Interplay between a Gaussian wave packet and a non-reflecting potential analyzed using the wigner equation

Abstract

Deterministic solutions of the Wigner equation (WE) are used for describing the time evolution profiles of a Gaussian wave packet interacting with a square barrier, a square well, and a sech-squared well. The deterministic calculation shows that coherent Wigner and Schrödinger equations yield closely similar solutions. Especially, for the sech-squared well, also known as a nonreflecting potential, the acceleration effect and reverse diffusion of a Gaussian wave packet are reconfirmed by simulating the time-dependent WE. For the dissipative simulation, we considered three scattering terms, capturing energy dissipation, momentum randomization, and spatial decoherence. Our calculation shows that nonreflection is maintained when using the energy dissipation term but not when using either the momentum randomization or the spatial decoherence term. Momentum randomization disturbs the ordered movement of a propagating Gaussian wave packet, making nonreflection fundamentally impossible. Spatial decoherence introduces an additional diffusion effect, preventing nonreflection.