# Canonical commutation relations

1. Mar 6, 2015

### 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]
[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∂∂x

Formula: [A,B]=AB-BA

Can someone give a hint?

Thanks!

2. Mar 6, 2015

### 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. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution

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