Fluctuation operator and partial wave

[spaghetti3451]

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.

 

[Jilang]

Is it because the the time components of the gauge fields are all eigenvectors of it?