What Are the Canonical Commutation Relations for r and p Components?

[Armani]

Hi ,

I need help with the this exercise:

a) Work out all of the canonical commutation relations for components of the operators r and p:
[x,y]
[x,py]
[x,px]
[py,pz]
and so on. Answer:
[ri,pj]=−[pi,rj]=iℏδij
[ri,rj]=−[pi,pj]=0
, where the indices stand for x, y, or z and
rx=x
ry=y
rz=z
where
p^=−iℏ∂∂xFormula: [A,B]=AB-BA

Can someone give a hint?

Thanks!

 

[BvU]

Hello Armani II, welcome to PF !

Somehow the template was lost, hopefully by accident. Its use is mandatory in PF, for good reasons ($\leftarrow\$click to see the guidelines).

1. Homework Statement
2. Homework Equations
3. The Attempt at a Solution

What is your attempt ? Ever look at something like $x{\partial\over \partial x}\ ... - {\partial\over \partial x}x\ ...$ ?