  Two-body interactions of elementary particles are useful in particle and
nuclear physics to describe qualitatively and quantitatively few- and many-body
systems. We are extending for this purpose the quantum inversion approach for
systems consisting of nucleons and mesons. From the wide range of
experimentally studied two-body systems we concentrate here on $\pi N$,
$\pi\pi$, $K^+N$, $K \pi$ and $K\bar{K}$. As input we require results of phase
shift analyses. Quantum inversion Gelfand-Levitan and Marchenko single and
coupled channel algorithms are used for Schr\"odinger type wave equations in
partial wave decomposition. The motivation of this study comes from our two
approaches: to generate and investigate potentials directly from data by means
of inversion and alternatively use linear and nonlinear boson exchange models.
The interesting results of inversion are coordinate space informations about
radial ranges, strengths, long distance behaviors, resonance characteristics,
threshold effects, scattering lengths and bound state properties.
