I need some books to learn the basis of linear operator theory and the spectral theory with, if it's possible, physics application to quantum mechanics. Can somebody help me?
Answer
I think a good, and classic, reference for your case is the following,
The very last chapter of Kreyszig deals with Quantum Mechanics.
And, once you've learned how to "translate" the language of Functional Analysis into that of Quantum Mechanics, you can go to more advanced texts in specific topics.
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