Advanced-undegrad/junior post-grad books on QM mathematics

In summary, the conversation is about recommendations for texts or notes that delve deeper into the mathematics of quantum mechanics and quantum field theory. The ideal material should be presented in the style of Nielsen and Chuang's Quantum Computation book and cover topics such as POVMs and basic functional analysis/operator theory. The person asking for recommendations is also looking for material that will help them better understand theoretical quantum mechanics papers.
  • #1
WWCY
479
12
Hi all,

I was wondering if I could get recommendations for texts/notes that delve deeper into the mathematics of QM as well as QM itself than what one finds in standard "Intro to QM" texts. Ideally it'd be presented in the style of Nielsen and Chuang's Quantum Computation book, but in greater depth. An introduction to QFT at the end would be a bonus.

If it helps, I'm looking for material that will help me better understand theoretical QM papers.

Many thanks in advance.

PS texts/notes like these https://www.mat.univie.ac.at/~gerald/ftp/book-schroe/schroe.pdf are much too difficult for me.
 
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  • #3
"An Introduction to Quantum Theory" by Keith Hannabuss perhaps?
 
  • #4
Cheers for the recommendations, do these go through topics like POVMs and basic functional analysis/operator theory?
 

1. What is the purpose of studying advanced undergraduate/junior post-graduate books on QM mathematics?

The purpose of studying these books is to gain a deeper understanding of the mathematical principles and concepts that underlie quantum mechanics. These books are designed for students who already have a basic understanding of quantum mechanics and want to further their knowledge and skills in the mathematical aspects of the subject.

2. What topics are typically covered in these types of books?

Topics covered in these books may include linear algebra, complex analysis, group theory, differential equations, and other advanced mathematical concepts that are relevant to quantum mechanics. They may also cover specific mathematical techniques used in quantum mechanics, such as Dirac notation and matrix mechanics.

3. Are these books suitable for self-study or do they require a teacher?

These books can be used for self-study, but it is recommended to have a teacher or mentor available for guidance and clarification. The material covered in these books can be complex and having someone to discuss and explain the concepts can be helpful in fully understanding them.

4. How do these books differ from introductory textbooks on quantum mechanics?

Introductory textbooks on quantum mechanics typically focus on the conceptual aspects of the subject, while advanced undergraduate/junior post-graduate books on QM mathematics delve deeper into the mathematical foundations and techniques used in quantum mechanics. They assume a higher level of mathematical proficiency and may include more rigorous proofs and derivations.

5. Can these books be useful for other fields besides quantum mechanics?

Yes, the mathematical concepts and techniques covered in these books can be applied to other fields such as theoretical physics, chemistry, and engineering. They can also be useful for students pursuing advanced degrees in mathematics or for those interested in research in related fields.

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