  There exists a simple relationship between a quantum-mechanical bound-state
wave function and that of nearby scattering states, when the scattering energy
is extrapolated to that of the bound state. This relationship is demonstrated
numerically for the case of a spherical well potential and analytically for
this and other soluble potentials. Provided that the potential is of finite
range and that the binding is weak, the theorem gives a useful approximation
for the short-distance behaviour of the scattering wave functions. The
connection between bound and scattering-state perturbation theory is
established in this limit.
