This is a course on Quantum Mechanics written and delivered
by Prof. Graeme Ackland at the University of Edinburgh between 2006 and 2011.
All content is released under a Creative Commons Attribution 4.0 license (CC BY 4.0). Feel free to reuse the material as you wish so long as you credit Prof. Ackland.
Lectures and Tutorials
Lecture Notes, Tutorial Sheets and Solutions
If you spot any errors or omissions in the lecture notes and problem
sheets let me know and they will be corrected in the online
version. Finalised course notes will be available shortly after the
lectures: they will be very similar to last year's which are available
now.
Ongoing Commentary and Feedback
Here I will make a note of feedback given to individual students, in
those cases where it seems relevant to the whole class.
In the problems class, it seemed that tutorial sheet 8 proved rather hard.
I have added two additional (easier!) questions online.
Turnout at the Wednesday morning problems class has dropped alarmingly.
THIS IS YOUR CHANCE TO GET FEED BACK ON YOUR WORK. If you don't show
up, don't complain about not getting feedback, and don't expect me to
take requests for more feedback seriously!
I have no preferred book for the course (some are listed below) - the main
one I use is "Introduction to the Quantum Theory" by Park.
You should attempt the tutorial problems in advance of the problems
class. Solutions are made readable after the tutorial to help you
avoid the temptation of looking at them before trying the problems
yourself. You probably can get a copy from last year's class or the
google cache, but doing so is more likely to hinder your learning than
help.
This course has a rather different style for Junior Honour Quantum Mechanics.
LECTURES: Will cover the foundations and proofs of various practical
techniques for doing quantum mechanics, illustrated with examples drawn for various physics problems..
TUTORIALS: Will give you the chance to train your skills by practice on a series of problems
Both lectures and tutorials will illustrate the formal Quantum and the
practical application by relating it to physical systems you will have
encountered in other courses.
REMEMBER: The Wednesday morning problem class is your chance to
get feedback on your work for Prof Ackland and the two demonstrators
I'm going to work on the assumption that anyone who doesn't come is
able to do the problems without needing assistance or feedback.
If you don't think I should work on that assumption, then come to the
problem session.
This is my fifth year of teaching the course: I also taught its
predecessor from 1995-2000.
That perpetual motion machine
At the last lecture, I was asked whether you could create energy by...
1/ pumping a system with photons just below its resonant frequency, within
the natural linewidth.
2/ thereby exciting the system
3/ collecting the radiation when it decays, at slightly higher frequency.
Assume that recoil and thermal broadening can be neglected - that's just engineering after all!
Well, obviously you can't, but I can't see why. A small prize
available for anyone who can figure it out.
Section 1:
( PDF )
Summary of things you should already know
Section 2:
( PDF )
Review: Time-Independent Non-degenerate Perturbation Theory
Section 3:
( PDF )
Dealing with Degeneracy
Section 4:
( PDF )
Degeneracy, Symmetry and Conservation Laws
Section 5:
( PDF )
Time--dependence
Section 6:
( PDF )
Two state systems
Section 7:
( PDF )
Hydrogen ion and Covalent Bonding
Section 8:
( PDF )
The Variational Principle
Section 9:
( PDF )
Indistinguishable Particles and Exchange
Section 10:
( PDF )
Self-consistent field theory
Section 11:
( PDF )
Fundamentals of Quantum Scattering Theory
Section 12:
( PDF )
Scattering in three dimensions
Section 13:
( PDF )
Further Concepts in Quantum Scattering Theory
Section 14:
( PDF )
Using Partial Waves
Section 15:
( PDF )
The quantum mechanics nobody really understands
For non-examinable interest, and of use in some optional courses, some fuller details about partial waves and Relativistic Quantum Mechanics.
Partial Waves Klein-Gordon; Dirac; More Dirac
Synopsis and revision guide:
( PDF )
Things to know in May
Exercises
There's a bit more maths in some of these than you might get in an exam. Maple will help if you're stuck
Sheet 1:
( PDF )
Mainly revision
Sheet 2:
( PDF )
Perturbations
Sheet 3:
( PDF )
More Perturbations
Sheet 4:
( PDF )
Time Dependence
Sheet 5:
( PDF )
Variational Method
Sheet 6:
( PDF )
Time-Dependence and Pseudopotentials
Sheet 7:
( PDF )
Bonding and Identical Particles
Sheet 8:
( PDF )
Counting states
Sheet 9:
( PDF )
Scattering
Sheet 10:
( PDF )
Bell's Theorem and Bedtime Reading
Problem solving is an integral part of the course and you are
strongly encouraged and to work
through the problems on the tutorial sheets and then to attend the class.
Two postgraduate students will act as course tutors.
You should also look at previous exam questions. Note that
Prof Ackland also taught the course from 1996-2001.
Solutions to Exercises
These will become available after the tutorial
Solutions to Sheet 1:
( PDF )
Mainly revision
Solutions to Sheet 2:
( PDF )
Perturbations
Solutions to Sheet 3:
( PDF )
More Perturbations
Solutions to Sheet 4:
( PDF )
Time Dependence
Solutions to Sheet 5:
( PDF )
Variational Methods, Molecules
Solutions to Sheet 6:
( PDF )
Time Dependent Perturbations and Radiative Transitions
Solutions to Sheet 7:
( PDF )
Bonding and Identical Particles
Solutions to Sheet 8:
( PDF )
Counting States
Solutions to Sheet 9:
( PDF )
Scattering
Solutions to Sheet 10:
( PDF )
Bell's Theorem and Bedtime Reading
Solutions to Additional Exercises:
( PDF )
Examination Papers
The examination is at the end of SECOND semester, except for
single-semester visiting students who have a bespoke paper at the end
of the first semester.
Previous Examination Papers can be found via the
central University Library site. This requires an Edinburgh University
login.
Although there will always be some rote-learnable sections, the
examination questions will probe whether you understand what
you've been taught, not simply whether you can remember it.
The purpose of this course is to
teach you some physics, not to help you pass the examination. If you
are interested in passing the examination, it is a good idea to
practice with some past papers.
There will be additional timetables sessions prior to the examination
period in which you can ask for feedback on your attempts at previous
examination papers. Remember that while a tutorial problem gives you
practice at testing you own understanding, an examination answer also
requires you to communicate that information to another human being
who marks the paper. A very instructive way to check this is to
attempt a paper under exam conditions and then get a friend to mark it
Recommended texts:
(1) F Mandl, 'Quantum Mechanics'' Wiley;
(2) D J Griffiths, 'Introduction to Quantum Mechanics', Prentice Hall;
(3) B H Bransden C J Joachain, 'Quantum Mechanics', Prentice Hall;
(4) R Liboff, Introductory Quantum Mechanics, Addison Wesley.
(5) D Park Introduction to the Quantum Theory, McGraw Hill