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American Journal of Physics

A three-particle problem in one dimension

J. C. Martinez

Published Feb 1, 1995• 2 citations
Publisher

Abstract

The problem of three particles of identical mass interacting with each other via a delta-function potential is studied within a simple framework inspired by the 2-particle system. We discuss the S matrix and the possibility of bound states arising for both bosons and fermions.
DOI
10.1119/1.17975

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An exactly soluble one-dimensional three-body problem is presented, in which the interaction between the particles consists of local two-body potentials between each two particles. Infinitely high step functions are chosen for the form of the three potential functions. This interaction allows only three-body bound states and no continuum states. We have considered three different choices of the mass ratios of the three particles and we give formulas in closed form for the energies and for the wavefunctions of all states.
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