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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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    $\begingroup$ @Masacroso, certainly in spirit, yes, but since that question was 6 years old, there are newer books available. $\endgroup$
    – Paul
    Commented Jul 6, 2017 at 22:12
  • $\begingroup$ @Paul yes, for this question seems very appropiate. I will quit the close vote. But I will leave the link to the old question. $\endgroup$
    – Masacroso
    Commented Jul 6, 2017 at 22:12
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    $\begingroup$ What is "superior analysis"? $\endgroup$
    – KCd
    Commented Jul 7, 2017 at 0:20
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    $\begingroup$ 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. $\endgroup$
    – symplectomorphic
    Commented Jul 7, 2017 at 5:24
  • $\begingroup$ 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. $\endgroup$
    – user3653831
    Commented Jul 7, 2017 at 9:27

5 Answers 5

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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

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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.

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  • $\begingroup$ I noticed the same thing. It's one of the books I've seen. $\endgroup$
    – user288972
    Commented Jul 6, 2017 at 22:38
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    $\begingroup$ This book (and particularly the mathematical prerequisite) has been the subject of this question math.stackexchange.com/questions/588541/…. $\endgroup$
    – Arnaud D.
    Commented Jul 7, 2017 at 8:08
  • $\begingroup$ @ArnaudD. Thank you. Very nice! $\endgroup$
    – TheGeekGreek
    Commented Jul 7, 2017 at 8:23
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As a physics student, I used this text in a class that was half mathematicians and half physicists:

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

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I will recommend few books and lectures on Quantum mechanics and quantum field theory from a mathematical perspective

A. Alekseev lectures on Quantum mechanics and Quantum field theory for mathematicians will give a good introductory taste for quantum theory, as you told you are from a mathematical background. Saurav Chatterjee notes on Introduction to quantum field theory for mathematicans will also be a good one for starting point as well.

Quantum Mechanics for mathematicians by A Leon Takhtajan.

Quantum Theory for mathematicians by Brian C. Hall.

Spectral Theory and Quantum Mechanics by Valter Morretti.

Quantum Field theory for mathematicians by Robert Ticciati.

Towards the mathematics of quantum field theory by Frederic Paugam.

Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators is also mentioned in the answer box as well

The book Foundations of Quantum Theory: From Classical concepts to Operator Algebra by Klaas Landsman is available free on Google books.

Also one book that I should add one is the book, A Combinatorial perspective on Quantum Field theory by Karen Yeats This one is a brief book dicussing the combinatorial inclination of the subject of Quantum Field theory, pdf format is also available, it is ought to be research oriented.

https://www.math.uwaterloo.ca/~kayeats/teaching/co739_w18/A+Combinatorial+Perspective+on+Quantum+F.pdf

Thanks

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