## Topic outline

# SPA6325 - QUANTUM MECHANICS AND SYMMETRY - 2019/20

Year: 3 | Semester: B | Level: 6 | Units: 1 | Credits: 15

**Prerequisites:**SPA5218 SPA6413**Lectures:**33 | Lec: 115 116 212 (notation)**Exam:**2.5 hour written paper (80%), coursework (20%)**Practical work:**none |**Ancillary teaching:**none**Course organiser:**Prof Steve Thomas |**Course deputy:**Dr C White

### Checklist for MO and DMO

### General Information

### Welcome to the Quantum Mechanics and Symmetry (SPA-6325) Home Page

Course Organizer: Prof. Steve Thomas

Deputy Course Organizer: Dr C White

Marker/Demonstrators: Enrico Andriolo GOJ 602

### Aims and Learning Outcomes

**Synopsis:**This course will give students grounding in a more formal approach to quantum mechanics and introduces them to the application of these tools in the quantum mechanical description of symmetries in particle physics.

Topics include: a mathematical introduction with basic notions of groups, Hilbert spaces, and linear operators; the formal axioms of quantum mechanics, Dirac notation; the free particle and the harmonic oscillator as the simplest quantum mechanical systems; time independent perturbation theory; multiparticle systems, identical particles; translations and rotations symmetries in quantum mechanics, time-reversal and parity symmetries; conservation laws and good quantum numbers, basic concepts in Lie Groups and Lie Algebras and their representations by way of the the rotation group, spin, addition of spin.

**Aims:**The aim of this course is to give students a general description of non-relativistic quantum mechanics in terms of Hilbert spaces and introduce the concept of spin and its relation to the representations of the rotation group.

**Outcomes:**Students successfully completing this course will understand what an abstract vector space is and how this concept underpins quantum mechanics in the form of the Hilbert space; be able to translate all they have previously learnt about quantum mechanics into this language; understand how quantum mechanical principles underly our picture of the sub-atomic and sub-nuclear world.

**Assumed Prior Mathematics Knowledge:**Students must have taken and passed MT1, MT2 and MT3. Regarding MT3 you must have passed with a mark of at least 60%. It is not a prerequisite that all students have taken MT4.

### Syllabus

- Mathematical introduction: groups, vector spaces and Hilbert spaces
- Dirac's notation, linear operators, projectors, self-adjoint and unitary operators. The postulates of quantum mechanics and some of their consequences
- Illustration of linear algebraic methods in simple quantum mechanical systems; concept of semi-classical states
- Symmetries in quantum mechanics; parity, time reversal, space and time translations; conservation laws.
- Representation of the rotation group in quantum mechanics: infinitesimal and finite rotations, orbital and spin angular momemntum
- Approximate methods: time-independent perturbation theory
- Multiparticle systems

### LECTURE SCHEDULE

Lectures: Monday: 15.00-17.00 GOJ PLT

Tuesday : 12.00-13.00 Banc. 3.26

### Lecture Notes

A compact set of printed notes from previous years will be made available here as the course progresses. Each week I will also post copies of my white board lecture notes. My white board notes expand on and, in several areas, go beyond the topics discussed in the printed notes.

**Lectures Notes**

### Marked Homework Deadlines

Homework Problem sets that are to be marked (weeks 2,4,6,and 8) must be handed in by

**4.00pm on Tuesdays**### Reading Week

No Lectures or Exercise Classes will be scheduled during this week.

### Marking Scheme

Assessment for this course is based on a 20% contribution from the 4 marked homework problem sets and 80% from the final examination in Semester 3.

### EXERCISE CLASS PROBLEMS

Please check below to find out which exercise class group you have been assigned.

**Group A**:**Thursday**11am - 12am**Queens Building LG3****Group B**:**Thursday**12am - 1pm**Queens Building LG6**Note that not every week has an exercise class been scheduled.

Exercise Classes begin in Week 1

### Homework

Homework problem sheets will be posted on this page. Solutions will eventually be made available from here.

Please note: There are 9 Homework Problem sheets in total**BUT ONLY WEEKS 2, 4, and 6 need to be handed in and marked.****These count as a maximum of 20 % towards the final Course Mark.**The non-marked homework problems are there as part of your learning process and you are__strongly encouraged to attempt them.__### Past Exam Papers and Solutions

### Text Books

You may find the following text books are useful for this course. The book by Sakurai is particularly recommended.

**Quantum Mechanics**B. H. Bransden & C. J. Joachain :*Prentice-Hall (2nd Edition)*

**Modern Quantum Mechanics**J. J. Sakurai :*Addison-Wesley (Revised Edition)*

### Exercise Class Problems

Solutions will be posted here.

### Online Lectures