Quantum High-level book on scattering in quantum mechanics

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The discussion focuses on the search for advanced texts on scattering in quantum mechanics, particularly those that delve into mathematical intricacies such as the analytic structure of the S matrix, its relationship with Green's functions, and the significance of poles in the S matrix within the complex plane. A notable point raised is the discrepancy in how scattering is approached in graduate quantum mechanics (QM) courses compared to quantum field theory (QFT) courses, highlighting the need for a unified treatment. Taylor's "Scattering Theory: The Quantum Theory of Nonrelativistic Collisions" is mentioned as a potential resource, although its suitability for advanced research-level inquiries is questioned. Additionally, Eden et al. is suggested as another possible reference for those seeking a deeper understanding of the subject.
king vitamin
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I'm interested in a book which treats scattering in quantum mechanics aimed at the research-level. I'm particularly interested in a text which focuses on mathematical details such as the analytic structure of the S matrix, the relation between the S matrix and various green's/two-point functions, the meaning of poles in the S matrix and the relevance to where they lie on the complex plane, etc.

One major point of confusion I've always had is that scattering is treated quite differently in graduate QM courses and QFT courses, and so a book which treats both in a unified way would be ideal.
 
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Do you know Taylor's "Scattering Theory: The Quantum Theory of Nonrelativistic Collisions"? I'm not sure if it is high-level enough for your purposes, though.
 
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I'd forgotten about Taylor, but looking it up I see that I've actually looked at it before when I had questions about scattering, thanks! I was aiming for a higher level but this definitely looks like a good place to start when I have questions.
 
Im currently reading mathematics for physicists by Philippe Dennery and André Krzywicki, and I’m understanding most concepts however I think it would be better for me to get a book on complex analysis or calculus to better understand it so I’m not left looking at an equation for an hour trying to figure out what it means. So here comes the split, do I get a complex analysis book? Or a calculus book? I might be able to Borrow a calculus textbook from my math teacher study that for a bit and...

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