The mechanism of the Coulomb breakup reaction of the projectile nuclei with neutron halo structure is investigated by the time-dependent Schrodinger equation in three-dimensional space. The time evolution of the internal wave function between the core nucleus and the halo neutron is calculated in the target Coulomb field treated as the time-dependent external field. Calculations are done for the "Be+ Pb system for which an experiment has been done recently. The calculated results support the picture of free-particle breakup mechanism: Only the core nucleus is affected by the target Coulomb field, while the halo neutron moves independently. As a result, we obtain large transverse and small longitudinal difference in the relative velocity between the core and the neutron after the breakup. The origin of the longitudinal velocity difference observed experimentally is left unresolved in our approach. PACS number(s): 25.60.+v, 25.70.De In the light nuclei around the neutron drip line, the neutron halo structure has been observed systematically [1]. Besides the spatially extended density distribution of the halo neutron, the drip-line nuclei have such characteristics that they easily breakup into the core nucleus and the halo neutron(s). Especially the large breakup cross section has been observed in the Coulomb excitation [2]. The Coulomb breakup is induced mainly by the electric dipole component of the target Coulomb field. The large Coulomb breakup cross section is related to the E1 strength distribution at low excitation energy [3].A question concerning the property of this low lying dipole strength is whether or not it has a resonance character representing the vibration of the halo neutron and the core [4].In the recent coincident measurements of the core and the halo neutron, the significant difference in the longitudinal velocity distribution between them has been observed in the Coulomb breakup reaction of "Li [5] and "Be [6]. It has been explained in terms of the Coulomb postacceleration effect by assuming the direct breakup mechanism [5,6]. Before the closest approach point where the breakup is assumed to occur, the projectile is decelerated by the target Coulomb field. After the closest approach point the core and the halo neutron move independently. Since only the core nucleus is accelerated by the target Coulomb field, the velocity difference is expected to occur between the core and the neutron.On the other hand, if the breakup proceeds by way of the resonant state, the core and the halo neutron would move together until they decay and the velocity difference would be small. Therefore, the measurements of the velocity difference are expected to be useful as a clock to measure the lifetime of the resonant state.The Coulomb postacceleration is a higher order effect in the perturbative treatment of the Coulomb excitation. To calculate the higher order terms is not easy in the breakup reaction into continuum states. Several approaches have been applied including a classical treatment of the breakup [7], a di...