The solutions of the Schrödinger equation on which the methods discussed up to this point were based are all ultimately defined by the Lippmann-Schwinger equation. The Green’s function contained in that integral equation is the kernel of the resolvent of the Laplacian on L2(IR3). We now turn to procedures that are based on the use of a family of Green’s functions introduced by Faddeev, which may be regarded as resolvent kernels of the Laplacian on weighted L2-spaces (on which the Laplacian is not essentially self-adjoint). The Green’s function (1.4) is one member of this family. There is a variety of ways of approaching these Green’s functions, but we shall do so by an avenue originally used by Faddeev.
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