Near coherent states of an electron in a time-dependent linear potential

We investigate quantum motions of an electron driven by a strong time-dependent linear potential in a one-dimensional (1D) quantum wire. An exact n wave-packet-train solution of Gaussian-type is constructed, whose center moves acceleratively along the corresponding classical trajectory. It is shown that the single Gaussian wave-packet solution recently reported by Luan and Tang [P.-G. Luan, C.-S. Tang, Phys. Rev. A 71 (2005) 014101] is the special case n=0 of our result. The interesting physical properties described by the n wave-packet-train solution are studied, which concern the nearly squeezing coherence property of the wave-function, the band structure of average energy composed of quantum levels and classical oscillations, and the probability densities spreading and collapsing like that of a free particle.