Symmetries of Quantum Mechanics (U04266)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : PHY-3-SymQM

Building on the material presented in the Quantum Mechanics course, this course aims to introduce the basic mathematical tools of Quantum Mechanics with a special emphasis on the connection between physical phenomena and mathematical modelling. The Hilbert space of physical states is reviewed as a particular case of a linear vector space. General properties of representation theory are discussed for the case of finite groups and are applied to quantum mechanical systems. Representations of the continuous groups U(1), SO(3), and SU(2) are presented and discussed in relation with invariance under translations and rotations. The general theory of angular momentum is introduced and applied to cases of physical interest. Quantum mechanical results are compared to their classical counterparts for a number of physical systems.

Entry Requirements

? Pre-requisites : Physics 2A: Forces, Fields & Potentials (PHY-2-A; Physics 2B: Waves, Quantum Physics and Materials (PHY-2-B); Foundations of Mathematical Physics (PHY-2-FoMP) or MP2A: Vectors, Tensors and Fields (PHY2-MP2A) and MP2B: Dynamics (PHY-2-MP2B), together with prior attendance at Quantum Mechanics (PHY-3-QuantMech).

Subject Areas

Home subject area

Undergraduate (School of Physics and Astronomy), (School of Physics and Astronomy, Schedule Q)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 4 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
12/01/2009	12:00	13:00	Lecture Theatre C, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	10:50	KB
Tutorial	Monday	12:10	13:00	KB
Lecture	Thursday	10:00	10:50	KB

? Additional Class Information : Workshop/tutorial sessions, as arranged.

Summary of Intended Learning Outcomes

Upon successful completion of this course it is intended that a student will be able to:
1. master the mathematical tools that are used for the description of elementary quantum systems;
2. model simple physical systems according to the postulates of quantum mechanics;
3. understand the importance of symmetry principles in classical and quantum systems;
4. use group theory to solve physical problems;
5. understand the general theory of angular momentum and its connection to the group of spatial rotations;
6. apply the above concepts to the study of new (unseen) problems.