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Commutator of
and

Angular momentum is defined by

So the components of angular momentum are

We wish to compute
which has all the coordinates and momenta in it.

The only operators that do not commute are the coordinates and their conjugate momenta.

So now we just need to compute.

It is not necessary (or wise) to use the differential operators and a wave function crutch to compute commutators like this one.
**Use the known basic commutators when you can.**

Jim Branson
2013-04-22