Homework Help: Commutatos and angular momentum

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1. Feb 4, 2015

Monalisa

1. The problem statement, all variables and given/known data
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

2. Relevant equations
[A,B]=(AB-BA)

3. 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

2. Feb 4, 2015

TSny

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. Feb 5, 2015

Sigurdsson

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. Feb 5, 2015

Monalisa

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. Feb 5, 2015