It is recalled that a ten year old calculation of all meson masses may explain the low value of the recently discovered Ds(2317) meson. This calculation was based on a fully relativistic quasiparticle theory, which has been applied to a large number of bound state problems and scattering processes. In this paper we want to show that also for one-dimensional systems the theory can be formulated in a compact way. After discussing the Lippmann-Schwinger equation for two nonrelativistic particles on a line, we show how to extend this momentum-space formulation to a Poincare invariant theory. We then apply this theory to a simple example and compare the reflection and transmission coefficients, as well as the total diffusion and the bound state spectrum, to the results obtained from the nonrelativistic case. Also the relativistic corrections to the spectrum of two harmonically bound particles are calculated. It is found that especially the higher excited states become less massive.

PACS numbers: 03.65.Pm, 11.30.Cp