Looking for Mathematically Rigorous QM Textbooks? Any Suggestions?

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SUMMARY

This discussion focuses on the need for mathematically rigorous textbooks in quantum mechanics (QM), highlighting the inadequacies of standard undergraduate materials. Participants recommend Brian Hall's book for those interested in a functional analysis approach, despite some reservations about this methodology. Additionally, Anton Capri's "Nonrelativistic Quantum Mechanics" and Galindo & Pascual's "Quantum Mechanics" are suggested as mathematically sound alternatives. The conversation emphasizes the importance of understanding concepts like Hermitian and self-adjoint operators in a rigorous context.

PREREQUISITES
  • Understanding of quantum mechanics fundamentals
  • Familiarity with Hermitian and self-adjoint operators
  • Basic knowledge of functional analysis
  • Experience with standard undergraduate QM textbooks
NEXT STEPS
  • Research Brian Hall's "Quantum Theory for Mathematicians"
  • Explore Anton Capri's "Nonrelativistic Quantum Mechanics"
  • Study Galindo & Pascual's "Quantum Mechanics"
  • Investigate the role of functional analysis in quantum mechanics
USEFUL FOR

Students and educators in physics, particularly those seeking a deeper mathematical understanding of quantum mechanics, as well as researchers interested in the theoretical foundations of QM.

Joker93
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Upon searching in this forum, i have found discussions about the standard undergraduate textbooks on QM not being so good in teaching you the foundations properly. A good example is the difference between Hermitian and self-adjoint operators. Some people are saying that we should study QM from a more mathematically rigorous(from the point of view of functional analysis) textbook.
So, do you have any suggestion?
I found Ballentine's book very good.
Thanks!
 
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George Jones said:
I don't recommend taking the functional analysis approach to learn quantum mechanics, but, if this is what you want to try, then Brian Hall's book is very good,

https://www.amazon.com/dp/146147115X/?tag=pfamazon01-20
Hello! But from other posts i thought that your opinion on the matter is that it is good to also see things from the functional analysis perspective. I think you had commented that the popular and standard textbooks on QM are not so good.
 
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Anton Capri - Nonrelativistic Quantum Mechanics and Galindo & Pascual - Quantum Mechanics are my favorite (i.e. mathematically sound) textbooks.
 
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