PHY-413

Welcome to the Quantum Mechanics B (PHY-413) Home Page

The Module Organiser is Prof Andreas Brandhuber, and the Deputy Module Organiser is Dr Theo Kreouzis.

Office Hours: Wednesdays 12:00-13:00. GOJ 217

Lecture Notes and Recommended Book: 

  • Freely available online resources include scans of handwritten lecture notes and typed up notes: NOTE the typed up notes are somewhat dated but cover large parts of the course, particular the formalism of quantum mechanics, angular momentum and spin (Lecture Note Sets 1 & 5 - 9); Lecture Note Sets 1 - 4 contain material already covered in QMA but are a useful source for revision.
  • Bransden, B.H. & Joachain, C.J. "Quantum Mechanics" Prentice-Hall (2nd Edition), (2000) ISBN 0-582-35691-1, the course roughly covers chapters 5, 6, 8, 12 (and parts of chapter 7).
  • For more details and the online notes follow the link above.

Background Reading: 

The following are sugested sources of material for students keen to delve deeper into the subject.  The library contains the books listed below, and College maintains journal subscriptions for the suggested articles.  You should be able to access the articles linked below from a College computer free of charge.

  • Feynman lectures on physics provide an interesting alternative source of information on this topic.  A number of copies of this text are available from the library.
  • Sometimes interesting articles appear on the arXiv.  See http://arxiv.org/archive/quant-ph for recent preprints.
  • Einstein, Podolsky and Rosen, "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?", Phys. Rev. 47, p777-780 (1935).
  • The Age of the Qbit (IOP publication).

Learning Outcomes

This course aims to provide a systematic introduction to some of the core concepts and techniques in Quantum Mechanics up to and including elements of perturbation theory. The course is designed to cater both for students who intend to take more advanced courses in quantum mechanics and for those for whom this is their last course in the subject.  By the end of the course students should have developed a familiarity with core concepts of QM, including the use of operators, angular momentum and spin, matrix mechanics and Dirac's bra-ket formalism and be able to apply time-independent perturbation theory in simple examples.

Syllabus

This course constitutes an introduction and revision, followed by an extended exposition, of the basic principles and applications of quantum mechanics. Topics include: Operators and the general structure of quantum mechanics, observables, orthonormality of eigenstates, expansion theorem, commuting operators, theory of measurement, Dirac formalism. The harmonic oscillator in operator formalism and as an example of matrix mechanics. Angular momentum theory, the rigid rotator and applications to rotation-vibration spectra of diatomic molecules. Spin in quantum mechanics illustrated with spin 1/2: matrix representations, Stern-Gerlach experiments and measurement theory exemplified. Addition of angular momentum. Time-independent perturbation theory and the variational method. Quantum systems with external electric and/or magnetic fields e.g. Stark effect and Zeeman effect.

Tools and Computing

You may find Mathematica a useful tool for visualising the wavefunctions computed within this course.  If you are interested in following up on this you may like to start by searching for "Functions Used in Quantum Mechanics" in the documentation centre. 

The following demonstrations may be of interest to you as well.  The source nb files of these examples (and many more) are downloadable from the Wolfram website, alternatively one can use the CFD web interface to directly manipulate these examples.

The material will be covered in a logicial sequential order, with ample time for discussion throughout the semester.

Deadlines

All homeworks are due in at 4pm on Thursday afternoons.

Exercises

Exercise sheets for problem classes will be posted here regularly:

Marking Scheme

Course Assessment: 20% of the marks for this course will come from homework assignments, the remaining 80% will come from the exam. You are encouraged to work through past papers in order to test your understanding of course material. Please note that any instance of plagiarism will be dealt with in accordance with college regulations, and you will find more information on this in the student handbook.

Homework

Homework sheets will be posted here every week on Thursday starting in Week 1. All assignments are due on Thursday 4pm the week after:

Lecture Notes and Book

Scans of my handwritten notes: Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 8, Week 9, Week 10, Week 11+12 These probably represent most closely what I present in class, but are no substitute for lectures as I vary examples and the presentation of concepts from year to year, and often discuss special topics not covered in these notes.

The topics of the course can also be found in chapters 5, 6, 8 and 12 (and parts of chapter 7) of Bransden, B.H. & Joachain, C.J. "Quantum Mechanics" Prentice-Hall (2nd Edition). The course does not follow this book strictly (or any other book or set of lectures) but is inspired by it. I import examples and lines of arguments from various sources, but this book is an excellent resource for reading up on things that we cover during the lectures and is the recommended book for QP and QMA as well.

There is an introductory set of slides available, which gives you a summary of core concepts (hopefully) covered in Quantum Mechanics A (QMA). It is highly recommended that you go through these before coming to QMB.  The summary slides can be downloaded from here.

Sets of (historical) lecture notes are also available: relevant sections are 1 (part QMA revision/part new material) & 5-9. They cover about 2/3 of the topics that I plan to discuss during the course. These can be downloaded from the links below.  

Past Papers

A full set of past papers should be available from the library website. For convinience the exam paper from last year can be found below: