Classical-quantum Interface of a Particle in?a?Time-dependent Linear Potential

We use a wave packets approach to analyze the non-trivial time-dependence solution of quantum mechanical systems of a particle in a linear potential. We relate the system of a free particle with that of a particle in a time-dependent linear potential by the use of the de Broglie hypothesis which is one important aspect of the study of the classical-quantum interface. Closed-form analytic results have been obtained as: (i) nonspreading Airy wave packets, (ii) Gaussian wave packets.