  We determine the exact time-dependent non-idempotent one-particle reduced
density matrix and its spectral decomposition for a harmonically confined
two-particle correlated one-dimensional system when the interaction terms in
the Schr\"odinger Hamiltonian are changed abruptly. Based on this matrix in
coordinate space we derivea precise condition for the equivalence of the purity
and the overlap-square of the correlated and non-correlated wave functions as
the system evolves in time. This equivalence holds only if the interparticle
interactions are affected, while the confinement terms are unaffected within
the stability range of the system. Under this condition we also analyze various
time-dependent measures of entanglement and demonstrate that, depending on the
magnitude of the changes made in the Schr\"odinger Hamiltonian, periodic,
logarithmically incresing or constant value behavior of the von Neumann entropy
can occur.
