The reader who is somewhat acquainted with the field of compressible fluid flow hears much about Stefan Bergman's method of integral operators. It took many years for him to develop this method which is based primarily on the theory of analytic functions and particularly on the theory of)functions of two complex variables. The method, as a whole, is scattered throughout many papers in mathematical journals, and as a matter of fact, in its present state, is accessible only to those who are fully acquainted with mathematical literature. In one of their papers, Professors R. von Mises and M. Schiffer greatly simplified the method in the subsonic casco The purpose of the present work is to represent the method in all its variations in such a way that a theoretical engineer or an applied aerodynamicist can use it in practical applications. A professional mathematician will find the discussion too elementary for him. The parts of Bergman's presentation which are most interesting mathe matically-the proofs-are mostly omitted in the present work. The emphasis was put upon the simplified representation of the final results and formulas, rather than upon the derivation of those formulas. In the preliminary remarks the author discusses various types of singularities in a very elementary way. The first two parts of the work deal with the subsonic case. In these sections the author followed mostly the paper of von Mises and Schiffer.
Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to incorporate all areas of new develop ment. Since among the newer books on scattering theory there are three excellent volumes that treat the subject from a much more abstract mathe matical point of view (Lax and Phillips on electromagnetic scattering, Amrein, Jauch and Sinha, and Reed and Simon on quantum scattering), I have refrained from adding material concerning the abundant new mathe matical results on time-dependent formulations of scattering theory. The only exception is Dollard's beautiful "scattering into cones" method that connects the physically intuitive and mathematically clean wave-packet description to experimentally accessible scattering rates in a much more satisfactory manner than the older procedure. Areas that have been substantially augmented are the analysis of the three-dimensional Schrodinger equation for non central potentials (in Chapter 10), the general approach to multiparticle reaction theory (in Chapter 16), the specific treatment of three-particle scattering (in Chapter 17), and inverse scattering (in Chapter 20). The additions to Chapter 16 include an introduction to the two-Hilbert space approach, as well as a derivation of general scattering-rate formulas. Chapter 17 now contains a survey of various approaches to the solution of three-particle problems, as well as a discussion of the Efimov effect.