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Journal of Mathematical Physics

One-Dimensional Three-Body Problem

James A. Hurley

Published Apr 1, 1967• 14 citations
Publisher

Abstract

The three-body problem in one dimension is examined to determine for what class of interactions the Schrödinger equation may be solved by separation of variables.
DOI
10.1063/1.1705281

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The three‐body scattering problem with finite pair potentials for one‐dimensional case is investigated. The asymptotic function χ0, which satisfies the three‐body Schrödinger equation in whole configuration space outside of compact domain Ω, where the supports of all three pair potentials cross each other, has been presented in a mathematically rigorous way. For large distances |x|→∞ the function χ0 determines the asymptotics of the solution up to the circular wave with smooth coefficient in whole configuration space. The method is based on analogies between few‐body scattering problem and diffraction one of the plane wave on the system of half‐transparent infinite screens. Presented here formalism are believed to be useful also for the few‐body scattering problem of higher dimensions.