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1. Homework Statement

1. Homework Statement

## Homework Equations

Here we have to express ##\psi(\theta,\phi)## in terms of spherical harmonics ##Y_{lm}## to find the angular momentum.

If ##\psi(\theta,\phi) = i \sqrt{\frac{3}{4\pi}} \sin{\theta} \sin{\phi} ##, it can be written as:

$$ \frac{i}{\sqrt{2}} (Y_{1,1}- Y_{1,-1})$$

since :

## Y_{1,\pm1} = \mp \sqrt{\frac{3}{8\pi}} \sin{\theta} e^{\pm i \phi}##,

But now as ##\psi(\theta,\phi)## has ##\sin{3 \phi}## instead of ##\sin{ \phi}##, how will it be represented ?

S.