# Showing functions are eigenfunctions of angular momentum.

Robsta

## Homework Statement

Verify by brute force that the three functions cos(θ), sin(θ)e and sin(θ)e−iφ are all eigenfunctions of L2 and Lz.

## Homework Equations

I know that Lz = -iћ(∂/∂φ)
I also know that an eigenfunction of an operator if, when the operator acts, it leaves the function unchanged apart from a multiplicative factor (the eigenvalue)

## The Attempt at a Solution

So, Lzcos(θ) = -iћ(∂/∂φ)cos(θ)
But I think that equals zero. There's no component of cos(θ) in the φ direction. There different variables. So I think that when the differential operator acts on it, it makes 0. But then the function isn't left unchanged. Can somebody help me resolve this in my head?

Homework Helper
You have ##L_z\psi = 0\psi## so ##\psi## is an eigenfunction of ##L_z## with eigenvalue ...

Robsta
Eigenvalue 0. Does that mean that any function orthogonal to the phi direction is an eigenfunction then? Because its differential Thanks for your help!

Homework Helper
What does the eigenvalue of 0 mean - physically? What does ##L_z## measure?

Robsta
Lz measures the angular momentum about the vertical (z) axis. The eigenvalue is the actual amount of ang. momentum. I've managed to crack this question now, thanks a lot for your help :)