand the description of quantum mechanics in terms of position or momentum representations using "wave functions"

  • Describe the harmonic oscillator and angular momentum within quantum theory

  • Appreciate features of quantum mechanics distinguishing it from classical mechanics, e.g. tunnelling, Heisenberg’s uncertainty relation and commutation relations

Module content

Syllabus

  • Time-dependent Schrödinger equation: general solution in terms of the energy eigenstates; continuity equation for the probability.

  • Space of wave functions: position, momentum and energy as Hermitian operators; commutation relations; Fourier transform of wave functions; measurement of observables in quantum theory; Heisenberg’s uncertainty relation between position and momentum observables.

  • Free quantum particle on a line: momentum eigenstates; the propagator; the evolution of Gaussian wave packets.

  • Ehrenfest’s theorem and the classical limit.

  • Scattering problem in one dimension; discussion of tunnelling.

  • Dirac's bra-ket notation: harmonic oscillator with ladder operators.

  • Angular momentum: angular-momentum algebra; spherical harmonics.

Academic and graduate skills

  • Academic skills: students will learn a fundamental theory describing the physical world through combining their mathematical skills learned in earlier Stages.

  • 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.

Assessment

Task Length % of module mark
Online Exam -less than 24hrs (Centrally scheduled)
Quantum Mechanics I		 2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
Online Exam -less than 24hrs (Centrally scheduled)
Quantum Mechanics I		 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)

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

S Gasiorowicz, Quantum Physics (2nd edition), J. Wiley (U 0.12 GAS)


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.