Show that this function satisfies Schrödinger equation for hydogen?

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Homework Statement


Show that function

Y = C sin θ (5cos2θ - 1 )ei\phi

satisfies Scrhödinger equation for hydrogen?

Homework Equations



hyds6.gif


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?
 
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You are supposed to simplify the mess - specifically you are trying to show that the whole mess can be simplified to a constant multiplied by the original wavefunction.

Welcome to wave mechanics xD
 
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