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# Quantum Mechanics I - MAT00024H

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

## 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

• None

### Prohibited combinations

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 2022-23

## 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 wave-mechanics description of quantum mechanics and its classical limit.

• Understand the abstract operator formalism of quantum mechanics and its application to simple harmonic oscillator.

• Appreciate features of quantum mechanics distinguishing it from classical mechanics, such as tunnelling and Heisenberg’s uncertainty relation.

## Module content

Syllabus

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

• The space of wave functions: the position, momentum and energy as Hermitian operators; commutation relations; the Fourier transform of the wave function as the momentum representation; measurement postulates for energy, position and momentum; Heisenberg’s uncertainty relation between the position and momentum.

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

• Ehrenfest’s theorem and the classical limit.

• Scattering problem in one dimension; discussion of tunnelling.

• Dirac’s bra-ket notation; the simple harmonic oscillator with ladder operators.

• 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
Closed/in-person Exam (Centrally scheduled)
Quantum Mechanics I
2 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (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.