The dynamics of quantum fluctuations of weakly coupled Bose–Einstein condensates (BECs) can be described by an effective Bose–Josephson Hamiltonian. By requiring that the mean-field approximation on this effective Hamiltonian reproduces the low energy dynamics of the Gross–Pitaevskii equation, we obtain parameters for the effective Hamiltonian. This approach is particularly suitable when the BECs are in the Thomas–Fermi regime. Considering the problem of the splitting of a trapped BEC into two BEC fragments, our results for the dynamics of the depletion, collapses and revivals of the phase coherence are in good agreement with a recent numerical microscopic calculation from Streltsov et al (2007 Phys. Rev. Lett. 99 030402). In addition, the excitation energy of the lowest symmetric mode, which is the first relevant mode for the symmetric splitting process, is reproduced with reasonable accuracy all the way from the mean-field Josephson regime to the Fock regime.
