Looking for Mathematically Rigorous QM Textbooks? Any Suggestions?

In summary, the conversation discusses the shortcomings of standard undergraduate textbooks on quantum mechanics and the recommendation to study from a more mathematically rigorous perspective. The books mentioned as good examples are Ballentine's and Brian Hall's books, as well as Anton Capri's and Galindo & Pascual's textbooks for a more mathematical approach.
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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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1. What are the key features of a good rigorous book on quantum mechanics?

A good rigorous book on quantum mechanics should have a strong mathematical foundation, covering topics such as linear algebra, calculus, and differential equations. It should also provide clear explanations of fundamental concepts, such as wave-particle duality and superposition, and include a variety of worked examples and exercises to solidify understanding.

2. How can I determine if a book on quantum mechanics is rigorous?

The best way to determine if a book on quantum mechanics is rigorous is to look at the credentials of the author and check for any reviews or recommendations from experts in the field. You can also skim through the book to see if it covers the necessary mathematical concepts and if it provides clear and thorough explanations of key concepts.

3. Are there any recommended textbooks for learning quantum mechanics?

Yes, there are many recommended textbooks for learning quantum mechanics, including "Introduction to Quantum Mechanics" by David J. Griffiths, "Quantum Mechanics: Principles and Applications" by Nouredine Zettili, and "Modern Quantum Mechanics" by J. J. Sakurai. It is important to choose a textbook that aligns with your level of understanding and learning style.

4. Is it necessary to have a strong understanding of mathematics to learn quantum mechanics?

Yes, a strong understanding of mathematics, particularly linear algebra, calculus, and differential equations, is necessary to fully grasp the concepts of quantum mechanics. However, there are also introductory books available that provide a gentler approach to the mathematics involved in quantum mechanics.

5. Can I learn quantum mechanics without a formal education in physics?

While a formal education in physics can be helpful, it is not necessary to learn quantum mechanics. With dedication and the right resources, anyone with a strong understanding of mathematics can learn the fundamentals of quantum mechanics. However, a solid foundation in classical mechanics and electromagnetism may also be beneficial.

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