|Delivery Type||Delivery length / details|
|Lecture||36 x 1-hour lectures|
|Seminars / Tutorials||8 x 1-hour seminars|
|Workload Breakdown||Every 10 credits carries a notional students workload of 100 hours: Lectures & tutorials = 44 hours; Worksheets (6 x 5 hours) = 30 hours; Private Study = 123 hours; Examinations = 3 hours.|
|Assessment Type||Assessment length / details||Proportion|
|Semester Exam||3 Hours Written Examination||100%|
|Supplementary Exam||3 Hours Written examination||100%|
On successful completion of this module students should be able to:
1. Illustrate the fundamental theory and applications of operator theory;
2. Define fundamental notions from operator theory and applications of operator theory and recognize their occurence and relevance in applied problems;
3. Solve specific problems from mathematical physics formulated in operator theoretic terms;
4. Perform algebraic and analytic computations based on operator techniques.
Modern quantum theory requires mathematical concepts and techniques going beyond traditional techniques encountered in standard textbooks. A proper understanding of these principals involves operator theoretic concepts, which will be presented in the module. The motivation is a description of open quantum systems.
- Introduction to Hilbert spaces, definitions of bounded, unitary, projective and self-adjoint operators. Applications of the spectral theorem and Stone's theorem.
- Introduction of the notion of abstract operator algebras.
- Motivating examples of operators from Mathemtical Physics. Mathematical formulation of Quantum Theory for closed dynamical systems.
- Introduction to the quantum theory of measurement. Completely positive mappings. Instruments and measurements. Lindblad's theory of dynamical semi-groups.
|Skills Type||Skills details|
|Application of Number||Throughout the module.|
|Communication||Students will be expected to submit written worksheet solutions.|
|Improving own Learning and Performance||Feedback will be given via tutorials.|
|Information Technology||Extensive use of spreadsheets.|
|Personal Development and Career planning||Students will be exposed to an area of application that they have not previously encountered.|
|Problem solving||All situations considered are problem-based to a greater or lesser degree.|
|Research skills||Students will be encouraged to consult various books and journals for examples of applications.|
|Subject Specific Skills||Using differential geometric techniques in modelling.|
This module is at CQFW Level 7