Excerpt from On the Eigenvalues Which Give Upper and Lower Bounds on Scattering Phases G normalization. It satisfies 0 5 9 u but is otherwise arbitrary. A bar over an expression means that the expression is exact. Eelfr) and ugl(r) are the exact and trial functions respectively. Wbl(r) c ugl(r) tiel(r). 7l and 7l are the L-th exact and trial phase shifts respectively. The total phase is the L-th phase shift less Ln/2. P(r) 2 0 is the weight function up(r) is the additional potential in the associated eigenvalue problem. For all values of u, up must satisfy the conditions imposed upon any potential in order that there be a well defined phase. [nl(r) is the eigenfunction of the associated eigenvalue problem with a phase shift 9 nu, where n 0, j; l, and with eigenvalue nl' About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.