A wavepacket analysis of the statistical behaviour of molecules that penetrate a slit-shaped micropore

A quantum mechanical approach is proposed to analyze the statistical dynamics of a methane molecule that permeates near the exit of a slit-shaped carbon membrane. Since a quantum wavepacket can be regarded as a statistical ensemble of classical particles which have a certain momentum distribution, calculation can determine the possibility that a particle can reach the outside surface of the membrane or escape from the membrane by integrating the flux of the probability density with respect to time. It is demonstrated that the method is efficient not only for the intuitive understanding of the dynamics but also for quantitative discussions.