Abstract
We analyze scattering in a system of two (distinguishable) particles moving on the half-line [Formula: see text] under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions, the two-body problem is of a non-separable nature. We will discuss the presence of embedded eigenvalues and using the obtained knowledge about the kernel of the resolvent, we prove a version of the limiting absorption principle. Furthermore, by an appropriate adaptation of the Lippmann–Schwinger approach, we are able to construct generalized eigenfunctions which consequently allow us to establish an explicit expression for the (on-shell) scattering amplitude. An approximation of the scattering amplitude in the weak-coupling limit is also derived.
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