Quantum Mechanics Book and resources on Hilbert Spaces

AI Thread Summary
The discussion centers on seeking advanced study resources in quantum mechanics prior to enrolling in a senior-level course. The participant currently uses Townsend's modern physics book and is interested in deepening their understanding of the mathematical formalism of quantum mechanics. They inquire about the suitability of Ballentine's book for their current level, given their background in linear algebra and ongoing studies in abstract algebra. Additionally, they seek recommendations for resources on Hilbert spaces that align with their mathematical knowledge, or whether to postpone this topic for later study. A suggestion is made that Townsend's "Modern Approach to Quantum Mechanics" could be a beneficial follow-up to their current textbook.
SheikYerbouti
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I am currently in a modern physics course and would to do more advanced study in quantum mechanics before taking the senior-level Quantum Mechanics course at my school. We use Townsend's modern physics book for the class that I am in right now; here is a link: https://www.amazon.com/dp/1891389629/?tag=pfamazon01-20. I would like to get deeper into quantum mechanics and try to understand the mathematical formalism of it better as well. I have heard that Ballentine is a fairly popular book, but is this something that I would be able to handle at my level? If not, what would be a more appropriate book? In terms of my math background, I have taken linear algebra and am in my first semester of abstract algebra; I will be taking real analysis and topology next semester. Are there any good resources to get into Hilbert spaces that are appropriate for my background, or should I attempt to study Hilbert spaces later?
 
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