Commutators of Angular momentum operator

[jaobyccdee]

The letters next to p and L should be subscripts.
[Lz, px] = [xpy − ypx, px] = [xpy, px] − [ypx, px] = py[x, px] −0 = i(hbar)
py

1.In this calculation, why is [x, px] not 0 even they commute?

2.Why is py put on the left instead of the right in the second last step? i thought it should be put on the right bec it's on the right of x in the third step, and we have to keep the orders for operators.

3.With L=rxp, why are we multiplying i(hbar) instead of multiplying by i/ (hbar), coz at the beginning, we change all the d/dx or d/dy or d/dz to px, py, pz, why aren't we multiplying i/(hbar) to compensate what we change for convenient calculation?

 

[Pengwuino]

Why do you think $[x,p_x]=0$? That should be one of the first things you learned about QM.

Your $p_y$ should be to the right, yes, but inevitably it doesn't matter considering $[x,p_x]$ is equal to a constant.

As for why you multiply by $i\hbar$, what do you mean "at the beginning"?