Behaviour of wave packets in the interaction and the Schrödinger pictures for tunnelling through a one-dimensional Gaussian potential barrier

Abstract

The interaction picture wave packet method is applied to hydrogen scattering with a model Gaussian potential barrier, the linear reaction model. Some new features for the behaviour of the interaction picture wave packet are pointed out. It also splits into two parts according to the separation of the original Schrödinger picture wave packet into transmitted and reflected parts. The interrelation between the two wave packets is discussed in detail. In contrast with the Schrödinger picture wave packet, the reflected part is so clearly defined that we can evaluate the reflection probability as a function of time.