Fluctuation operator and partial wave

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spaghetti3451
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Can someone please explain to me why the expression ##[-\Box + U''(\Phi(r))]## is called the fluctuation operator?

I was also wondering how to derive the following for the ##l^{th}## partial wave of the above operator:

##-\frac{d^2}{dr^2}-\frac{3}{r}\frac{d}{dr} + \frac{l(l+2)}{r}+ U''(\Phi(r))##

Any help would be very helpful.
 
Is it because the the time components of the gauge fields are all eigenvectors of it?