Interaction of Wave Packets with an Oscillating Gaussian Barrier

We use classical, semiclassical, and quantum mechanics to examine a propagating wave packet that encounters an oscillating Gaussian potential barrier. The wave packet can be transmitted, reflected, or partially reflected and partially transmitted. The final wavefunction is constructed both semiclassically and quantum mechanically, and we examine the agreement between these two methods. It is believed that multiple oscillating Gaussian potential barriers may serve as a quantum pumping mechanism for ultracold atoms [1]. We have chosen to study first a simpler case, that of a single oscillating Gaussian barrier, with the intention of using these results for studying cases with multiple barriers.