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## Homework Statement

Verify by brute force that the three functions cos(θ), sin(θ)e

^{iφ}and sin(θ)e

^{−iφ}are all eigenfunctions of L

^{2}and L

_{z}.

## Homework Equations

I know that L

_{z}= -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, L

_{z}cos(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?