Undergraduate Course: Quantum Mechanics for Mathematicians (MATH10107)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This is a basic course on quantum mechanics for mathematics students, departing from the basic postulates and discussing a number of examples which illustrate the key role played by linearity. |
| Course description |
The discovery of the quantum theory of nature is arguably the most far-reaching scientific revolution of the twentieth century. In the first quarter of that century it became apparent that everyday assumptions about the nature of the world begin to break down when objects the size of atoms are involved.
It is the mathematics of the quantum world which is the main subject of this course. The basic ideas are now readily accessible at the undergraduate level and provide a marvellous illustration of the importance of linear spaces, linear operators, eigenvalues and differential equations in a central context in modern mathematics. (It is not intended to go into technical detail about infinite-dimensional spaces etc). This course does, however, motivate the need for a precise theory of self-adjoint operators in infinite-dimensional spaces.
Apart from its intrinsic interest, a further justification for this course is that quantum ideas are now becoming important in many areas of pure mathematics: quantum groups (algebra), quantum cohomology (topology/geometry), quantum cryptography, quantum information.
The course will include (some of) the following topics:
- Basic postulates of quantum theory, wave function, probabilistic interpretation, Dirac notation
- Schrödinger equation and examples: potentials, bound states, tunnelling.
- Operators, Heisenberg uncertainty principle, correspondence principle. Harmonic oscillator, wave packets, dispersion.
- Symmetries in quantum theory: hydrogenic atoms and their spectrum
- Scattering, WKB approximation
|
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2024/25, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 18,
Supervised Practical/Workshop/Studio Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
73 )
|
| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 20%, Examination 80% |
| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Be fully conversant in the basic concepts of quantum theory: wave function, probabilistic interpretation
- Solve the Schrödinger equation in some simple potentials and interpret the states
- Solve harmonic oscillator-like systems using operators and verify the uncertainty and correspondence principles in simple cases
- Apply symmetry considerations to solve for the spectrum of simple systems
- Solve simple scattering problems
|
Reading List
Recommended in addition to materials provided:
- (*)Brian Hall, Quantum Theory for Mathematicians, Springer 2013 (Selected chapters)
- Keith Hannabuss, An introduction to Quantum Theory, OUP 1997
(*) available to download from the University Library |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | QMM,Quantum mechanics,Schrödinger equation,Heisenberg uncertainty principle |
Contacts
| Course organiser | |
Course secretary | |
|
|
University Homepage