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I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on multielectron systems,molecules, etc.

Not going ahead in the application part, I want to focus on the foundations of QM part which I find really interesting. But I have very limited knowledge of mathematics. I have read Curtis "An introduction to Linear Algebra", Gallian "Group Theory"(1-10 chapters only) and have a little bit of knowledge on differential geometry.

With this as my Mathematical background, which would be the best book (a bit mathematical) for introduction to Quantum Mechanics which includes an introduction to Hilbert Space and functional analysis?

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  • $\begingroup$ Just wondering if you've had a chance to check out Kreyszig, yet. I really think it's a great book, and would definitely recommend it to anyone beginning a study of functional analysis. $\endgroup$ – Adrian Keister Oct 30 at 17:58
  • $\begingroup$ Yes it is an excellent book and I would love to follow it, but what I want is a physics book dealing with mathematics not the other way around. $\endgroup$ – RandomXYZ Oct 30 at 18:01
  • $\begingroup$ Oh, I see. Let me edit my answer for you. $\endgroup$ – Adrian Keister Oct 30 at 18:02
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For a physics book with a good introduction to Hilbert space, I would recommend von Neumann's Mathematical Foundations of Quantum Mechanics. Definitely considered a classic, it is, still, unfortunately typewritten. Von Neumann was more sensitive to mathematical niceties, as Griffiths put it in a footnote somewhere in his QM book.

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