MAS3802 : Quantum Mechanics
- Offered for Year: 2019/20
- Module Leader(s): Dr Thomas Billam
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 1 Credit Value:||10|
To introduce the mathematical description of the wave theory of matter and other aspects of basic quantum theory.
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.
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen exam|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||12||0:10||2:00||Office hours|
|Guided Independent Study||Independent study||1||38:00||38:00||Studying, practising, and gaining understanding of course material|
|Guided Independent Study||Independent study||5||3:00||15:00||Preparation and writing up of assessed assignments.|
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: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
The format of resits will be determined by the Board of Examiners
|Prob solv exercises||1||M||10||Five 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 problem solving exercises are expected to consist of five assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments 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 assessments have a secondary formative purpose as well as their primary summative purpose.