TABLE OF CONTENTS In the preceding chapters, we have used the coordinate-space representation for wave functions and operators. It is a familiar representation and one in which the scattering amplitude can be extracted by examining the asymptotic behavior of the wave function.
Although the results of Chapter 5 were obtained straightforwardly, in some situations the coordinate-space representation can be awkward. There is another symbolic, or operator, formalism that is very powerful when applied to the derivation of general results and relationships. This formalism dispenses with many of the labels that are needed to specify the wave function in coordinate space and that would tend to obscure the meaning and hinder certain manipulations. Once having derived a new result in the operator formalism, in which the manipulations are very easy and transparent, one typically takes the coordinate-space representation to extract the scattering amplitude and to carry out numerical calculations.
In this chapter we shall rederive some of the earlier results to establish a familiarity with the formalism and derive some new results that will be useful and will also deepen the understanding of some of the material encountered in later chapters. Among the new results is a generalization to rearrangement collisions of the Gell-Mann-Goldberger transformation that we encountered in the simpler case of an optical potential or a one-channel problem in the last chapter. The other new result of note is Watson s multiple-scattering series.
We shall not rigorously justify the manipulations of this chapter nor review in any detail the representation theory...
