Introductory books on quantum mechanics

Click For Summary
The discussion centers on the mathematical foundations of quantum mechanics, particularly the use of linear operators on Hilbert spaces. Participants express curiosity about why authors frequently reference Hilbert spaces when the concepts seem to rely on pre-Hilbert inner product spaces. The convergence of sequences, exemplified by the series 1 = 1/2 + 1/4 + 1/8 + ..., is highlighted as a crucial aspect in quantum state spaces. The conversation also acknowledges the helpfulness of shared tips and resources for further exploration. Overall, the dialogue emphasizes the importance of understanding the mathematical framework underlying quantum mechanics.
mvillagra
Messages
21
Reaction score
0
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?
 
Last edited by a moderator:
Physics news on Phys.org
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.
 

Thread 'The Power of QM and QFT'

We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following; https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/66a6a6005101a2ffa86cdd48/original/a-derivation-of-maxwell-s-equations-from-first-principles.pdf 'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s...
View full post »

Thread 'Importance of Hanbury Brown and Twiss experiment'

I read Hanbury Brown and Twiss's experiment is using one beam but split into two to test their correlation. It said the traditional correlation test were using two beams........ This confused me, sorry. All the correlation tests I learnt such as Stern-Gerlash are using one beam? (Sorry if I am wrong) I was also told traditional interferometers are concerning about amplitude but Hanbury Brown and Twiss were concerning about intensity? Isn't the square of amplitude is the intensity? Please...
View full post »

Thread 'Elementary question about comparing notations of inner product'

First, I need to check that I have the 3 notations correct for an inner product in finite vector spaces over a complex field; v* means: given the isomorphism V to V* then: (a) physicists and others: (u,v)=v*u ; linear in the second argument (b) some mathematicians: (u,v)=u*v; linear in the first argument. (c) bra-ket: <v|u>= (u,v) from (a), so v*u . <v|u> is linear in the second argument. If these are correct, then it would seem that <v|u> being linear in the second...
View full post »

Similar threads

I Why do ##t## and ##-i\hbar\partial_t## not satisfy the definition of a linear map/operator in Hilbert space?
Replies
4
Views
2K
A Would it matter which inner product I choose in quantum mechanics?
Replies
4
Views
2K
A How to derive the quantum detailed balance condition?
Replies
0
Views
1K
I Bra Ket is equivalent to inner product always?
Replies
7
Views
1K
I Is Quantum Mechanics Infinitely More Complex than Classical Mechanics?
2
Replies
55
Views
5K
I Why we need completeness of eigenfuntions for QM to be internally consistent?
Replies
13
Views
2K
I Interval in Quantum Mechanics?
Replies
9
Views
2K
What Are the Dimensions of Hilbert Space Elements in Quantum Mechanics?
Replies
14
Views
2K
I Ways of measuring open quantum systems
Replies
1
Views
2K
I Why are Hilbert spaces used in quantum mechanics?
Replies
26
Views
8K