# Introductory books on quantum mechanics

## Main Question or Discussion Point

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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## Answers and Replies

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George Jones
Staff Emeritus
Gold Member
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!!!

George Jones
Staff Emeritus
Gold Member
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