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Quantum Book on Mathematics of QM

  1. Jan 30, 2015 #1

    ShayanJ

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    I want to read a book on mathematics behind QM and by that, I don't mean just functional analysis. Its been a long time that I hear about things like *-algebra, C*-algebra, Weyl algebra, Heisenberg group, Stone-von Neumann theorem and things like these and I want to understand them. Can anyone suggest a book that covers them?
    At this point I prefer a physics-style math book on these but real-math books are OK too.
    Thanks
     
  2. jcsd
  3. Jan 30, 2015 #2

    jedishrfu

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    Last edited by a moderator: May 7, 2017
  4. Jan 30, 2015 #3
    I'm currently trying to get through https://www.amazon.com/Quantum-Mechanics-Mathematicians-Graduate-Mathematics/dp/0821846302. It includes these topics in its contents, and so far has been satisfyingly rigorous and readable, as long as you keep a blackboard or a pad of scratch paper handy.
     
    Last edited by a moderator: May 7, 2017
  5. Jan 30, 2015 #4

    ShayanJ

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    Not completely, but actually that's not what I want. Maybe I should've used a math prefix! The point is, I want to learn the things I mentioned in my first post and I want to learn them in the way people think about them today. My purpose is not just to help me learn QM better, I like the math because of the math too. But Dirac's book doesn't cover those subjects and also is a physics book. What I want, is at least a physics-style math book.
     
    Last edited by a moderator: May 7, 2017
  6. Jan 30, 2015 #5

    ShayanJ

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    That's more like it, thanks. But I still appreciate if someone comes up with a book a bit more mathematical in nature!:D
     
    Last edited by a moderator: May 7, 2017
  7. Jan 31, 2015 #6

    dextercioby

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    Brian Hall wrote his book: "Quantum Theory for Mathematicians" which is "stronger" than Takhtajan's. The most rigorous QM textbook is written by Galindo and Pascual (I'd recommend learning QM from it for a graduate text). Another good book is written by G. Folland: "Harmonic Analysis in Phase Space".
     
  8. Feb 18, 2015 #7

    vanhees71

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    There's also the quantum volume of the four-volume mathematical-physics book by Thirring. Those strip off nearly all physics from the physics ;-)). Mathmeaticians must love it.
     
  9. Feb 18, 2015 #8

    micromass

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