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I feel that there are quite a few good and rigorous books on the mathematical foundations of quantum mechanics, but I am currently looking for a book that covers mathematical statistical quantum mechanics rigorously?

Is there any book on the market that you can recommend? Sometimes, I feel it is nice to have a rigorous book at hand when I am doing physics, which is the main reason why I would like to have such a book.

I especially like books that use quite some functional analysis.

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    $\begingroup$ Quantum Physics: A Functional Integral Point of View by Glimm and Jaffe (they're theoretical physicists). That's the closest I can think of, which should suffice since it is rigorous, but I find it hard to follow (they leave a lot up to the reader). $\endgroup$
    – Chris Gerig
    Commented Mar 27, 2015 at 1:54
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    $\begingroup$ books.google.com/books?id=YuR4VQOQQUIC $\endgroup$
    – Steve Huntsman
    Commented Mar 27, 2015 at 2:39
  • $\begingroup$ I'm not sure what you mean by "mathematical statistical quantum mechanics", but I second the recommendation of Glimm and Jaffe (though it is really more about quantum field theory than quantum mechanics). For a mathematical book on quantum mechanics, I like Quantum Theory for Mathematicians by Brian Hall, and also Quantum Mechanics: Foundations and Applications by Arno Bohm. $\endgroup$
    – Idempotent
    Commented Mar 27, 2015 at 3:24
  • $\begingroup$ What are these "good and rigorous books on quantum mechanics"? I have had trouble finding any... $\endgroup$
    – Igor Rivin
    Commented Mar 27, 2015 at 14:33
  • $\begingroup$ well, at least for my standard of rigorousness "Quantum Mechanics for Mathematicians" by Leon A. Takhtajan is okay. $\endgroup$
    – Physicist 2.0
    Commented Mar 28, 2015 at 0:57

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The two volumes by Bratteli and Robinson. The book on lattice gases by Simon also has material on quantum statistical mechanics.

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D. Ruelle, Statistical mechanics. Rigorous results, Benjamin, NY 1969.

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