Introductory books on quantum mechanics

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Discussion Overview

The discussion revolves around introductory books on quantum mechanics, focusing on the mathematical framework, particularly the use of linear operators and Hilbert spaces. Participants explore the implications of these mathematical concepts in the context of quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express interest in the mathematical aspects of quantum mechanics, specifically the role of linear operators on Hilbert spaces.
  • There is a question regarding why authors frequently refer to Hilbert spaces when the discussion seems to involve inner product (pre-Hilbert) spaces.
  • One participant introduces the concept of convergence in relation to sequences and its relevance to state spaces in quantum mechanics, referencing a specific text (Ballentine).
  • Another participant acknowledges the responses received and expresses intent to explore the suggested resources further.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants raise questions and explore different aspects of the mathematical framework without resolving the inquiries posed.

Contextual Notes

Participants reference specific mathematical concepts and texts, but there are unresolved questions regarding the definitions and implications of Hilbert versus pre-Hilbert spaces.

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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