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Angular Momentum Operator

  • #1
The operators used for the x and y components of angular momentum are:

7B%5Cpartial%7D%7B%5Cpartial%7Bz%7D%7D%20%20-%20z%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%7By%7D%7D).jpg


7B%5Cpartial%7D%7B%5Cpartial%7Bx%7D%7D%20%20-%20x%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%7Bz%7D%7D).jpg


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.
 

Answers and Replies

  • #2
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
 
  • #3
vela
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It would also help if you showed us your calculation of the commutator so we can see where your error is.
 
  • #4
Ah I got it solved in the end. Just made a minor mistake. Thanks!
 

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