Orbital Angular Momentum and Uncertainty?

[LarryS]

The Uncertainty Principle is largely mathematical. For any two probability densities, if one is the Fourier Transform/Inverse Fourier Transform of the other, then the product of their variances is always greater than zero. Thus, energy and time, and momentum and position, via the squared modulus of their wave functions are related in this manner. But how does orbital angular momentum (not spin) fit into the above picture? It is my understanding that orbital angular momentum can only take on values that are integer multiples of h. As always, thanks in advance.

 

[malawi_glenn]

You also have the uncertainty principle for observables that does not commute, see this post: https://www.physicsforums.com/library.php?do=view_item&itemid=207

thus you will have an uncertainty between L_x and L_y if you know what L_z is.

 

[nicksauce]

If we have a commutation relation of the form
[A,B] = iC
Then we have an uncertainty relation
dAdB >= |<C>| / 2

The relevant commutation relations for orbital angular momentum are
[Lx,Ly] = ihLz
[Ly,Lz] = ihLx
[Lz,Lx] = ihLy

Which leads to uncertainty relations for the orbital angular momentum in different direction. If we know Lz perfectly, then there is uncertainty regarding the values of Lx and Ly.