Scattering Wave Functions at Bound State Poles

The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the details of the potential through the corresponding Jost function but is given uniquely in terms of the binding energy. The generalisations to higher partial waves and one-dimensional scattering are given.