Module Information

Module Identifier
MAM8520
Module Title
MATHEMATICAL FOUNDATIONS OF QUANTUM THEORY
Academic Year
2009/2010
Co-ordinator
Dr Rolf Gohm
Semester
Intended for use in future years
Pre-Requisite
MA10110
Pre-Requisite
MA20110
Pre-Requisite
MA21410
Other Staff
 

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

OPERATORS ON HILBERT SPACES
  • Introduction to Hilbert spaces, definitions of bounded, unitary, projective and self-adjoint operators. Applications of the spectral theorem and Stone's theorem.
C*-ALGEBRAS
  • Introduction of the notion of abstract operator algebras.
APPLIED OPERATOR THEORY
  • Motivating examples of operators from Mathemtical Physics. Mathematical formulation of Quantum Theory for closed dynamical systems.
OPEN QUANTUM 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