Mathematical Fundamentals of Quantum Mechanics


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 and PHYS2017 (or MT10212) are likely to struggle.

Textbooks and websites

Details here.

Examples Classes

Students taking this course should ensure they are registered for an appropriate examples class.

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!

Extra examples class

There will be an extra examples class 3-5 on Thursday 12th December in University Place, 2.220


Guidance on the format of the exam and on the relevance of questions from the previous exams for PHYS20602 and PHYS30201 is provided here. These exams, along with bottom line answers and feedback are on Teachweb, except for the 2009 bottom-line answers for PHYS20602 which are here.

21st Jan: 2009 answers revised, error in last line corrected.

21st Jan: revised bottom line answers for the 2013 paper here.


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


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

Clesch-Gordan coefficients and instructions on usage .

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


Examples 1: covers the material of the first four lectures. (Note the basis in question 15 should be taken to be orthonormal)

Solutions 1:

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

Solutions 2: now includes the missing solution to (7vi)!

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

Solutions 3: Error in solution to qu 5 corrected; in the paragraph starting "Finally", cos and sin were swapped.

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

Solutions 4

Examples 5: Error in question 5 corrected: 1/30→1/15π

Solutions 5 (complete)

Work in progress:

More material to come...