Spherical square well
= Spherical square well
{title2=$V(r)=-V_0\mathbf1_{\{r<a\}}$}
A <spherical square well> is a central potential equal to a negative constant inside a sphere and zero outside it. For an <S-wave scattering> state with exterior wave number $k$, the interior wave number obeys $\kappa^2=k^2+2mV_0/\hbar^2$. Continuity of the reduced radial wave and its derivative gives $\kappa\cot(\kappa a)=k\cot(ka+\delta_0)$, relating the depth to the <scattering phase shift>.