Quantum mechanical books for mathematicians

I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential geometry. I would like to study the Semiclassic Analysis, but perhaps I must first study the foundations of quantum mechanics. So I would like to know what book you recommend me to begin studying quantum mechanics. I'm primarily interested in a mathematical point of view. I have seen some books of this type, but I would like to have some other opinion.

Thanks for every reply

Here is a new book, freely available for now, that might be what you are looking for.

http://www.math.columbia.edu/~woit/QM/qmbook.pdf

I would recommend the book Quantum Mechanics for Mathematicians by Leon A. Takhtajan published by AMS. I cannot say much about this book, except some anecdote: I bought this book two years ago before beginning my bachelor studies in mathematics. It is on my shelf since then and sometimes I take a look at a few pages. Two years ago, I understood nothing, and the book is kind of a measure, how my math skills grew. Indeed, now I can have a look at it and actually understand whats going on in some parts. The thing is, it uses all the branches you've mentioned. Especially differential geometry and functional analysis. So it is quite advanced, but highly formal and definitely for mathematicians.

As a physics student, I used this text in a class that was half mathematicians and half physicists:

• Teschl, Gerald. Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators (2^nd ed.). Providence, R.I.: American Mathematical Society, 2014.

Perhaps Frankel's The Geometry of Physics, An Introduction, although this may not be an exact match for your intention.