Prove P=h/i(d/dx) from Axioms: Get an Answer

[Palindrom]

O.K.

So we have a list of axioms.
Could someone please prove to me that these axioms dictate
P=h/i(d/dx)?
I'm interested in a proof, and if there isn't, why choosing this operator of all the operators that could keep the axioms?
Thanks!

 

[dextercioby]

The proof is pretty long,it can be found in any book on QM (Cohen-Tannoudji,Sakurai,...),i believe i typed it once (search for it),ain't going to do it again.It comes naturally,yes from the axioms and from the coordinate representation of the fundamental commutation relations:
[\hat{x}_{i},\hat{p}_{j}]_{-}=i\hbar \delta_{ij} \hat{1}

Daniel.

 

[Palindrom]

I looked in Cohen Tanoudji, didn't find it.

Could you give me a key word or phrase to find the proof you wrote?

 

[quantumdude]

See pages 59-61 of the following document:

http://fafalone.hypermart.net/lectures.pdf

edit: Use the page numbers on the actual pages, not Adobe's page numbers.

 

[Palindrom]

See pages 59-61 of the following document:

http://fafalone.hypermart.net/lectures.pdf

edit: Use the page numbers on the actual pages, not Adobe's page numbers.

First of all, thank you.

Now, we're getting to what's bothering me. In this doc., they simply define <p| as some kind of twisted Fourier Transform, which is what we did in our course as well.
Why? Why this? This is supposed to represent the old and familiar linear momentum.

 

[dextercioby]

https://www.physicsforums.com/showthread.php?t=59548

They're linear functionals.

Daniel.

 

[Palindrom]

Thanks, I'll go over it all and come back if I have complains...