Barrier repulsion delayed by wave packet contraction

Abstract

We investigate a structureless particle (represented initially by a squeezed Gaussian wave packet) with a vanishing initial momentum expectation value in the vicinity of a step potential by calculating its position expectation values during the scattering process. The time-dependent Schrodinger equation (TDSE) was solved using the Crank-Nicolson (C-N) method, and the numerical wave packet obtained was used to compute for the position expectation value vs. time. The simulation showed that: (a) the step potential exerts a repulsive force on the initially “motionless” particle during the interaction, (b) a negative statistical correlation between the position and momentum of the particle causes a temporary contraction of the wave packet width, and (c) this wave packet contraction delays the onset of the barrier repulsion.