Introductory books on quantum mechanics

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SUMMARY

This discussion centers on introductory books on quantum mechanics, specifically addressing the mathematical foundations involving linear operators on Hilbert spaces. Participants highlight the importance of understanding convergence in sequences, exemplified by the series 1 = 1/2 + 1/4 + 1/8 + ..., which converges to 1. The reference to Ballentine's work emphasizes the relevance of these mathematical concepts in quantum state spaces. The conversation also reflects a collaborative environment where users share resources and tips for further exploration.

PREREQUISITES
  • Understanding of linear operators in Hilbert spaces
  • Familiarity with inner product spaces
  • Basic knowledge of convergence in mathematical sequences
  • Awareness of quantum mechanics principles
NEXT STEPS
  • Explore the mathematical framework of Hilbert spaces in quantum mechanics
  • Study the concept of convergence in sequences and its applications
  • Read "Quantum Mechanics and Path Integrals" by Richard Feynman
  • Investigate the role of linear operators in quantum state spaces
USEFUL FOR

Students of physics, mathematicians interested in quantum mechanics, and anyone seeking to deepen their understanding of the mathematical structures underlying quantum theory.

mvillagra
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The math part seems really interesting too, it is mainly based on linear operators on hilbert spaces. But, it seems to me that it only uses inner product (pre-hilbert) spaces, then why these authors (and also paper authors) refers always to hilbert spaces?
 
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mvillagra said:
The math part seems really interesting too, it is mainly based on linear operators on hilbert spaces. But, it seems to me that it only uses inner product (pre-hilbert) spaces, then why these authors (and also paper authors) refers always to hilbert spaces?


Convergence.

What does

1 = 1/2 + 1/4 + 1/8 + ...

mean?

It means that the sequence of partial sums converges to 1, i.e., has limit 1.

Much the same thing often is necessary in the state spaces of qauntum mechanical systems. See the third-last and second-last paragraphs on page 26 of Ballentine.
 
thank you very much for your answers, that was fast!

I will certaintly take a look at these tips!
 
mvillagra said:
thank you very much for your answers, that was fast!

I will certaintly take a look at these tips!

Welcome to Physics Forums mvillagra!

I split your post into two threads. The math/physics part remains here, and the book part has been moved to

https://www.physicsforums.com/showthread.php?t=309230

in the Science Book Discussion Forum.

Sorry for any confusion that this has caused.
 

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