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## Homework Statement

Show that function

Y = C sin θ (5cos

^{2}θ - 1 )e

^{i[itex]\phi[/itex]}

satisfies Scrhödinger equation for hydrogen?

## Homework Equations

## The Attempt at a Solution

I derivated the required elements of the equation but ended up to some messy equation with lots of sines and cosines here and there.. I checked the derivations with WolframAlpha and got the same result so they are ( I hope) correct. What exactly am I supposed to do?