  We study a three-body system with zero-range interactions in a
one-dimensional harmonic trap. The system consists of two spin-polarized
fermions and a third particle which is distinct from two others (2+1 system).
First we assume that the particles have equal masses. For this case the system
in the strongly and weakly interacting limits can be accurately described using
wave function factorized in hyperspherical coordinates. Inspired by this result
we propose an interpolation ansatz for the wave function for arbitrary
repulsive zero-range interactions. By comparison to numerical calculations, we
show that this interpolation scheme yields an extremely good approximation to
the numerically exact solution both in terms of the energies and also in the
spin-resolved densities. As an outlook, we discuss the case of mass imbalanced
systems in the strongly interacting limit. Here we find spectra that
demonstrate that the triply degenerate spectrum at infinite coupling strength
of the equal mass case is in some sense a singular case as this degeneracy will
be broken down to a doubly degenerate or non-degenerate ground state by any
small mass imbalance.
