The Inverse Scattering Problem (Classic Reprint)

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Excerpt from The Inverse Scattering ProblemIt is a customary procedure in mathematical physics to make predic tions about particular physical situations on the basis of a general theory and then to compare those predictions with experimental data. This procedure is, of course, necessary to check the validity of a new theory. But when a physical theory has evoked sufficient confidence because of its continuing success over many years one need no longer look upon such a procedure as a test of the theory. Rather, the theory becomes a tool by means of which one can describe in detail the various special cases arising when particular conditions are added to the general theoretical assumptions. Experimental data for a special case are then useful to measure or make determinate those physical quantities of the general theory which otherwise are arbitrary. In the application of a trusted theory to special cases it still seems to be customary, however, to proceed in the same way as in the verification of a new theory. One makes certain assumptions about the relevant physical sit nation, one predicts the consequences of these assumptions on the basis of the general theory, and finally one makes an empirical check of the assump tions by means of experimental data. The assumptions can be corrected accord ing to the experimental results and the procedure repeated until the desired accuracy is reached. In the case of an old and tested theory, however, it would appear more logical to adopt a different procedure, if possible. A gain in time, accuracy and understanding might be expected if one were able to recon struct directly from the experimental data the physical conditions correspond ing to a special case of the general theory.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.