Show that function
Y = C sin θ (5cos2θ - 1 )ei[itex]\phi[/itex]
satisfies Scrhödinger equation for hydrogen?
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?