Book recommendation for beginners who are physics students but aligned to mathematics

Question

I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on multielectron systems,molecules, etc.

Not going ahead in the application part, I want to focus on the foundations of QM part which I find really interesting. But I have very limited knowledge of mathematics. I have read Curtis "An introduction to Linear Algebra", Gallian "Group Theory"(1-10 chapters only) and have a little bit of knowledge on differential geometry.

With this as my Mathematical background, which would be the best book (a bit mathematical) for introduction to Quantum Mechanics which includes an introduction to Hilbert Space and functional analysis?

Answer 1

For a physics book with a good introduction to Hilbert space, I would recommend von Neumann's Mathematical Foundations of Quantum Mechanics. Definitely considered a classic, it is, still, unfortunately typewritten. Von Neumann was more sensitive to mathematical niceties, as Griffiths put it in a footnote somewhere in his QM book.

Answer 2

Adding to Adrian's answer, I found "The Mathematical Language of Quantum Theory" (2012) by Heinosaari & Ziman to be a great physics book which at the same time is rigorous and quite accessible (undermined by the fact that their first chapter is called "Hilbert space refresher").