# Operators Commutation

1. Nov 15, 2012

Can someone please explain to me how do we get the following:

[P(x), L(y)]= i h(cut) P(z)

P(x) is the momentum operator with respect to x
and L(y) is the angular momentum operator with respect to y.

I have also attached the solution. I am stuck at the underlined part. I do not know how to proceed from there.

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2. Nov 15, 2012

### dextercioby

Px and Py commute, as per Born-Jordan commutation relations. Thus the term from with their commutator is 0 when you apply the general formula

[A, BC] = [A,B]C+B[A,C] with [A,B] =0

Last edited: Nov 15, 2012
3. Nov 15, 2012

How did you obtain the general formula that you have stated in your reply?

4. Nov 15, 2012

it should be as follows:
[a,bc]=[a,b]c+b[a,c]

5. Nov 16, 2012

### andrien

[x,px]=ih/2∏ is the usual commutation rule,if that is what you are asking.
EDIT:if you want to know how to get that underlined term then just write the commutator explicitly and see that pz commutes with px.

Last edited: Nov 16, 2012
6. Nov 16, 2012

### jfy4

You got it right in post #4. Just work it out staring from $[A, BC]$ and write out the commutator, then in the middle add zero in a fancy way.

7. Nov 16, 2012