Reference for mathematical time-independent perturbation theory

Physics Asked by Iván Mauricio Burbano on December 1, 2020

I was wondering if anyone knew of a reference which treat time-independent perturbation theory in a mathematical fashion. All of the mathematical textbooks in quantum mechanics that I know of do not treat this subject. I am hoping that such a reference would treat:

  1. Perturbation theory of the pure point spectrum in a more systematic way than physics textbooks do. It seems to me that by using appropriate notation one should be able to give a clear account of degenerate perturbation theory in all orders.

  2. Perturbation theory of the continuous and residual spectrum. In particular, is it possible to give a unified account of all of the spectrum as a whole.

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