The Scattering of Three Impenetrable Particles in One Dimension

Abstract

A special one‐dimensional quantum mechanical three‐body problem with an interaction among the particles is solved exactly. The interaction is introduced in such a way that the particles retain their order along a line, and hence the particles are impenetrable. The assumption of impenetrability is consistant with the existence of bound states in all accessible channels, and the probabilities for direct and exchange scattering of one bound pair and one free particle are calculated both below and above the breakup threshold. Above the breakup threshold, the probabilities for breakup and free particle scattering are also found. The absolute squares of all elements of the scattering matrix are given explicitly, and the scattering matrix is shown to be unitary.