Gaussian wave packet solution of the Schroedinger equation in the presence of a time-dependent linear potential

A way to get a general solution of the Schroedinger equation in the presence of a time-dependent linear potential is presented using an invariant operator that is linear in both p and q, within the framework of the Lewis-Riesenfeld invariant theory. The linear invariant operator proposed in this work is demonstrated to be an Hermitian operator which has a Gaussian wave packet as its eigenfunction. A detailed analysis is given for the characteristics of the Gaussian wave packet of the system under the influence of an external driving force.