Commutatos and angular momentum

  • #1
4
0

Homework Statement


Let e and f be unit vectors. Le = eL is the definition of the component of angular momentum in direction e. Calculate the commutator [Le,Lf ] in terms of e, f and L

Homework Equations


[A,B]=(AB-BA)

The Attempt at a Solution



we know that L=r x p, in classical mechanics, and in quantum physics we have the operators for angular momentum in cartesian coordinates for example, but in my problem I have just two direction, e and f, and I am obtaining as answering 0. How can I do this exercise ? thanks
upload_2015-2-4_23-34-19.png
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,956
3,313
Welcome to PF!

Since you know the commutation relations for the Cartesian components of L, it might be a good idea to write out e##\cdot##L and f##\cdot##L in terms of the Cartesian components of L.
 
  • #3
25
1
Are the unit vectors ##\hat{e}## and ##\hat{f}## some arbitrary unit vectors in Cartesian space? In that case, it might be easy to start with something simple such as ##\hat{e} = \hat{x}## and ##\hat{f} = \hat{y}## and then moving into a more general case.
 
  • #4
4
0
but, and about the z component for example, if I do this in two coordenates, the answer will be zero, maybe is zero the solution, I do not know
 
  • #5
BvU
Science Advisor
Homework Helper
14,093
3,520
Why zero ? Follow Sigurdsson's sound advice and post your workings, please.
 

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