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I am searching for rigorous mathematics books or notes for time dependent perturbation theory.

For introductory quantum mechanics there is the excellent book spectral theory and quantum mechanics by Valter Moretti and for time-independent perturbation theory there is the book Perturbation theory for linear operators from Kato which is a good book.

Is there any book that treat time dependent perturbation theory with rigorous mathematics?

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During my bachelor, I found quite useful the book Quantum Mechanics Vol.2 by Cohen-Tannoudji, which treates the basics of time dependent perturbation theory really well in my opinion, and with some examples. However, there are other books more focused on a time dependent analysis of Quantum Mechanics like Introduction to Quantum Mechanics: A time dependent perspective by David J. Tannor, which is also quite good.

I hope you find these references useful!

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  • $\begingroup$ tks for your answer but those books that you indicate me are not the level i am searching for. $\endgroup$ Jan 18, 2020 at 10:59
  • $\begingroup$ Cohen-Tannoudji's book is a great introduction but definitely not on the rigorous maths side. $\endgroup$
    – fqq
    Oct 23, 2020 at 10:06

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