Off-Shell Continuations of the Two-Particle Transition Matrix with Bound States

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Abstract
The general framework of a recent proposal for constructing classes of two-particle off-shell transition matrices consistent with given bound-state binding energies and a given set of phase shifts for all energies is presented. This establishes certain properties of the underlying potential which previously needed to be assumed. The large arbitrariness in the choice of bound-state wave functions and the lack of correlation, in general, between the choice of bound-state wave functions and the values of the binding energies are demonstrated. A specific method for actually executing the construction program is proposed which should be useful when there exists reason to prefer a particular bound-state wave function.