Mathematical Foundations of Quantum Physics (MA4014)
This website contains information on the lecture “Mathematical Foundations of Quantum Physics” given in winter 2016 at Cardiff University, School of Mathematics.
Resources
There exists a tremendous number of books and lecture notes on quantum mechanics. Here I list a few, including some that are written specifically for mathematicians.
Books
- Brian Hall: Quantum Theory for Mathematicians (Springer, 2013)
A modern big book on quantum mechanics, written specifically for mathematicians and with a strong emphasis on spectral theory. Contains most of what we will discuss in this course, and several further topics. - Keith Hannabus: An Introduction to Quantum Theory (Oxford University Press, 1997)
An easy to read first book on quantum mechanics, written for mathematics students. Has the advantage of being very accessible, but does not cover everything that we will need. - A. Galindo, P. Pascual: Quantum Mechanics I (Springer 1990)
A physics book which can also be enjoyed by mathematicians, although it does not follow the definition-theorem-proof approach. Most of what will be discussed in this course is treated also in Galindo/Pascual. - John von Neumann: Mathematical Foundations of Quantum Mechanics (Princeton University Press, 1955)
One of the very first mathematical treatments of quantum physics, written by von Neumann himself. Nowadays, the book looks a bit old in comparison to more modern approaches. Nonetheless, it still contains a very clear and precise exposition of the mathematical foundations of quantum mechanics. - Michael Reed, Barry Simon: Methods of Modern Mathematical Physics I. Functional Analysis. (Academic Press, 1972)
This book is not about quantum mechanics, but rather a classical textbook about mathematics (functional analysis, in particular operators on a Hilbert space) that is used in quantum mechanics. It is a demanding book for a first contact with the subject, but contains lots of very useful information.
Lecture Notes
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Websites
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Exercises
Here you can download the exercise sheets for this module.
In addition to the exercises, I also offer some quizzes consisting of quick questions for you to test your understanding of the material presented in the lecture:
Lectures
Here you find a list of all the topics covered in the lecture. This list just serves as a reminder of what has been discussed, it is not a replacement for a book/lecture notes.
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