Undergraduate

modules

Modules

MAS3802 : Quantum Mechanics

Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To introduce the mathematical description of the wave theory of matter and other aspects of basic quantum theory.

Module Summary
Quantum mechanics is the theoretical framework used to describe the most fundamental properties of matter. It has a rich mathematical structure and it has provided the impetus for many advances in mathematics. It also has many practical applications, including the modelling of atoms, molecules and semiconductors. Recently, quantum theory has been used extensively to model superfluids and supercooled gases, and there are even attempts to build computers which function by the laws of quantum mechanics.

This module introduces quantum mechanics in terms of waves and explains how to formulate and solve the Schrodinger equation for matter waves, with appropriate mathematical examples and physical interpretation. Examples include “quantum particles” in different potentials, and their scattering and wave-mechanical interference. It also provides a more formal approach based on simple operator theory, touching on the “measurement problem” and the physics of macroscopic (many-particle) quantum systems.

Outline Of Syllabus

Wave mechanics overview: mathematical solution of ordinary/partial differential wave equation and wave interference. The collapse of determinism and the uncertainty principle. Schrodinger's equation and concept of quantum-mechanical wavefunction. Mathematical solutions of finite, infinite square wells: energy quantisation, superposition states and the correspondence principle. Wave dynamics on potential barriers. The harmonic oscillator and Hermite polynomials. Formal structure of quantum mechanics: fundamental postulates; operators, eigenvalues and observables; the “quantum measurement” problem; brief introduction to many-particle quantum mechanics and outlook.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyIndependent study140:0040:00Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study53:0015:00Preparation and writing up of assessed assignments.
Total100:00
Jointly Taught With
Code Title
MAS8802Quantum Mechanics
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A90N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8802Quantum Mechanics1N/A
Other Assessment
Description Semester When Set Percentage Comment
Report1M10Five assignments, worth 2% each.
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The written exercises are expected to consist of two assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and the mini-project allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these are thus formative as well as summative assessments.

Reading Lists

Timetable