Variational Principles for Three-Body Breakup Scattering

In the preceding paper we derived a Kohn-type variational principle for the scattering amplitude for the breakup of a bound pair by an incident third particle. In this paper an alternative derivation is presented. The new derivation, based on the Faddeev equations, though rather formal, is rigorous; the preceding derivation was not. This procedure sheds some light on the manipulations in the earlier derivation. We also derive an "adjoint" Kohn-type variational principle in which the operator $H\ensuremath{-}E$ acts on the final-state wave function. The "adjoint" result has some convergence difficulties but these have been overcome by techniques described. Finally, a Schwinger-type variational principle is derived and its connection with the recently proposed variational principle of Pieper, Schlessinger, and Wright is discussed.