Boundary Conditions on the Generator-Coordinate Amplitude for Scattering

Abstract

It is shown that the short-range part of the generator-coordinate amplitude $f$, which is left after the long-range part proportional to the scattering wave $g$ has been removed, may be expanded to any degree of accuracy, as far as its integral properties are concerned, into a finite sum of well-behaved, square integrable functions. In that sense the amplitude $f$ obeys the same boundary conditions as the scattering wave function $g$. A simple method for solving the Hill-Wheeler equation is presented.