Quantum mechanics for mathematicians

It may not have the specific topics you want, but I like Leon Takhtajan's book entitled, coincidentally, Quantum Mechanics for Mathematicians.

Books like Dirac tended to frustrate me with drawn-out developments of "this is a ket, this is a bra, they have such-and-such properties and we combine them in the following ways." Takhtajan is kind enough to come out and say "take a Hilbert space and a self-adjoint operator."

I was recently looking for such a book and I found two that look promising:

• An Introduction to the Mathematical Structure of Quantum Mechanics by F. Strocchi. This is a small book and assumes that you have prior knowlegde of functional analysis (in particular C* algebras).
• Quantum Mechanics in Hilbert Space by Eduard Prugovecki. This book is large as the first three parts are functional analysis and the last two parts deal with quantum mechanics. No C* algebras here though, only Hilbert spaces of operators.

If you want to look at a book that centralizes the role of an algebras of observables (operator algebras) in quantum theory, you should look at the book written by one of the founders of this approach. I recommend "Local Quantum Physics" by Rudolf Haag.

Furthermore, I think Reed and Simon's Vol.1 "Functional Analysis" will be very helpful here. Read the first two, and the last three chapters. While you are doing this, I strongly recommend you use Vaughan Jones' notes on Von Neumann Algebras (http://www.math.berkeley.edu/~vfr/MATH20909/VonNeumann2009.pdf). There is a section in there about Bosons and Fermions.