  We study dynamics of two interacting ultra cold Bose atoms in a harmonic
oscillator potential in one spatial dimension. Making use of the exact solution
of the eigenvalue problem of a particle in the delta-like potential we study
time evolution of initially separable state of two particles. The corresponding
time dependent single particle density matrix is obtained and diagonalized and
single particle orbitals are found. This allows to study decoherence as well as
creation of entanglement during the dynamics. The evolution of the orbital
corresponding to the largest eigenvalue is then compared to the evolution
according to the Gross-Pitaevskii equation. We show that if initially the
center of mass and relative degrees of freedom are entangled then the
Gross-Pitaevskii equation fails to reproduce the exact dynamics and
entanglement is produced dynamically. We stress that predictions of our study
can be verified experimentally in an optical lattice in the low-tunneling
limit.
