Position and momentum commutators

[benabean]

Can I write:

$[\hat{p^2},\hat{x}]\hat{p} = \hat{p}[\hat{p^2}, \hat{x}]$

in relation to position and momentum operators?

 

[malawi_glenn]

What do you think? can you show that you can do it?

I think this is a good exercise in commutator algebra for you :-)

 

[thesage]

$\hat{C}[\hat{A},\hat{B}]=\hat{C}\hat{A}\hat{B}-\hat{C}\hat{B}\hat{A}$
$[\hat{A},\hat{B}]\hat{C}=\hat{A}\hat{B}\hat{C}-\hat{B}\hat{A}\hat{C}$
These two can't be the same as they are operators and the order matters.

 

[malawi_glenn]

hey come on, don't write the answer just like that

 

[benabean]

I was just wondering if there was an identity for such an expression. (Looking at thesage's post, it was a silly assumption; i should have remembered that expansion!)

It stems from trying to prove that $[\hat{H},\hat{x}\hat{p}] = [\hat{H},\hat{p}\hat{x}]$.

I did get this proof in the end. I was going wrong by not writing out p_hat explicitly, hence were my original post came from.

Thanks for your feedback,
regards benabean.