What Are the Best Textbooks for In-Depth Study of Rigorous Perturbation Theory?

[MathematicalPhysicist]

Anyone has any recommendation for a textbook/s that doesn't shun away from proofs of theorems?

I read Murdock's text, but he says himself that he doesn't cover it all.
And Bender's methods is more on exercising the methods than understanding them.

Any?

Thanks.

 

[A. Neumaier]

Anyone has any recommendation for a textbook/s that doesn't shun away from proofs of theorems?

Reed and Simon, Methods of Modern Mathematical Physics, Vol. I+II

Thirring, A course in mathematical physics, Vol. III

 

[MathematicalPhysicist]

And all the pertubation theory theorems (the main ones) are proven in Reed's and Simon's?

I really should be reading this series if I want to really be a mathematical physicist. :-)

Thanks.

 

[A. Neumaier]

And all the perturbation theory theorems (the main ones) are proven in Reed's and Simon's?

R&S is quite thorough, and mathematically rigorous. Moreover, each Chapter comes with long, detailed notes on references where proofs can be found for all the stuff they didn't prove. Only the newer things (post 1980?) are not included - but most of perturbation theory is very old.

 

[Klockan3]

Have you tried Ballentine? Way more rigorous treatment of quantum mechanics than the books you see in undergrad.

 

[A. Neumaier]

Have you tried Ballentine? Way more rigorous treatment of quantum mechanics than the books you see in undergrad.

But very far from being a rigorous text with rigorous proofs.

 

[Pinu7]

Mathematical Aspects of Classical and Celestial Mechanics by Arnold etc. (not to be confused with the textbook Mathematical Methods of Classical Mechanics by the same author) is clear, excellent, and encyclopedic. However, most of the proofs are missing and are to be supplied by the reader. Not necessarily a bad thing though.