# Commutatos and angular momentum

## 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

[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

TSny
Homework Helper
Gold Member
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.

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.

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

BvU