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I have completed three sequences of courses in QM, and I'm very much eager to to do the functional analysis of QM on my own in my spare time.

Can someone suggest some books? I like books with mathematical rigor, and I'm taking this step to understand the mathematical foundations of Hilbert Spaces used in QM.

Also, please do let me know the pre-requisites to study the book(s) you're mentioning.

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This functional analysis textbook is quite good, it even has a chapter dedicated on some of the mathematical foundations of quantum mechanics without using this name. This book is quite compact though, the classic text by Walter Rudin is more detailed. Prerequisites are topology and measure theory.

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