= Radial Schrödinger equation for a central potential
{title2=$-\frac{\hbar^2}{2m}(R''+2R'/r)+[V(r)+\hbar^2l(l+1)/(2mr^2)]R=ER$}
For a spherically symmetric <potential energy> $V(r)$, <separation of variables> with $\psi=R(r)Y_{lm}(\theta,\phi)$ reduces the <Schrödinger equation> to the displayed radial equation. Writing $u=rR$ instead removes the first <derivative>:
$$
-\frac{\hbar^2}{2m}u''+
\left[V(r)+\frac{\hbar^2l(l+1)}{2mr^2}\right]u=Eu.
$$
The angular contribution acts as a centrifugal barrier. Boundary behavior and <wavefunction normalization> must still be imposed; an arbitrary radial function is not an <energy eigenfunction>.
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