Calculating Quantum Commutators: [x,xp]

[kel]

I have a question where I need to calculate commutators, but I just need to check one detail of this.

I need to work out [x,xp]

What I need to check is the following:

[x,xp] = xxp - xpx

but does this then mean that I get (x^2 p - X^2 p)
or (X^2 p - something else)??

Sorry about the lack of formatting, but hopefully you'll get what I mean.

Thanks
Kel

 

[neutrino]

Assuming that you're talking one-dimension, is [x,p] = 0?

 

[Doc Al]

What I need to check is the following:

[x,xp] = xxp - xpx

but does this then mean that I get (x^2 p - X^2 p)

No. Since x & p do not commute, you cannot swap their order.

 

[kel]

So, I'll need to work that part out literally in order ie xpx ?

Thanks, I'll give it a go
Kel

 

[dextercioby]

HINT:

[A,BC]=B[A,C]+[A,B]C

Daniel.

P.S. Certain care with the ops x & p_x is needed.