Gwybodaeth Modiwlau
Course Delivery
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
Assessment Type | Assessment length / details | Proportion |
---|---|---|
Semester Exam | 3 Hours Written Examination | 100% |
Supplementary Exam | 3 Hours Written examination | 100% |
Learning Outcomes
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.
Brief description
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.
Content
- 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.
Module Skills
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. |
Team work |
Notes
This module is at CQFW Level 7