Do Lx and Lz Angular Momentum Operators Exhibit an Uncertainty Relation?

[leviathanX777]

The operators used for the x and y components of angular momentum are:

Show that Lx and Lz obey an uncertainty relation



2. No relevant equations.

The Attempt at a Solution

I'm going on that the assumption that if LxLy - LyLz does not equal zero then they don't commute and have an uncertainty relation. However I can only get this equal to zero and don't know how to show the uncertainty rrelation if I achieve one.

 

[Plutoniummatt]

I'm going on that the assumption that if LxLy - LyLz does not equal zero then they don't commute and have an uncertainty relation. However I can only get this equal to zero and don't know how to show the uncertainty rrelation if I achieve one.

if you mean:

[Lx, Ly] = LxLy - LyLx

then it does not equal to zero, angular moment is the cross product: r x p

so Lx = y.Pz - z.Py Ly = x.Pz - z.Px

where x and y and z are position operators and Px, Py and Pz are momentum operators, stick those into your commutator and try again, you should end up with

[Lx, Ly] = ihLz

where h is the reduced Planck constant. and Lz is the Angular momentum operator for z axis

 

[vela]

It would also help if you showed us your calculation of the commutator so we can see where your error is.

 

[leviathanX777]

Ah I got it solved in the end. Just made a minor mistake. Thanks!