Quantum What are some recommended books for understanding the mathematics of QM?

[ShayanJ]

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

 

[jedishrfu]

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

 

[slider142]

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. 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.

 

[ShayanJ]

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

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.

 

[ShayanJ]

I'm currently trying to get through https://www.amazon.com/dp/0821846302/?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.

That's more like it, thanks. But I still appreciate if someone comes up with a book a bit more mathematical in nature!:D

 

[dextercioby]

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".

 

[vanhees71]

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.

 

[micromass]

Halls book is very good and it is one of my favorites. I just wish he did a bit more with representations. And he ignores operator algebras completely. But this is because there are many approaches to the mathematics of QM.

For other interesting approaches, I recommend:
The lecture notes of Woit: http://www.math.columbia.edu/~woit/QM/
Strocchi: https://www.amazon.com/dp/9812835229/?tag=pfamazon01-20