  We analyze the attosecond electron dynamics in hydrogen molecular ion driven
by an external intense laser field using ab-initio numerical simulations of the
corresponding time-dependent Schr{\"{o}}dinger equation and Bohmian
trajectories. To this end, we employ a one-dimensional model of the molecular
ion in which the motion of the protons is frozen. The results of the Bohmian
trajectory calculations do agree well with those of the ab-initio simulations
and clearly visualize the electron transfer between the two protons in the
field. In particular, the Bohmian trajectory calculations confirm the recently
predicted attosecond transient localization of the electron at one of the
protons and the related multiple bunches of the ionization current within a
half cycle of the laser field. Further analysis based on the quantum
trajectories shows that the electron dynamics in the molecular ion can be
understood via the phase difference accumulated between the Coulomb wells at
the two protons. Modeling of the dynamics using a simple two-state system leads
us to an explanation for the sometimes counter-intuitive dynamics of an
electron opposing the classical force of the electric field on the electron.
