Book on Mathematics of QM

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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
 

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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
I'm currently trying to get through https://www.amazon.com/dp/0821846302/?tag=pfamazon01-20&tag=pfamazon01-20. 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.
 
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Have you read the classic by Dirac? It was the seminal book that put QM on a firm mathematical footing.

https://www.amazon.com/dp/0198520115/?tag=pfamazon01-20&tag=pfamazon01-20
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.
 
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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".
 
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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.
 
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