Quantum Theory
Sven Bachmann (University of British Columbia)Sep 8, 2026 — Dec 22, 2026
About the course
The goal of MATH 512 is to introduce mathematical methods of quantum theory. No prerequisite of quantum physics is required. The course will cover some aspects of functional analysis, operator theory and the calculus of variations with short excursions into representation theory and operator algebras. The physical axioms of quantum theory will be introduced and elementary results will be discussed. We will introduce the Hilbert space formulation of quantum theory, discuss quantum dynamics and its relation to spectral properties of linear operators. We will also study the role of symmetries in quantum physics, in particular the rotation group thereby introducing the intrinsically quantum notion of spin. The course will conclude with a short study of strongly interacting systems and the role of locality in their analysis.
Registration
This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.
Enrollment Details
- Course Name
- Quantum Theory
- Date
- Sep 8, 2026 — Dec 22, 2026
- Course Number
- MATH512
- Section Number
- 101
- Section Code
Instructor(s)
For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website
Other Course Details
Class Schedule
First day of teaching: Wed Sep 09; Last day of teaching: Monday Dec 07. University closed Sep 30, Oct 12, and Nov 11. Midterm break: Nov 09-11.
- Monday, Wednesday, and Friday 11:00 – 11:50am (Pacific Time)
Remote Access
This will be a hybrid course delivered by Zoom. The instructor will lecture at a blackboard using a camera to allow remote participants to see the content. There will be course notes (hand written, possibly typed up) made available as the course progresses. Office hours will be conducted over zoom.
Availability
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.
Grading
There will be
- Five homework assignments
- One final exam
The course grade will be given by $$ \max \left\{ 0.75G_H + 0.25G_F, 0.5G_H + 0.5G_F \right\} $$ where $G_H$ is the average grade of the assignments and $G_F$ is the grade of the final exam.