 Spherical square well

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 ${\kappa }^2=k^2+2m{V}_0/{\hslash }^2$. 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.