Commutator Relation: What is [\hat{A}\hat{B}, \hat{C}\hat{D}] Equal to?

[M. next]

What is the commutator [$\hat{A}$$\hat{B}$, $\hat{C}$$\hat{D}$] equal to? How to distribute what's inside?

 

[andrien]

=(ab)(cd)-(cd)(ab)

 

[Fredrik]

Use the rule [A,BC]=B[A,C]+[A,C]B. It's very easy to prove, so I suggest that you do that as an exercise.

 

[DocZaius]

Use the rule [A,BC]=B[A,C]+[A,C]B. It's very easy to prove, so I suggest that you do that as an exercise.

Do you mean [A,BC]=[A,B]C+B[A,C]?

 

[Fredrik]

Do you mean [A,BC]=[A,B]C+B[A,C]?

Ah, yes of course. Thanks.