PHY-325

Welcome to the Quantum Mechanics and Symmetry (PHY-325) Home Page

Course Organizer:  Steve Thomas

Deputy Course Organizer: Gabriele Travaglini

Marker: 

Aims and Learning Outcomes

The aims of the course are to give the students a grounding in the more formal and axiomatic approach to quantum mechanics and introduce them to the application of these concepts in atomic and high energy particle physics

Students successfully completing this course will: understand what an abstract vector space is and how that 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 underlie our picture of the sub-atomic and sub-nuclear world.

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; time-dependent perturbation theory; degeneracies due to presence of symmetries.
  • Multiparticle systems;

Schedule

Lectures: Tuesday 15.00-16.00 and Thursday 10.00-12.00

Exercise Classes: Thursday 15.00-17.00 . There are two one hour classes. Students attend only one class each. First classes start on Thursday 24th January 2013. 

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.

White Board Lectures              Older Course Notes

Week 1                                                     Notes1 (weeks 1-3)

Week 2                                                     Notes2 (weeks 4-5)

Week 3                                                     Notes3 (weeks 6-9)

Week 4

Week 5

Week 6

Week 8

Week 9

Week 10

Week 11       Addendum

Week12

 

Deadlines

Homework must be posted in the QMS box on the first floor of the Physics building by 2.00pm on Thursdays.

Marking

Assessment for this course is based on a 20% contribution from the weekly exercises and 80% from the final examination in Semester 3.

Homework

Homework problem sheets will be posted on this page each Thursday. Solutions will be discussed in the Exercise Class on Thursday afternoons and will be available here a few days later. Homework must be posted in the QMS box on the first floor of the Physics building by 2.00pm on Thursdays.

Assignments

                      

Past Exam Papers

Exam 2 010               

 

Exam 2011                 

 

 

References

The following references are recommended for the course:

 

  • Quantum Mechanics 
    B.H. Bransden & C.J.  Joachain
    Prentice-Hall (2nd Edition)
  • Modern Quantum Mechanics
    J.J. Sakurai.
    QM Library: QC174.1 SAK
     
  • The Principles of Quantum Mechanics
    P.A.M. Dirac
    QM Library: QC174.1 DIR