S Matrix for the One-Dimensional N-Body Problem with Repulsive or Attractive δ-Function Interaction

Abstract

For $N$ particles with equal mass, interacting with repulsive or attractive $\ensuremath{\delta}$-function interaction of the same strength, the $S$ matrix is explicitly given and shown to be symmetrical and unitary. The incoming and outgoing states may consist of bound compounds as well as single particles. The momenta of the particles and compounds are not changed in the scattering, but particles are exchanged, such as $ABC+DE\ensuremath{\rightarrow}ADC+BE$. Only distinguishable particles are considered.