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

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    @Masacroso, certainly in spirit, yes, but since that question was 6 years old, there are newer books available. – Paul Jul 6 '17 at 22:12
  • @Paul yes, for this question seems very appropiate. I will quit the close vote. But I will leave the link to the old question. – Masacroso Jul 6 '17 at 22:12
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    What is "superior analysis"? – KCd Jul 7 '17 at 0:20
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    I quite liked Brian Hall's newish book Quantum Theory for Mathematicians; Teschl (mentioned below) wasn't to my taste. I'd suggest browsing in these options to get a feel for their varying emphases and proximity to the physics. – symplectomorphic Jul 7 '17 at 5:24
  • I'm not sure how useful is this for you, but I'd also use as a reference a good quality textbook for physicists, like Claude Cohen-Tannoudji's book. I think it is useful to develop a bit of physicist intuition when learning quantum mechanics. As a physicist, when I try to understand mathematics concepts, I usually try to look beyond the books "for physicists" like the "math methods" books. They often leave out important discussions on the meaning of the mathematical concepts and feel more like cookbooks. – Magicsowon Jul 7 '17 at 9:27

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:

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

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