Summary: We study a model of three mutually interacting identical particles confined in a one-dimensional space, giving correlated states without one-body approximations. Certain types of quantum dynamics are illustrated with the model: quantum tunneling of position exchange and interparticle vibration (lattice vibration or phonons). The former is meaningful in the case that the identical particles are distinguished by their internal degrees of freedom. The unitary time evolution is simply written down in terms of the coherence of energy eigenfunctions. Our model clearly describes how the interparticle interaction divides one of the normal modes of the relative motion into tunneling and vibration of the particles.