Many-body system with a four-parameter family of point interactions in onedimension

We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual delta-function potential. We examine a system consisting of many particles of equal masses that are inte racting pairwise through such a generalized point interaction. We follow Mc Guire who obtained exact solutions for the system when the interaction is t he delta-function potential. We find exact bound states with the four-param eter family. For the scattering problem, however, we have not been so succe ssful. This is because, as we point out, the condition of no diffraction th at is crucial in McGuire's method is nor satisfied except when the four-par ameter family is essentially reduced to the delta-function potential.