Mathematical Fundamentals of Quantum Mechanics

2014-2015

Dr Judith A McGovern



Who should take this course?

This course is an alternative to PHYS30101 (Applications of Quantum Mechanics); all students must take one or the other.

There is considerable overlap in material, but the approach in this course will be much more mathematical, and as such it prepares students for future courses in QM and quantum field theory, as well as other course in which QM is used. MPhys students who wants to keep their options open should consider taking this course.

In spite of the title, this is a Physics course with relatively little new mathematics in it after the first three weeks, but an ability to use mathematics confidently is expected. Students who have taken some previous theory courses (advanced dynamics, Lagrangian, complex variables) are more likely to be comfortable with the style of the course. Students who failed to obtain good marks in PHYS20101, PHYS20141 and PHYS2017 (or MT10212) are likely to struggle.

Anyone unsure whether to take this course should start working though the notes of lectures 1-4.

Textbooks and websites

Details here.

Examples Classes

This course will be covered in the examples classes which cover third year core, series "A".

Examples classes will start in week 3. They are not like 1st year workshops, they are more like tutorials for which you do work in advance. It is very important that students work at examples sheets in their own time, and aim to complete the sheets as best they can before the classes. Working together is encouraged!

News

27/11/14: The list of known misprints has been updated (these have all been corrected in the versions of documents available from links below.)

From now on, there is a slight mismatch between the examples sheets (which are thematic) and the examples class schedule; the last class for most students is before the final three lectures. I will make clear what has been covered at the appropriate time, and will try to hold a final examples class towards the end of the last week.

Exam

Last year's guidance on the format of the exam (which is unchanged from last year) and on the relevance of questions from the pre-2013/4 exams for PHYS20602 and PHYS30201 is provided here; this will be revised before the end of term. These exams, along with bottom line answers and feedback are on Teachweb, except for the 2009 bottom-line answers for PHYS20602 which are here.

Lecture Notes

At the start of term these are the notes from last year. Updating will be done on a running basis.

Lectures 1-4

Lectures 5-6

Lectures 7-8

Lectures 9-10

Lectures 11-13

Lectures 14-15

Lectures 16-18

Lectures 18-20

Lecture 21

Appendices

Useful notes on hydrogen wave functions, delta functions, Gaussian integrals and units in EM

Clebsch-Gordan coefficients and instructions on usage .

A guide to matrix representations and basis changes for those who still find them puzzling..

Examples

Examples 1: covers the material of the first four lectures.

Solutions 1

Examples 2: covers the material of lectures 5&6.

Solutions 2

Examples 3: covers the material of lectures 7-10.

Solutions 3:

Examples 4: covers the material of lectures 11-15.

Solutions 4

Examples 5:

Handouts