of indistinguishable particles and show the qualitatively different behavior for bosons and fermions.

In detail, this paper is organized as follows. Section \[sec:model\] gives a brief review of the considered waveguide Hamiltonian as well as the applied techniques, namely the $K$ matrix formalism while employing the local frame transformation. Thereafter, Sec. \[sec:scattering\_observables\] introduces and discusses the relevant scattering observables for 1D multichannel collisions as well as provides their connection to the physical $K$ matrix for the case of 1D geometries. Section \[sec:results\_discussion\] is devoted to the analysis of our results while our summary and conclusions are given in Sec. \[sec:conclusions\]. The Appendix provides among others some technical concepts used to derive the physical $K$ matrix.

Waveguide Hamiltonian and $K$-matrix approach {#sec:model}
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In the following we study the collisional behavior of two particles within a harmonic waveguide. Hereby indistinguishable or distinguishable particles are considered. The harmonic nature of the confining potential does not couple the center of mass (CM) coordinates with the relative ones and permits us to treat their motions separately. The Hamiltonian accounting for the CM motion simply describes a CM excitation in a harmonic potential. This solution is well known and thus of no further interest. The 