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I am presently doing a course on functional analysis. I have done courses on quantum mechanics before. I see that many functional analysis books have an ending chapter on quantum mechanics.

So are there any open research problems left to tackle in this field of functional analysis related to quantum mechanics?

Thanks in advance.

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    $\begingroup$ The study of random and non-random Schroedinger operators provides a plethora of open problems. Take a look at the corresponding journal literature. $\endgroup$
    – user38355
    Aug 1, 2013 at 10:44

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As I cannot write a comment: there are several, I think the best I can do is to give an excellent reference: "Schrödinger operators: With application to quantum mechanics and global geometry" by Barry Simon, a leading expert in particular as far as Schrödinger operators are concerned.

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