Exact space-time propagator for the wave (second-order in time) equation in a layered ysstem, made up of a layer sandwiched between two other different semi-infinite layers, is obtained by means of the multiple scattering theory (MST) approach. The MST approach is made possible due to obtained effective potentials localized at interfaces and responsible for reflection from and propagation through them. The obtained spacetime propagator exactly solves the considered wave equation for any initial value and allows for following in time the processes of reflection and transmission. The solution for an initial Gaussian wave packet is obtained, analyzed, numerically visualized and discussed for the case of the perpendicular-to-interfaces incoming wave. In particular, the contribution of the backward-moving components of the wave packet is revealed.

分层系统中波（时间上的二阶）方程的精确时空传播子由夹在其他两个不同半无限层之间的层组成，通过多重散射理论 (MST) 方法获得。MST 方法之所以成为可能，是因为获得了位于界面处的有效电位，并负责从它们反射和通过它们传播。获得的时空传播器精确地求解任何初始值的所考虑的波动方程，并允许及时跟踪反射和传输过程。初始高斯的解针对垂直于界面的入射波的情况，获得、分析、数值可视化和讨论了波包。特别是，揭示了波包向后移动分量的贡献。