  We present a new analysis framework called "Correlation Analysis Tool using
the Schr\"odinger equation" (CATS) which computes the two-particle femtoscopy
correlation function $C(k)$, with $k$ being the relative momentum for the
particle pair. Any local interaction potential and emission source function can
be used as an input and the wave function is evaluated exactly. In this paper
we present a study on the sensitivity of $C(k)$ to the interaction potential
for different particle pairs: p-p, p-$\mathrm{\Lambda}$, $\mathrm{K^-}$-p,
$\mathrm{K^+}$-p, p-$\mathrm{\Xi}^-$ and $\mathrm{\Lambda}$-$\mathrm{\Lambda}$.
For the p-p Argonne $v_{18}$ and Reid Soft-Core potentials have been tested.
For the other pair systems we present results based on strong potentials
obtained from effective Lagrangians such as $\chi$EFT for p-$\mathrm{\Lambda}$,
J\"ulich models for $\mathrm{K(\bar{K})}$-N and Nijmegen models for
$\mathrm{\Lambda}$-$\mathrm{\Lambda}$. For the p-$\mathrm{\Xi}^-$ pairs we
employ the latest lattice results from the HAL QCD collaboration. Our detailed
study of different interacting particle pairs as a function of the source size
and different potentials shows that femtoscopic measurements can be exploited
in order to constrain the final state interactions among hadrons. In
particular, small collision systems of the order of 1~fm, as produced in pp
collisions at the LHC, seem to provide a suitable environment for quantitative
studies of this kind.
