Controlling quantum motions of a trapped and driven electron: an exact analytic treatment

We consider a harmonically trapped and strongly driven electron in a one-dimensional (1D) quantum wire. A set of exact complete solutions of the time-dependent Schrodinger equation is constructed, which shows the properties of generalized squeezed coherent states. The corresponding probability densities behave like some breathing and oscillating wave-packet-trains. The resonance ladders of the expectation energy are found and the transition probabilities between two stationary states are exactly calculated. The results reveal that the quantum motions of the considered system can be controlled by adjusting the laser driving field.